We have been discussing analysis of two-dimensional continuum and three-dimensional continuum, so we will continue with that discussion and we expect to close that discussion in this lecture and we will start discussing about problems of plate bending and shell elements, this is the topics for today's lecture. So in the previous class we considered three-dimensional elements and derived the structural matrices rectangular hexahedron, isoparametric hexahedron, and tetrahedron elements, and we worked out a simple problem also. Now we will continue with that, so this is a eight-noded element with 3 degrees of freedom per node, so 24 degrees of freedom, this is isoparametric hexahedron element for three-dimensional solids. Now in today's class what we will do is we want to consider problems of again a kind of a two-dimensional approximation to solids of revolution, solids which we obtain by revolving around one of the axis, so that kind of objects geometry is well treated using cylindrical polar coordinates, so we will quickly review the equations of elasticity in cylindrical polar coordinates, so the coordinate system here is, this is a Cartesian coordinate system X, Y, Z, and in cylindrical polar coordinates we have R, Theta and Z, so this is the position vector R, I mean coordinate R, this is angle Theta and this is height is Z. Now the relationship between Cartesian and cylindrical polar coordinates is shown here X is R cos Theta, Y is R sin Theta and Z is same as Z, so in cylindrical polar coordinates the independent coordinates are R Theta, Z and T, and stress components we denote as sigma R R, sigma Theta Theta, sigma Z Z, sigma R Theta, sigma Z Theta and sigma R Z, strain component correspondingly have the similar notation epsilon R R, epsilon Theta Theta, epsilon Z Z and so on and so forth. The displacement components are denoted by U R, U Theta, U Z and we will agree to call them as simply as UVW, and the body forces uppercase F R, F Theta and F Z, so how this, you know this axisymmetric solids are produced, suppose you have a generator plane with area A and suppose if it revolves around axis Z it produces an object like this, so these, the focus of our discussion is on studying this type of objects, so in this case we need to model only this generator plane and we can conduct complete the analysis for this object. Now with that in mind let's review the equations of elasticity, we have seen these equations in Cartesian coordinates, so the equilibrium equations upon making using this transformation we can show that it gets transformed to three equilibrium equations are here and the strain displacement relations again gets modified and they are shown here, and the stress strain relation also gets modified and we are assuming the body is isotropic, a linearly elastic and isotropic, so the kind of objects that we are studying here have a rotational symmetry about an axis, so Z axis is the axis of symmetry and there is a rotational symmetry about that, this type of structures as I was mentioning briefly in the previous lecture are encountered widely in engineering, this is a cross section of a nuclear reactor structure, you can see this outer shell it's a cylindrical, it's a cross section, in plan it is circular, so you can see that these shells have rotational symmetry about the vertical axis. Now what exactly is a consequence of this symmetry on equations of elasticity, so the objects that we are considering are characterized by geometry with these features, they are three dimensional axisymmetric solids, they are not necessarily prismatic, not necessarily thin or thick, so these two conditions if you recall were necessary for implementing plane stress and plane strain models we are relaxing that, the loads, the surface tractions are independent of theta, they are only functions of R and Z, and similarly body forces there is no body force in the theta direction and the other body forces in R and Z directions are independent of theta, under these assumptions the displacements in the theta direction will be 0, and the other two displacements U and W, U in R direction, W in Z direction will be independent of theta, so this is the postulate on displacements, the material itself we are going to assume linear, homogeneous, elastic and isotropic, so as a consequence of this what happens, now we have V equal to 0, U is independent of theta, W is independent of theta, so the implications of this on strains if you look at epsilon RR is dou U by dou R it will be nonzero, epsilon theta theta is U by R plus dou U by dou theta, now dou U by dou theta is 0 because V is 0 and this will be simply U by R which is not 0, epsilon ZZ of course derivative of W with respect to Z is nonzero, epsilon RZ again it involves derivative of U with respect to Z and W with respect to R that would be nonzero, but the other shear strains epsilon R theta, dou U by dou theta is 0 because U is independent of theta, dou V by dou R is 0 because V is 0, similarly this is 0 therefore this shear strain becomes 0, similarly we can show that epsilon Z theta is also 0, so there are 4 nonzero strain components, now we can now look at the constitutive laws, we have sigma RR given by this which is again nonzero, sigma theta theta is nonzero, sigma ZZ is nonzero, sigma theta Z is 2G epsilon theta Z, but epsilon theta Z is 0 therefore this is 0, sigma ZR is 2G into epsilon ZR, epsilon ZR is not 0 therefore this stress will be nonzero but the other shear stress sigma R theta will be 0 because epsilon R theta is 0, so now we have 4 stress components, 4 strain components and 2 displacement components, so there are 8 unknowns and we need now 10 equations, so these are strain displacement relations 4 in number, this is stress strain relations 4 in number, now the other 2 equations are obtained from the equilibrium equations, now these are the equilibrium equations whatever I showed here are replicated here except that the terms which are 0 are now indicated in red, so consequently what happens, one of the equilibrium equation is satisfied identically and we are left with 2 equilibrium equation. So the summary is we have 2 unknown displacements, 4 strain components, 4 stress components which are nonzero and unknown, therefore there are 10 unknowns, we have 2 equilibrium equations 4 strain displacement equations and 4 stress strain relation, so these can be solved in the classical theory of elasticity there are ways of introducing a stress function and developing solutions based on the set of 10 equations. Now our objective is to develop the finite element model for this, so with that in view we will just see now the strain we will assemble them in a 4 cross 1 vector as shown here epsilon RR, epsilon ZZ and epsilon theta theta and the strain they are related to displacement through these relations after introducing all the simplifications resulting from assumptions of axis symmetry of geometry loads and boundary conditions, so the element field variables will be U, R, Z, W, R, I am not showing T explicitly, it can be introduced subsequently T is the time, so right now I am not doing that, stress will be these are the 4 stress components, so we have 4 strain components related to displacement, 2 displacement components which are not known, 4 stress components which are related to strain through this and using this relation they in turn get related to displacements. Now D is the matrix of that relation stress and strain, this is for an isotropic linearly elastic material, this is the D matrix, E is the Young's modulus, nu is Poisson's ratio. Now we want to now develop a finite element model for this, now we will start with a triangular element, so it has 3 nodes and at each node there are 2 degrees of freedom shown here and these 1, 2, 3 are the nodes and the nodal coordinates are R1, Z1, R2, Z2 and R3, Z3, this is Z axis, this is our R axis. Now so the nodal degrees of freedom are U1, U2, W1, W2, sorry U1, W1, U2, W2, U3, W3, so consequently we interpolate the field variables within the element in terms of these nodal coordinates, nodal degrees of freedom using this interpolation, where I encountered this triangular element earlier in the context of plane stress problems, so the same shape functions will be relevant here also, so we write this as UW is N into UE, this vector is 2 cross 1, N is 2 cross 6 and UE is 6 cross 1, so based on this I write now the expression for kinetic energy where ME is the mass matrix given by H rho N transpose N DA naught, so now we want to express the strain in terms of nodal displacements, for that we first write the strain displacement relations for polar coordinates it is written in this form, this is the actually the strain displacement relations we want to write it in this form, and for UW I introduce N into UE and this matrix into the matrix of shape functions is our B matrix, so this is 4 cross 6 and this is 6 cross 1, so that this is 4 cross 1, now based on this the strain energy is given by half UE transpose into the stiffness matrix UE and this stiffness matrix is given by H into integral over A naught B transpose DB DA naught, so this is the, this development parallels what we have done earlier for plane elements, stress elements, so we can go ahead and use the shape functions and evaluate, if you recall for the triangular element we knew the shape functions, there were linear functions and we were able to evaluate the mass and stiffness matrix exactly, so I am not going to develop those elements but I am just giving a few steps so that if necessary you can proceed and evaluate these matrices. Now we can consider now a slight relaxation on the requirements that we spelt out for analyzing axisymmetric solids, suppose if we consider the situation in which the body is axisymmetric it is supported axisymmetrically but the applied loads are not axisymmetric, so the problem would still be 3 dimensional, can we solve this problem using 2 dimensional models is a question. Now since the system is linear, material is linear and we are assuming strain displacement relations to be linear, principle of superposition holds good, so the proposition here is that we will expand the applied loads surface tractions in a Fourier series in theta, okay, so if we applied the lowercase FR and FZ are the surface tractions I expand them in Fourier series as shown here and cosine terms will produce behavior which is symmetric about theta equal to 0 and sine terms will produce behavior which is anti-symmetric about theta equal to 0, now and F theta it's a body force in theta direction will be expanded like this, I am assuming now that there is a surface traction in theta direction also not body force this, now using the orthogonality property of sine and cosine functions we can evaluate these Fourier coefficients, FRN, FZN and FRN bar, FZN bar, F theta N and F theta N bar, so this is straight forward, this is simple application of Fourier's logic, so for N equal to 0 we get this and for N equal to 1, 2 etc the sine and cosine terms etc are given here. Now the whole idea, the idea of this formulation is we will develop one finite element model for each of these terms and we will produce an ensemble of models and we will synthesize the total response by summing over the responses for each of the, you know models each one corresponding to one component of these excitations, so how to do that we will just quickly see a few steps. Now since surface tractions are expanded in Fourier series we will also expand the displacements in the Fourier series, so this is written as nu N sine N theta plus nu N bar sine N theta, this is V and U V is expanded in this form, now strain displacement relations, these are the strain displacement relations, now we are considering the 3 dimensional strain displacement relations, what we do is we split the strain vector into a component with 4 cross 1 elements and a 2 cross 1 element, if the body is axisymmetric this will be 0, this is anyway it will be present even for axisymmetric solids or general solids as well. Now stress strain relations we will write separately for these 4 components and for these 2 components, they are not coupled in a linear isotropic elastic material those things won't be coupled, so sigma 1 I write it as D1 epsilon 1, sigma 1 is these 4 components RR theta theta ZZ RZ, this is given by this in terms of the strains epsilon RR epsilon theta theta epsilon ZZ and epsilon RZ, similarly sigma 2 is given consist of the shearing strain sigma R theta and sigma Z theta and it is related to epsilon R theta and epsilon Z theta through this transformation. Now the expression for energies this is the kinetic energy, this is the strain energy, the strain energy has 2 parts, this is a breakup that is done to facilitate computation, there is no physical arguments for this, and similarly the virtual work done can also be written in this form. Now what is the implication of using Fourier decomposition on displacement components on the evaluation of energies? So now we can carry out integration with respect to theta, this was over the volume element, now on theta if you can calculate the, you can carry out the integration and we get these expressions. Now TE the total element kinetic energy is taken to be summation of kinetic energy for various Fourier components, given the orthogonality of these basis functions, sinusoidal basis functions and the fact that system is linear there won't be any coupling between the energy contributions from different Fourier terms. So this, therefore I get, if I sum all the kinetic energies over the Fourier coefficients I get the total kinetic energy and similar statement is valid for this also. Now we have to consider the nature of these terms for N equal to 0 and N not equal to 0 separately, for N not equal to 0 this is the expression for kinetic energy. Now if we now use and similarly this is strain energy and this is the work done, so this is written for nth component in the Fourier expansion, so this is also written for the nth component in the Fourier expansion, similarly virtual work done also this is a contribution from nth component in the Fourier series, here this integration we get a RS DS, this is surface traction, they work done by the surface traction, this RS is actually value of R on the surface S. Now the axisymmetric motion that is N equal to 0, sorry the N equal to 0 term needs to be handled separately and it has axisymmetric and anti-symmetric motion, this is pure torsion and this is, this consists of these terms, that is N equal to 0 is done separately. Now the idea of this decomposition is each one of these problems can be tackled as a two dimensional problem in analysis, so you can develop a two dimensional finite element model for each of these terms separately, so that can be systematically done I am not going to get into the details, I am just giving you the main idea on how to do that, so the motion corresponding to each harmonic is determined separately and each component problem can be solved as a two dimensional problem, and we can develop finite element model for each of these component problems, because if you see now the structure of these energies they resemble that, resemble what we have handled earlier, so this is some simple ideas associated with analysis of axisymmetric solids. Now the next part of our discussion we will now move on to problems of plate bending, so this figure explains the basic nomenclature that we use in the study of plates, so here is a rectangular plate, plate is an object which is bounded by two faces, T is the thickness and this plane is called the middle plane, and this is the least lateral dimension and this is the thickness, this surface is called the edge, this top surface is called the face. Now in a problem like this the loads can act transfers to the middle plane or in line with the middle plane, the problem of loads acting in line with the middle plane can be tackled using plane stress models, whereas the question now is how to treat the analysis of this type of structures under transverse loads, that is known as plate action. So this action where the structure deforms due to in plane loads is called membrane action, so membrane action can be analyzed using plane stress elements, now the bending action is due to transverse loads, this is what we are going to discuss in today's lecture. Now there are a few assumptions, we build a theory for behavior of these plates by making few assumptions, so I will run through these assumptions, so in this slide there is two columns here, the first column states the assumption and the second column has few commentaries on these assumptions, so what we will do is first we will run through the assumptions and then discuss the consequences and comments on that, so the first is the material of the plate is elastic, homogeneous and isotropic, the body is initially flat, that is the next assumption, the thickness of the plate is small, the thickness of the plate is small compared to its other dimensions, the smallest lateral dimension of the body is at least 10 times larger than the thickness. Next we make certain assumptions on magnitudes of deflections, the deflections are small as compared with the plate thickness, for example the maximum deflection is taken to lie between T by 10 to T by 5, this range can be viewed as limits for validity of thin plate theory, the slope of the deflected middle surface is small compared to unity, the consequence of that terms with squares of the slopes can be neglected, then there is no deformation of the middle surface during bending, then the deformations are such that straight lines initially normal to the middle plane remain straight and normal to the middle plane, the thickness of the plate remains unaltered, okay. Finally the stresses normal to the middle surface are negligible order of magnitude, so these are the basic assumptions we make, we can quickly run through the implications of these assumptions, many of these assumptions are also made in analysis of beams, so some of the comments that I am going to make may be valid in that context also, so let us see. Now the material of the plate is elastic, homogeneous and isotropic, this is not a fundamental assumption, it is not a basic requirement to develop a plate theory, we can develop alternative theories which relax these assumptions, for example inelasticity and anisotropy may be desired for economic designs and optimal usage of material, for example in problems of earthquake engineering we want to design structures to behave inelastically in a controlled manner, similarly in composites and RCC etc. we introduce anisotropy to enhance the performance of the structures, structural material, so this is a simplifying assumption if necessary these assumptions can be relaxed. Now the body is initially flat, this is valid for plate theory, in the theory of shells the body can be initially curved, so for a plate theory this is required, then the thickness of the plate is small compared to its other dimensions, the smallest lateral dimension of the body is at least 10 times larger than its thickness, now this is a fundamental assumption this is what defines what a plate is, so T being much less than or equal to L, T is a thickness being much less than the least lateral dimension is the most fundamental assumption from a physical point of view, if this condition is not satisfied we are not talking about plates, okay, so the typical range for T by L is this, 0.001 to 0.4, if it is of the order of 0.001 we can use a membrane theory like a string, you know two dimensional analog of a string, if it is in the range of about 0.1 thin plate theory can be used, if it is in the range of 0.4 then we need to use thick plate theory, so this is one of the important assumptions, the deflections are small as compared with the plate thickness and other descriptions given here. Now this enables us to write equations, you know the equations now can be formulated in terms of initial undeformed geometry, products of deformation parameters can be neglected, then validity actually if you make these assumptions and carry out a computation if you are interested you can test the validity of these assumptions by actually performing the calculations of squares of displacement terms, products of slopes and things like that, in the course of solutions we can really verify, for example the terms that we have ignored in the strain displacement relations we can compare with the terms that we have retained and see whether they are indeed small or not, so it is possible to posteriori kind of check if these assumptions are met or not, if these conditions are violated we can develop a geometrically non-linear theory by retaining all other assumptions, all other assumptions means the earlier assumptions okay and some of the things that to follow, as magnitude of the admissible displacement increases the tendency for material non-linear behavior needs to be taken into account, so if you are including non-linear strain displacement relations and if the displacements are large the material has a tendency to enter into inelastic regimes as far as stress strain relations are concerned, so that also has to be borne in mind. Next there is no deformation of the middle surface during bending, this actually helps us to define the neutral plane and it is not valid when in-plane loads are also present, it is not valid for large deformations, then the deformations are such that straight lines initially normal to the middle plane remain straight and normal to the middle plane, the thickness of the plate remains unaltered, now this is not going to be in a scientific sense satisfied, for example lines which are initially normal to the middle plane will not remain normal to the middle plane after deformation, they may not remain straight and thickness need not remain unaltered, but the point is the resulting errors in the kind of situation that we are considering are negligible for thin plates, that is the range of applicability of the theory that we are developing, the transfer shearing strains acting on planes normal to the middle plane are neglected, the assumptions can be relaxed, these assumptions are also not fundamental, you can relax these assumptions, and we for example while discussing Euler-Bernoulli beam theory if we include a shear deformation, contribution of a shear deformation to transverse deflection we saw that we can develop an alternate theory known as Timoshenko beam theory, so the assumptions that we are discussing here in the context of plate are the Kitko-Flau assumptions, so if you relax some of these assumptions there are other theories like midline plate theory which allows for thick plates and a contribution of shear deformations to transverse deflections, so there are further higher order plate theories which are available in the existing literature, so the point is that this assumption can be relaxed and we can develop alternative theories, so the thickness of the plate remains unaltered in the consequences normal strains are neglected, the stresses normal to the middle surface are of negligible order of magnitude, this again valid for small values of T by L, the plate thickness does not change during deformation, not valid in the vicinity of concentrated loads and as the value of the thickness increases this assumption is not valid, now what is the meaning of this assumption, the deformations are such that straight lines initially normal to the middle plane remain straight and normal to the middle plane, so this is I have shown the undeformed cross section of a plate and MN is the line which is actually it is a surface normal to the plane of this screen which this is a middle plane, this is a middle plane and the MN is at 90 degrees to the middle plane, this is before deformation, now after deformation so we can sketch this, so MN the middle surface this is in according to our assumption M bar N bar is where MN goes in the deformed geometry and this angle remains as 90 degree, that's what we are saying, now it is possible that it remains straight but it may be at an angle for example the MN may be like this, so here there is a shear deformation this angle alpha, here there is no shear deformation but still this surface is remaining plane or this line is remaining as straight but it can also deform in a more you know non-linear way across the thickness, so then in which case we need higher order theories to be developed, so what we are doing in thin plate theory is this situation, in midline plate theory we can use this situation, so when it comes to computation of kinetic energy we are considering a mass element and contribution to kinetic energy due to this deflection is taken into account, but a section like this, for example a section like this would rotate in the deformed configuration and there can be inertia against this kind of rotations, so if thickness of the plate increases not only we need to allow for shear deformation but also we need to take into account contribution to kinetic energy from rotary inertia terms, so some of these need to be included if you wish to develop you know refined theories for plate behavior, so the one that we are discussing is the theory that is valid for thin plates, so these assumptions 4 to 7 listed in the table are known as Kirchhoff-Lauw assumptions, now the straight line normal to middle surface before deformation remains straight, normal to the middle plane with no change in their lengths after deformation that's what we have been emphasizing, if the initial and final position of the points on the middle surface are known the initial and final positions of all points of the plate will be known, so these are consequence of the assumptions that we have made, the strain field can be calculated at all points in the plate in terms of the middle surface alone, okay, in terms of the deformation of, now the plate problem can be thus tackled as a problem in 2 dimensions, okay, so this is what will emerge now as we go through the analysis, now in dealing with 3 dimensional elasticity problem we talked about stress and strain components but in engineering theories like actually vibrating rod, beams, plates, etc. we talk about stress resultants, they are the integrals of stresses across the cross sections of the structure under consideration, so in a plate the stress resultants are shown here there will be bending moments about X axis, twisting moment MXY, twisting moment MYX, bending moment MYY and shear force QY and QX, so these are the stress resultants in a plate problem, so how do you compute, how the normal stress and bending moments are related, so you integrate across the thickness of the plate as shown here and you get what is a bending moment, that means sigma XXZDZ, so you take the moments of the stress about the middle plane and you get this, similarly MYY on this phase we get this, MXY is because of the shearing stresses we get this, shear force again because of shearing stresses and they are integrals over the surface, so these are quantities per unit length. Now let's again examine some of the implications in terms of our ability to formulate the problem, because we have made these assumptions what happens to the displacement stress and strain fields, now plane sections initially normal to the middle plane, remain plane the consequence of that is epsilon XZ, XYZ is only function of X and Y, the dependence on Z is not there, and similarly epsilon YZ is function of X and Y only, it remains plane and normal to the middle plane that means the shearing strains are 0, if you make only this assumption the shearing strains are independent of Z, here you are going ahead and telling that it also remains normal to the middle plane therefore this is 0, and we will have the same length would mean epsilon ZZ is 0, that means thickness of the plate doesn't change epsilon ZZ is therefore 0, now epsilon ZZ equal to 0 means dow W by dow Z is 0, that means W of XYZ is independent of Z and it is W of X, Y, so it is enough if we study this at the middle plane that's what we will do. Now you consider epsilon ZZ based on the constitutive law, epsilon ZZ is given by this, now we are assuming that epsilon ZZ is 0, but actually this may not be true that is epsilon ZZ equal to 0 need not imply that sigma ZZ is equal to this, okay, so we abandon this constitutive law in our formulation, we won't really use this constitutive law, now you look at now epsilon XZ is 0, the shearing strains are 0 that means dow W by dow X plus dow U by dow Z equal to 0, consequently it means U of XYZ is minus Z dow W by dow X, similarly epsilon YZ is 0 implies that V is minus Z dow W by dow Y, so I am basically able to express U and V in terms of W, now epsilon XZ equal to 0 means sigma XZ must be 0, similarly epsilon YZ equal to 0 means sigma YZ must be equal to 0, but this cannot be true since we want these stresses to be not equal to 0 so that the corresponding stress resultants are not 0, if we take these constitutive laws to be valid the implication is the shearing stresses will be 0 and therefore the stress resultants are also 0, now this is not true, so what we do is we will abandon these two constitutive laws in our formulation, now next we are assuming that sigma ZZ, sigma XX is much larger than sigma ZZ and sigma XX YY is also much larger than sigma ZZ, so we can neglect sigma ZZ in the formulation of constitutive laws, so we will write epsilon XX actually it is given by this, now we will knock off this term and retain only this, similarly epsilon YY when I write I will use this, the shearing strain is given by this, okay, the remaining constitutive laws are already abandoned, there are only three constitutive laws which we will be using with this simplification, now therefore the constitutive law for thin plate theory is having these components sigma XX, sigma YY, sigma XY given by this, now if you go back and check with the constitutive law that we use for plane stress elements it turns out that the constitutive law that is emerging here is identical to what was used in plane stress theory, but you should be careful you should not interpret bending of a plate as a problem in plane stress, there are many variable points for example sigma XX, sigma YY, XY, XZ, sigma YZ need to be non-zero in a plate bending problem and functions of XY and Z, this is not true in a plane stress problem, the only point of commonality is that the relationship between stresses and strains that is these strains and the three corresponding stresses is identical to what was seen in a plane stress model, now we now need to compute the strain energies and kinetic energy, so that is where we are now moving towards, so we have now U is given by minus Z dou W by dou X, V is given by minus Z dou W by dou Y, epsilon XX now I can express in terms of W, it is minus Z dou square W by dou X square, epsilon YY minus Z dou square W by dou Y square, shearing strain is minus 2Z dou square W dou X dou Y, so we write now the strain in terms of this curvature, curvatures are rate of change of slopes, dou square W dou X square, dou square W dou Y square and this dou square W dou X dou Y and we define epsilon as minus Z into chi, where chi is the vector of curvatures as defined here. Now sigma is D into epsilon and D is this matrix, so we are now ready to write the expression for strain energy and kinetic energy, the strain energy is given by sigma transpose epsilon DV naught and in terms of using this constitutive law it is epsilon D epsilon DV naught, now I will use this now for this and write for epsilon minus Z chi and I will be able to write integrate over the depth and that leads to this term H cube by 12 and the remaining terms are chi transpose D chi DA, this is the strain energy, kinetic energy is half rho H W dot square DA, as I already mentioned we are including only this contribution to kinetic energy from only W. Now we can now consider the problem of formulating a finite element for analyzing plate structures, so we will start with considering a thin rectangular element with 4 nodes with 3 degrees of freedom per node and there are 12 degrees of freedom, the field variable is W of X Y, T, the order of the highest derivative present in the Lagrangian is 2, see the chi transpose D chi is there, chi itself has dou square W by dou X square the highest order of derivative of the field variable is 2, so the degrees of freedom should be, it should include derivatives up to 2 minus 1, so there are now 2 special variables therefore at any node the degree of freedom will be W dou W by dou X and dou W by dou Y, since there are 4 nodes with each node having 3 degrees of freedom the number of generalized coordinates in our representation must be 12, so these are the broad features that we can reduce before we embark upon developing the model. So the geometry of the model this is rectangular plate these are the axis X, Y, Z and I introduce X by A as XI and Y by B as eta and those coordinates are also shown here, this is eta and XI and this is Z coordinate, along Z we need not make any transformation this W is shown as a corresponding displacement here. Now theta X is the twist about X axis, theta Y is the twist about Y axis and theta Z is a twist about Z axis, 1, 2, 3, 4 are the nodes and we will now write the expressions for energies in such an element. Now the displacement field within this element what is the displacement field? This is W of X, Y, T, this has to be now written in terms of nodal values of the field variables which should be, the degrees of freedom should be W dou W by dou X, dou W by dou Y, so there are 3 nodal coordinates here, degrees of freedom here, so the W need to be represented in terms of these 12 nodal you know displacement values, so how do we represent that? So we will start with, this is a Pascal's triangle we need 12 terms from this, so I will start with 1 X Y, X square, X Y Y square, then X cube, X square Y, X Y square Y cube, when I reach this stage I have exhausted 10 terms, I have to pick 2 more terms now, so 2 more terms in this what we do is we select this term and this term, okay, so if I select this then I will not be able to, I have to select one more term, then I will not be able to honor the requirements of geometric invariance, that means if I were to change the nomenclature of X and Y axis the representation of W will change, because suppose if I retain this and retain any other element it is not symmetric in X and Y, so this is why we take these 2, so this is the representation that we can think of. Now the steps for formulating the stiffness and mass matrices are quite similar to what we have done conceptually, but the questions we should now ask is this element a conforming element, okay, so by that I mean are the quantities W, dow W by dow X and dow W by dow Y are continuous across the plate element boundaries, so it turns out that this element will not be a conforming element, so we will just see some of the details now. So I will now, I will have to select now these 12 generalized coordinates, so I will write, now I will write this W in terms of X, I and eta and this is expression, there is a slight abuse of notation, these alpha 1 to alpha 12 are not necessarily this, this is in X, Y coordinates, this is in X, I eta coordinate, but it's alright because I am not going to use this representation further, this is to explain the concept I have used this. Now this can be put in a matrix form as shown here, alpha is a vector of alpha 1, alpha 2 to alpha 12, and if I multiply this I get this function, this I call it as P into alpha, now I need to represent W dow W by dow XI and dow W by dow eta, so I can differentiate this to get dow W by dow XI I get this, you can quickly see that 1 is 0, psi is 1, eta is 0, this is 2 psi etc., similarly dow W by dow eta is this, that means I am differentiating this with respect to eta, first 2 terms are 0, next is 1, 0, XI, 2 eta, so on and so on. Now there are now 12 unknowns, but we know the value of W dow W by dow psi and dow W by dow eta at the 4 nodes, that is XI equal to plus minus 1 and eta equal to plus minus 1, so there are 12 equations and 12 unknowns, so I can write this expression, that means I can relate the nodal, the vector of nodal displacements to these generalized coordinates alpha through a matrix which enforces these conditions. So if we do that I will now call the nodal degrees of freedom in terms since I am introducing now XI and eta coordinates it will be like this, okay. Now W1 B into theta X1, theta Y1 here node 1, this is at node 2, node 3, node 4, this AE matrix you can show that it turns out to be this, I mean it is a matter of simple coding you can verify this. So now alpha itself can be computed subsequently as AE inverse into W, so now W is given by this P into alpha, now this alpha is given by AE inverse into WE, so with this I will be able to now write WE which is this vector in terms of this product this into AE inverse and that I have given this name as N1, N2, N3, N4, each one here is a one row and three element matrix, so the transpose of that is shown here, so this can be verified, this requires some effort, this can be verified that we will get this. The symbolic softwares can be used to code this up and verify, now I raise this question of whether the element is conforming or not, so how do we verify that? So now let us consider the edge 2, 3 that is XI equal to 1, okay, now along this edge now I will compute W, theta X and theta Y and see if I were to add one more element here what happens to these quantities across the edge 2, 3, so if you recall if these quantities theta X, W and theta Y depend only on nodal coordinates at 2 and 3 then adding one more element will retain the continuity of these functions across this edge, but if the value of any of these variables also depend on values of these coordinates then if you add one more element here there won't be a continuity here because when I take a point on this edge and view it as a member of this element it is influenced by 1 and 4, similarly the point on this edge considered as a member of the neighboring element which I am going to add will depend on other two nodes which are outside this, so consequently there will be lack of continuity of the field variable across the edge, so now the question is that condition satisfied or not, this is something that we need to verify, so what we do is we will consider now the edge XI equal to 1 and these functions NJ transpose J equal to 1, 2, 3, 4, J is the nodal coordinates this XJ and eta J that you are finding are the coordinates for the jth node, so now by putting J equal to 1, 2, 3 and 4 I can get these 4 functions and we using XI equal to 1, this is on this edge, so it is a simpler version of this quantities, now using that for W along this edge I can write the expression W2 into this, beta theta X2 into this, W3 and beta theta X3, I get this function, so now based on this you can see that W depends on nodal values of W2, W3 and theta X2 and theta X3, that means it is basically depending on W representation for W along XI equal to 1 depends on values of degrees of freedom at 2 and 3, so consequently we can conclude that W depends on nodal values of this and similarly we can also show theta X also depends only on these nodal coordinates, so it emerges that W and theta X will be continuous across the edge 2, 3 if another element were to be attached along this edge, so there is no problem as far as W and theta X are concerned but how about theta Y, now theta Y is given by minus 1 by a dou W by dou XI and we have to evaluate this, so this requires some calculations, so if I now use this representation for XI equal to 1 and differentiate with respect to XI I get these functions and based on that along this edge I need these four quantities I do this, and if you now carefully examine these expressions and you look at theta Y along XI equal to 1 it turns out that its value depends upon W and theta X at nodes 1, 2, 3 and 4, in addition to of course values of theta Y at nodes 2 and 3, okay, that means it is influenced by W and theta X also, so consequently it so happens that it violates the condition that for theta Y to be continuous between element it should depend upon nodal displacements at nodes 2 and 3, so that means this element is not a conforming element, this element is named a ACM element after the scientist who formulated this element, it is still being used therefore in spite of this apparent undesirable feature the element is still used therefore we can go ahead and formulate the matrices, so we will see the consequence of that in the next class, so at this juncture we will close this lecture, in the next lecture what we will see is we will complete this formulation and derive the mass and stiffness matrices and then let us examine how to develop a conforming element, so one idea would be to use products of beam trial functions in the two directions, we have used the cubic polynomials for analyzing beams, so if you assume that plate is made up of two beams which are orthogonal to each other then we can utilize products of beam functions that, the shape function that we use for the beams and we can develop an element and let us see how that happens in the next class, we will conclude this lecture at this stage.


What's up everybody, Jason here for jasperjasecasebreak.com, last break of the night guys, Jasper's diamond dozen baseball is back guys, this is volume 2 this time. Case break number 4 and again you get 12 cards per case. Of course there will be 12 cards in this break guys, chances from great hits, chances from sealed box redemptions. And since there is only 9 cases guys, most teams, most spots only have a few hit possibilities. And of course there's some of the sell she hits. So I don't know what's already been pulled from the first couple that I didn't do with Joe did or anybody else did, but I pulled the top 2 there. So we'll see what else is still remaining. But there's some nice hits in general guys. Here's a dice roller here, let's roll. And it is a 5 out of 3, 8 times, good luck. 1, 2, 3, 4, 5, 6, 7, 8. 5, 3, 8, Carl down to Trevor. Alright 8 times, 1, 2, 3, 4, 5, 6, 7, 8. Guardians down to the A's. Alright so Carl you have the Guardians, as well as the Reds, Angels, Twins, Socks, White Socks that is. Zack Smith of the Brewers, Carl with the Orioles, Giants, Astros, Diamondbacks, Rockies, Braves, Jake with the Red Socks, Carl with the Phillies, Mariners, Tigers, Cardinals, Reyes, National, Zack, Smith with the Pirates, Jake with the Royals and Padres, Carl with the Yankees and Dodgers, Zack with the Cubs, Carl with the Mets, Rangers, Marlins, Blue Jays and then Trevor with the A's. But yeah Carl I mean honestly man I feel like if you're interested in it for tomorrow man I don't know if obviously I'm sure Saturdays usually can be a little bit more busier but I think that Eminence can go tomorrow. I mean I would think that we do have a lot of customers that are buying into Eminence that are like overseas too so obviously the hours are a little bit different. So usually our Eminence spots tend to sell like overnight because it's like during the day overseas you know. So I think we can probably sell those two full spots definitely over the night and then I can repost more so I wish it could have went tonight but it doesn't look like it. But like I said I think when people wake up or when overseas customers wake up they'll notice that it's down to two left and they'll definitely get in on that. Also too guys we'll generate a case number we've done two, four and nine. So let's do a quick little generator here too as well. So I'm going to go one through eight because technically nine's not even possible anymore. And six, yes six is possible so we'll do six okay. Alright sure we're going to close them guys. So again guys we have six and again case six right there Diamond doesn't. Alright first one we have is a Ronald Acuna Jr. And it's out of two ninety nine. Okay we'll take that right there that's a nice little Acuna. Is that supposed to be like a short print maybe it's a short print that's why it's in there. Brace that is Carl. And we have a Randy Johnson 24 out of 50. That is from five star Diamondbacks edition Randy Johnson going to Carl as well. And here's the customers really quick before I continue going on. Then we have twins get two hundred and fifty dollars in break credit. Carl you also have the twins. I'll send you two hundred and fifty dollars in break credit and you can use that on whatever else you want. Nice. We have Lumberjacks that is a piece of Bade Roots game used bat. How about that? Eighty nine out of one hundred. Nice one there for the Yankees and that's also going to Carl. We have a Nolan Aronato seventeen out of twenty seven Cardinals edition also going to Carl. We have a big poppy David Ortiz two out of twenty five from top Sterling. Red Sox going to Jake Smith.  Cincinnati Reds ten out of ten Johnny Bench same thing Sterling. Cincinnati Reds that is going to Carl. We have a Juan Soto on card autograph there that is Nationals edition going to Carl last spot mojo. And then we have a Mike Trout edits a blue to one fifty Trout going to Carl. Then we have a Rookie of the Year favorites black refractors that's from Chrome Megabox nine five Dustin May. And that's a one of one actually look at that it's kind of hiding in there. You see that right there one of one. Nice Dodgers going to Carl Dustin May is back this season. Then we have a wander Franco gold. It is like a four five hundred dollar card right here. That is a PSA ten out of twenty twenty two baseball number to twenty twenty two as well. Nice one there for the Rays and Carl. And then last but not least how about a Julio Julio Rodriguez that is a on card autograph. And that is from top archives to ninety nine.  So this must be a cell sheet here right. Where's this Julio at. Unless it wasn't. I don't see it on the cell sheet but we will take it. Mariners also going to Carl last Bob Mojo on the pack filler. So there you go man. Very nice. Another case down guys. So I'll post another one up for tomorrow. And again some very nice stuff popping out of here as well. Very very solid. So I'll send you two hundred fifty dollars and break there right now Carl. And I am off here. And let's do it again tomorrow guys. Appreciate it. Jasper's case breaks dot com.


وَأَقُولُوا فِي القُرْآنِ مَا جَاءَتْ بِهِ أَيَاتُوهُ فَهُوَ الْكَارِيمُ الْمُنْزَالُونَ وَأَقُولُوا قَالَ اللَّهُ جَلَّ جَلَالُوهُ وَالْمُصْطَافَ الْهَاديِ وَلَا أَتْ أَوَّالُونَ الحمد لله رب العالمين له الحمد الحسن والثناء الجميل وشدوى الله إلا الله وحده لا شريك له وشدوى النسيدنا ونبينا محمد صلى الله عليه وعاليه وعاليه وأصحابه والتابعين لهم بحسان إلى يوم الدين أما بعد في هذا الفيديو إن شاء الله تعالى سأتحدث عن رمضان والعمل بالعلم رمضان المنظر هو منظر where we implement the knowledge that we have what we've understood from the religion of Allah becomes actions that are manifesting on our limbs ولذلك الله سبحانه وتعالى يسرن القرآن ونود أن تلكم الجنة وردتمها بما كنتم تعملون جنة is inherited by people who act upon the knowledge that they have إن النذاء الله says فلا تعلم نفس ما أغفية لهم من قررتي عيونين جزاءاً بما كانوا يحملون that they do not know no one knows that which has been prepared for them in jannah because of the actions and the hard work that they exerted the work they put in the effort that they put in that is why they inherit in jannah that is why they are getting a great place in paradise so actions of the knowledge that you have gained is a means to enter jannah الله سبحانه وتعالى يسرن النذاء فقوب كيبو فيها هم والغاوون it was narrated that بجعفر محمد بن عالي he commented on this verse فقوب كيبو فيها هم والغاوون صورة الشعراء ay 94 he commented on this verse and he said that this verse is referring to قوم وصف الحق والعدلة a people who've prescribed and they described and they've explained the truth and justice to the people بألسلتهم but only on their tongues وخالفوه إلى غيره but they opposed it in their actions and they did other than that which they were prescribing for the people and that's what the ay is referring to by according to his great Imam also the Prophet ﷺ he said knowledge that doesn't benefit يعني the knowledge that doesn't become an action implemented is like a treasure that's not paid anything from it knowledge leads to actions and that is the two things we were created to achieve is knowledge and also actions messengers and prophets were sent for that reason الله سبحانه وتعالى he says هو الذي أرسل رسوله بالهدى ودين الحق اللي يبهره على الدين كله هو الذي الله is the one أرسل رسوله يسأل مسجر بالهدى with guidance ودين الحق and the true religion هو الذي الله is the one أرسل رسوله هو الذي يعني العلم النافر ودين الحق يعني العمل الصادح النبي was sent to bring beneficial knowledge and righteous action that is the goal and objective of why prophets were sent and also the purpose in which we were created and Allah brought us into this world is that we come with beneficial knowledge and righteous action the evidence for beneficial knowledge is قوله تعالى الله الذي خلق سبع سبعوات ومن الأرض مثلهن يتنزل الأمر بينهن لتعلموا أن الله على كل شيء قدير وأن الله قد أحاط بكل شيء الله tells us that he created the seven heavens the seven earths and that which is between it لتعلموا so you know so the seven heavens seven earths and the creation in between that all of that Allah created it and the reason why he created them all is what لتعلموا so we can have knowledge of what لتعلموا أن الله على كل شيء قدير that Allah has ability over everything وأن الله قد أحاط بكل شيء علما and that Allah has infinite knowledge over everything so the first reason is knowledge the second reason why we were created is actions الله سبحانه وتعالى says وما خلقت الجنة والإنسة إلا لي عبدون I did not create the jinn all the ins except washin and in another eye Allah says فمن كان يرجو لقاء ربي فليعمل عمل صالحا ولا يشرك بعبادة ربيه أحدا and the action that we do has to be based on sincerity and also in accordance to the sunnah of the prophet عليه الصلاة والسلام then it's called a righteous action and beneficial knowledge is the knowledge that leads you to beneficial actions among righteous actions أبو الدرداء رضي الله تعالى عنه a great companion he said إنما أخشى من رب يوم القيام I fear my Lord Allah سبحانه وتعالى the day of judgment أن يدعوني that he calls me على رؤوس الخلائق that Allah to mark وتعالى he calls me in front of everyone فيقول له he says to me يا عوي مر فأقول لبك ربي فيقول لي ما عملت في ما علمت that Allah to mark وتعالى calls me and he says to me يا عوي مر فأقول له I say لبك here I am your Lord in obedience to you and then it said to me what did you implement from what you knew the knowledge that you had the understanding that was given to you what did you implement from it you were given knowledge but what from that knowledge did you implement it was also narrated from حسن البصري رحمه الله he said إذا ظهر الناس العلمة if the people show knowledge وضيع العملة and they forsake knowledge sorry they forsake righteous action حسن البصري رحمه الله he said إذا ظهر الناس العلمة if the people show and they bring out knowledge to the people وضيع العملة but they leave off righteous action وتحابوا بالألسوني and they show love to each other on their tongues they pretend they love each other وتباغضوا بالقلوب but in the heart they hit each other وتقاطعوا بالأرحامي and they boycott the family and their relatives and they cut the ties of kinship العانهم الله الله distances them from his mercy فأصمهم وعما أبصارهم الله سبحانه وتعالى he defends them and blinds them from seeing so it's a people who show knowledge لكن they forsake action they don't do the knowledge and the understanding of what they know عليبن الحسين رحمه الله he said كان نقش خاتمي حسين ابن علي عليبن الحسين he's took him out of his father حسين ابن عليبن أبي الطالب so he's the grandson of عليبن الحسين he's took him out of his father حسين حسن الحسين are the two children of عليبن أبي الطالب حسين ابن علي كان نقش خاتمي حسين ابن علي عليم تفاعمل on his ring that he wore it said on it عليم تي you have the knowledge now implement it that was written on his ring there was a reminder for him whenever he would look at it it will remind him that you now have the knowledge implement the knowledge that you have implement the knowledge that you have don't just make it information that you gathered and the action and the implementation you are far from it ابن سمك رحمه الله he said كتب رجل كتب رجل إلى أخي له a brother wrote a letter to another brother of his and he was saying to him يا أخي إنك قد أوتي تعلمة my brother you have been given knowledge إنك قد أوتي تعلمة you were given knowledge فلا تطفي أن نور علمك بظلمة الذنوب do not extinguish the light of that knowledge that you were given with the darkness of sins فتبقى في الظلمة and then you remain in darkness يوم يسعى أهل العلم بنور علمهم the day when the people of knowledge are going to be moving and walking in the light of their knowledge this is the advice he gave him he said to him my beloved brother knowledge has been given to you you have understanding of the religion don't extinguish that light that knowledge Allah gave you do not extinguish it with the darkness of sins and what will happen you will then be in darkness and the people of knowledge the real people of knowledge who lived by their knowledge they are going to be in the lights of their knowledge because they implemented what they knew they implemented what they knew ابن القيم رحمه الله he said ابن القيم said that knowledge is the leader of action it is leader the leader is knowledge and action follows so when you have knowledge your actions follow والعمل تابع الله and the actions are the one that follows and it's entrusted with it a leader a commander a general has to have soldiers or else what fight or what battle is he going to participate in the same way a person who has knowledge has to have actions that follow up that knowledge or else what is the benefit of that knowledge look how deep he looked at it العلم ابن القيم so the month of Ramadan my beloved brother and sisters is a month of implementing your knowledge learning jurisprudence rulings regarding Ramadan don't spiritually uplifting yourself nurturing yourself upon Islamic ethics and living by that changing your life for the better a lot of people what they do is they look at every new year and they set themselves goal and they say this year I'm going to achieve this this year I'm going to do this and this year I'm going to do that well guess what you are now fasting the month of Ramadan have you set yourself goals things that you're going to do in Ramadan and things that you will insha'Allah after Ramadan is gone set yourself that goal insha'Allah may Allah forgive me for anything I might have said that was wrong or incorrect and Allah and His Messenger are free from those mistakes and errors سبحانك اللهم بحمدك أشد والله إلا الله أستغفرك وأتوبه if you're enjoying these videos and you'd like to keep up to date with all of the courses we're going to be running make sure you head over to amauathome.com


Item number, SCP-153, Object Class, Euclid. Special Containment Procedures. Specimens of SCP-153 are to be kept isolated in acid-resistant containers, measuring no less than 10 meters by 10 meters by 5 meters, partially filled with sewage and organic material at Bio Research Area 12. Within 34 hours, both the level of organic content and the structural integrity of each container must be checked. Under no circumstances are these containers to be connected to any internal or external plumbing system. Specimens of SCP-153 almost certainly still exist in the wild. Any reports of people mysteriously disappearing from showers and bathtubs must be investigated immediately. Specimens must be equipped with infrared and ultraviolet sensors to circumvent SCP-153's camouflage. Specimens should be brought alive to Area 12 if at all possible. Description. SCP-153 appears to be a species of nematode, or roundworm, that can reach up to 8 meters in length and 8 centimeters in diameter. Specimens of SCP-153 live in sewers and drain pipes, and while specimens of SCP-153 can live off of most any organic material, they prefer to consume animal tissue. Specimens of SCP-153 excrete a highly acidic substance, similar to data expunged, from their mouths and gullets, and they have the ability to camouflage themselves, both outside and in. This SCP-153 has developed a hunting technique, where a specimen will swim up a shower or bathtub drain, dissolve the drain cover with its acidic saliva, and camouflage its gullet to look like a standard drain.  This entire process usually takes less than a few seconds. Addendum 153-01 Specimens of SCP-153 are to be kept isolated from each other, except under controlled breeding conditions. Dr. Kovalanskaya. Addendum 153-02 Incidents in Peru suggest that specimens of SCP-153 have started attacking people through sink drains, toilets, data expunged. Researchers are investigating how such an apparently simple animal can develop such relatively sophisticated hunting techniques. Addendum 153-03 Dr. Kovalanskaya has received approval to start a breeding research program with SCP-153, with emphasis on genetic engineering. The program data expunged, as well as a potential method of organic waste disposal. Addendum 153-04 A controlled release of SCP-153 instances has been proposed, as a potential containment method for stalling the spread of SCP-2717. Approval Pending. Lesson complete. If you missed the previous orientation, go watch SCP-152, Book of Endings, right now. Or for the complete course, watch this playlist.


Hello and welcome back to my channel. My name is Jackie and I'm an aspiring writer who is currently attempting to map out three different book ideas using the anatomy of story. And as I was editing this video I just realized that I had no introduction because originally I hoped to put premise and structure together but my premise video ended up being 40 minutes so that wasn't going to happen. So in this video I'm tackling step two of the process which is John Truby's seven elements of story structure. So we're now going to remind about five weeks to when I started this process. I have now moved on to step two of the anatomy of story which is structure. And I have some thoughts on this chapter. The positive, it is a really easy chapter to get through. There are seven key points you need to address and Truby describes them and then there are exercises. So that was really nice especially when I compare it to some of the later chapters in the book which are very theoretical like symbols or they just have a lot of lengthy examples like scene weave where he's broken down a number of films or television episodes scene by scene. So that is useful but it feels like a real slog to get through it. So this was nice and straightforward. The cons, one is that I don't think structure is the best word to describe this title because it isn't really about how your book should be organized. It's more these are seven key elements that your book needs to address or your story needs to address in order to be a good story but that's obviously not a big deal. He can call his chapters whatever he wants but if you're looking at this chapter expecting to get into plot and outlining it's not really at that stage yet. Then the final element which could be a pro or a con is after you've gone through the seven elements you need to include and then at the end of the chapter there's the summary slash list of steps you need to follow. It isn't just finding those seven elements. It's sort of you find the seven elements and then you need to go back and do other stuff which I think the way it's structured works really well but if you're expecting it to be straightforward following the chapter content you might be a little bit disappointed or frustrated. So what are the seven elements? The first one is weakness and need. So this is your protagonist's weakness and need at the beginning of the story. Number two is desire. Desire is distinct from need in that need is something almost fundamental to their character as we meet them at the beginning of the book that they need to address in order to become their best self and to get everything they want. So one of the examples in the book is from Tutsi where the need is Michael has to overcome his arrogance towards women and stop lying and using women to get what he wants whereas his desire is the woman he's fallen in love with. So the desire is like the goal or the objective that the character wants to go after but they're never going to be able to achieve it unless they address the need first. Number three is the opponent and if you've seen some of my past videos on trying to figure out my antagonists you'll not be surprised that I was quite looking forward to this one. Something to keep in mind with this current exercise is that the next chapter is on character so that's going to get into protagonist antagonists opponents and so on in far more detail. This the main point he makes is that your opponent and your protagonist should be going after the same goal so it's sort of starting with the most fundamental important thing you need to address and then in the next chapter we'll start fleshing it out. Four is the plan. So what's the plan the protagonist will follow in order to achieve their desire? Five is battle which as someone who writes fantasy and soft sci-fi and actiony type of things I love. Six is self-revelation so this is the moment when the character realises they need to change in some way usually to address that need I mentioned earlier and it's only through this self-revelation that they become the person they need to be who can defeat the opponent and then seven the final one is new equilibrium so we're at the end of the story now and what is the new normal and how is that different from where the character started so those are the seven key steps of story structure and when it comes to the exercises at the end of the chapter the way he recommends doing it is one start with a list of different story events so this is just almost brainstorming what are all of the initial ideas you have about what could happen in your story then two put them into a rough order and three look at your seven steps oh good then once you've looked at the seven steps you need to look at the psychological and moral self-revelation so that's step six in the seven and the point he makes here is rather than just having like a psychological revelation so something that tells him something about himself try to make it a moral one as well and the distinction is a psychological need and revelation is something that just affects the character whereas a moral one is something that affects the people in the world around them so for example let's say my need is to stop eating chocolate so I can be a healthier person this is a psychological need because it isn't having a detrimental impact on the people or the world around me now if my need was something like I need to get past my drug addiction because my drug addiction is having a detrimental impact on my family I'm stealing money from the shed bank account I'm lying about where I am people are up all night worried about me I'm bailing on my commitments you know that is more of a moral need because it is having an impact on the people and world around them so the revelation is what's the revelation that gets them past that then once you've looked at the revelation you go back to the need at the beginning of the book because as you can see in the examples I just gave they go hand in hand and from here you actually start moving through the seven steps sort of for a second time so revelation step six go back to step one which is the need then the next thing he says to look at the problem and the desire so problem what's not working in your character's life desire what do they want to achieve or get or change and from there it just follows the rest of the step so opponent plan and battle so the way this is organized it forces you to go through the process twice which I don't think is a bad thing especially when you want to make sure you're really focused on the revelation and the need but it did sort of surprise me when I was looking at this last night I went what didn't I already do this so something to be aware of when it comes to me and where I'm up to in the process so I started this for the first of my three ideas my fantasy hot mess which has already been drafted and what I've done is the first three bits of that exercise so I listed the story events but they were already in order because I've written the book and then I did my seven key elements of story structure so this is what I have now and I think it's going to be interesting to contrast this to when I do it again focusing on the self revelation and need if you're not interested in me going into a whole lot of detail about this project I'll put a timestamp somewhere and you can skip ahead something else to keep in mind is that this book did have actually four point of view characters when I read it last time but now I've narrowed it down to three so I've sort of done this for all three of those characters now context this is a late Victorian early Edwardian era fantasy with some steampunk elements I'd like to make more steampunk elements if they can fit mainly because I like the fashion which I know is a very bad motivation but the outfits are cool anyway the world is a university city sort of like Oxford that's extremely powerful in the global political landscape maybe just European political landscape I need to figure it out so first character is Peri she is a university student who is majoring in engineering and magic hates magic loves engineering she's also exhibiting at the international exhibit second character is Aubrey he is the third son of the king who also has magic skills has been locked up for them for all of his life and sort of tried to escape but didn't quite succeed and now is like on a mission for his father which takes him to this city Deremon and then the third character is one of the masters at the school who is a magic master and very very angry about events that happened approximately 20 to 30 years before the book started and he is intended to be the antagonist so weakness and need for Peri her weakness is blind faith her belief in Deremon the superiority of science and her distaste for magic and history her need is something I struggled with and the more work I do I'm not sure how much I need this character in this book but I love this character so I'd love to make it work so her need is she needs to learn to question the current system and respect the world outside of science to question marks I sort of said to reach full potential which I don't love because it's very vague or to break free from the prison she's created for herself so I thought and that could work prison could work as a symbol for this book because like there is a literal prison underneath the school um there that's where the climactic battle scene happens and so I like the idea that she's created this prison for herself in the rigidity of focusing on science and engineering in the future and letting go of the past and that also works well with the other characters because Aubrey's literally escaped from being locked up for the last 15 years 11 years I don't remember long time and I think Jairadin who's the antagonist he's also in a bit of a prison of his own making so that could work Aubrey weakness arrogance suspicious only relies on himself believes everyone is out to get him need needs to learn to trust and rely on others in order to achieve his goal and there's also this element of he needs to trust others to prove he too can be trusted the goal proving himself to his father by himself more freedom escaping from constant surveillance which is sort of buying himself more freedom and then Jairadin ambitious and angry too angry to appreciate what he has and need needs to let go of his anger to be free from Daruman and experience love again I hate that wording but oh well I've actually continued this for like sort of the main cast of characters but we'll be here all day if I do that so we'll stick with the point of you ones okay desire Perry to get recognized at the exhibit to buy her freedom Aubrey to buy his freedom from his father by delivering the McGuffin which I need to name Jairadin to destroy rain who's another character and everything he stands for so this is a little challenging because these goals don't really line up which is one of the challenges I have with this book and that they might like they're all in the same world but do they need to be part of the same story then opponent so mentioned Jairadin and the big challenge here is how do they all want the same goal and I think I mentioned when I was looking at premise the idea of pitting them against each other as fighting over the soul of Daruman very much like Batman and the Joker fighting over the soul of Gotham and the way that works is Jairadin the antagonist he wants to return it to what he considers to be its former glory Aubrey wants to hand the keys to the city to his father the king for more power for Perry I'm sort of thinking like it's a prison but it's her prison like almost like I don't know it's hers it's her home she grew up there she even as she wants to escape in some way she still loves it and wants to keep it safe there's also the idea that she wants to save it for rain who's the other character I mentioned earlier who's sort of her father figure in this book um and then I was also brainstorming like maybe she wants to leave the city but she still believes in what it stands for because it's this city that's like the pinnacle of science and engineering and technology and looking at the future and progress and that's everything she believes in plan so the plan hasn't really changed it's Aubrey and Perry team up to find the MacGuffin which is sort of the metaphorical key to Daruman and power in Daruman when they realized that Jairadin has sort of obtained it he hasn't directly bit his sort of gotten in cahoots with the person who has it um and learn more about his plan they decide to stop him so it's sort of they have one plan which is get the MacGuffin and then that turns into stop this guy battle I have nothing to write here I've written this I love the battle scene um I in fact the battle scene is one of the things I kept from the original draft that I did back when I was 19 or 20 and I like rewrote it a little bit but I love the choreography and the epicness and the rawness of it so yeah battles love them self revelation so self revelation is a challenge and this is where I can see the benefit of the exercise like sort of doing it backwards next so starting with self revelation and then going back through the process again because what I've got here is for Perry Daruman isn't pure good it's built on destruction and ruined a lot of good I've written it ruined a lot of the good and the bad I don't think that's what I meant to write she needs to draw on both science and magic to triumph rather than blindly pursuing the future and enduring the past Aubrey basically building trust between him and Perry um he doesn't need to do everything alone he can trust and rely on others and Jairadin I haven't done a revelation because he's not going to have one or at least not until too late that's why he experiences a downfall because he gets so wrapped up in what he believes that he never has that revelation of seeing what he has and you know he can actually have a good life despite of everything he's lost um and then finally new equilibrium so they've saved Daruman but they have the knowledge that it isn't the utopia that they thought it was so from here I need to go through and do the rest of the steps so revelation and then go through the process again and then I need to try this for my other two books but I would love it if you could comment on this video now and let me know like does this sound like a good story to you or does it sound like a mess because I was writing like I was working on this and thought oh I'm getting excited about this story again and I'm starting to think like it could be a good story but obviously there are still elements I need to figure out so I'd love to know your thoughts now when it's in this state I've been trying to go through the rest of the structure steps for this idea and I keep running into trouble when I get to the desire stage so I've actually started going through it twice now and I've done the self revelation I've done the weakness and need problem and then desire and I'm okay with the revelations I think I'm just going to focus on psychological ones rather than moral ones because it's my brain isn't big enough to do moral ones as well but also I feel like trying to focus on moral ones as well at this moment is causing more harm than good it's stopping me from making progress rather than helping me get to the next step so I'm focusing on psychological revelation which I'm fairly happy with what I've got for the two main characters then weakness and need I'm okay with that as well problems I'm okay with that too and then I get into desire and the main issue I have is that because the revelation weakness and need and problems are all things inherent to the characters and their lives in general when I think about desire I think about what they want in general when no the desire is supposed to be the thing that they want in the book and I don't really know how to approach that so if I talk about their desire in general well peri like iterations include how can I innovate how can I create new technology how can I bring the science and knowledge and government of this city to the rest of the world or how can I escape from this city and build a life of my own where I'm not constantly in the shadow of this institution where I've lived my entire life so all of these are you know real desires for her but they're not what the book is about so I'm in this position where originally the book is sort of originally about how do we get the MacGuffin and then it's how do we stop this guy who has the MacGuffin and I keep trying to bring it back to that and go okay how can I link these desires into that how can I make like her desire that's the initial springboard and then it turns into what the plot is and I don't know if that's the best way to be doing this because the point of this exercise is to figure out what's wrong with this book and whether there's hope and if I keep reverting to the existing story that defeats the purpose but if I don't do that then I'm not actually sure what the book's about anymore I'm not actually sure how these characters become part of the same story so I'm struggling a little bit and I'm not sure what to do so I mean part of me thinks maybe I should just try doing two stories one where I sort of weave it into the existing plot which is MacGuffin then bad guy and one where I just go okay let's talk about these characters desires in general and see where it goes. This is going to take a while hello it has been a while and not because I spent so long working on the other book but because I've had a lot of freelance work on over the past I think seven weeks now so it's actually been over a month since I last looked at the structure exercises from the Anatomy of Story and I haven't actually continued working on my seven pieces for my fantasy hot mess book so now the freelance work has slowed down a bit I am still working on a project but thankfully the clients agree to an open deadline so I can be no more relaxed like I am still working on it but I'm not having to do it in every hour outside of my day job so now I want to continue with the structure exercises for my DID mystery book which is a brand new idea that doesn't have anything yet and my happily ever after super villain tries to take over heaven book which I tried plotting out last year for NaNoWriMo but didn't end up writing and the good news I guess is that I couldn't sleep tonight or last night last it's the same night so I couldn't sleep I've been up since midnight I gave up trying to get back to sleep around two it's three a.m now so I've got plenty of time before Drew wakes up to get this done it has now been 35 minutes and I've actually gotten through both of the other ideas so I guess I was going to say it's surprising how quickly you can do book outlining exercises when you haven't written the book yet but in hindsight that isn't actually that surprising because for the book I'd already written there was a whole lot to unpack and figure out whereas there's nothing in these ones yet so naturally it's going to be faster so here's what I've got for the DID mystery book her weakness is that she is scared of being out of control and she tries to control everything so rigidly that she's unable to handle when things don't go her way and her need is that she needs to be able to accept her altars in herself and the reason I feel like being in control freak works is because like think about being in a body that you're sharing with say seven other people and they might take over without warning if you are the one who is in the body most of the time you're probably going to want to avoid that it's probably going to be really scary especially when you have no idea what's going on when you're not the one at the front so I think that works and that ties in well with how I want the altars to each be finding out different clues about the mystery and ultimately working together to find the culprit the problem is that one of her altars has witnessed a murder and she needs to clear her name so then the desire is to find the murderer and clear her name the opponent is the killer who's going to let her take the fall for his crime the plan I think will be in two phases so the first one will be she is like desperately trying to stay in control so she can find all of the clues and figure out this mystery the second phase is to start finding ways to communicate with her altars so they can start working together and put all of the pieces together the battle is confronting the killer and trying to get a confession out of him the self revelation is the idea that she doesn't need to be scared anymore that she and her altars can work together they can find systems to work together and they can find a new equilibrium and then of course the final stage is new equilibrium so that's the point where she has accepted herself in her altars she's healthier and happier the killer's behind bars so I'm not sure how long that took to go through that but I'll bet you a hundred bucks it was shorter than going through the previous book so you can see why this exercise was much faster when going through it with a new idea for the second one happily ever after I actually went back and looked at some of the videos that I filmed for nano rime last year because I'm away at the moment this is why the background is unusual and I forgot to check the notes about happily ever after before I left and because the first stage of the structure exercise is listing out different scene ideas I wanted to see what I already had what was a bit disappointing is that I didn't really have much and seeing the videos made me remember oh yeah this is the reason why I decided not to write about that idea for nano rhino because other than the setup I really couldn't think of anything so I realized that for this idea I'm basically in the exact same position I'm in for the DID mystery one so I listed a couple of different scene ideas and then got into the seven key points of story structure and to give you context for who I'm referring to here when I say villain I mean the main character of this story this is the villain who's been sentenced to hell and wants to take over heaven when I say hero that's not the hero of the book it's just one of the heroes from heaven who sort of works as a social worker I guess in hell um so there is a villain character and a hero character but the villain is the protagonist and the hero is like one of the opponents slash sidekick so just for clarity so weakness and need our protagonist weakness is having an ends justify the means mentality not surprising for a villain so he doesn't care who he hurts to get what he wants also has no sense of personal responsibility um he sees himself as a victim he doesn't think he deserves to be in hell he was just his villain he was doing his job and that's that he shouldn't be punished for doing his job his need is he needs to learn to consider others and the greater good desire wants to get into heaven and he actually feels entitled to it he has paid his dues he was just doing his job now it's time to experience his reward the opponent so there are two major opponents I think one is the system which doesn't really believe that villains can change and it doesn't give them the support or resources to change I'm not sure if this system needs to be embodied by a character so I think that's something I'll be looking at when I get into the character exercises which come after structure and then the second opponent is that hero character I mentioned so the social worker this is someone who's an opponent because like they lock horns they clash but also like a sidekick in fact I think there's a I can't remember all of the terms because it's been over a month since I read this chapter but there's there are like a couple of different ally characters and there's a fake ally but I think there's also like a fake opponent who is opposing the main character before they're greater good they're pushing them to be better so that's who this person is for the plan again I think this is going to be a two phase one so the first phase is how can he like gain the system how can he level up through hell until he gets to heaven and then I think the second one is you know he realises does he even need to play the system can't he just stage a coup the battle this will be a literal battle a battle for heaven where he's forced to change his ways I'm not sure what the moment of revelation is going to be like whether it's going to be he sees the damage his caused or whether like he sacrifices himself for the hero character for self revelation there are a few here but they're all wrapped up in the idea of transitioning from being a bad guy to a good guy so if there's value in being the good guy the ends don't justify the means other people have value too surprisingly and also there's hope for reform so how to change the system so it's possible for others to improve a new equilibrium is a new afterlife system that's focused on helping people improve and the villain takes on the social worker role what's interesting about this is that I did come up with this idea last year it was before I saw the last season of the good place I don't know if it was out yet or if I just hadn't watched it yet and it's basically like if you haven't watched the end of the good place mute me for the next three seconds but it's basically the end of the good place where they come up with a new system for the afterlife that encourages people to improve so I'm not sure if that's a problem I don't think so because the execution will be different but yeah it's interesting how different creators can independently arrive at the same idea so that brings me to the end of the structure step in the anatomy of story and I'm feeling pretty good mainly because it's been over a month now I've got them back into it but in general I think if this was the only structure step in the book I would be a little worried I'd feel like everything was very vague and I didn't have a very good outline but I feel okay because there is a different plot step later in the book where you expand these seven steps 222 and I think by then when I've already done the character work and I think moral journey and symbols all come before plot so I think once I've got all of that in place I should have a lot more to work with when it comes to fleshing out the plot so all in all I feel like I've made a good start I do have the basics here I do need to flesh them out obviously but yeah I'm making progress which is the main thing so I hope you enjoyed this video if you did as always please give me a big thumbs up remember to subscribe leave a comment below with how you're going with your work in progress I think this video will be out either right before Nana Raimo starts or once you've just started so let me know how your preptober went and what you're planning to do for your Nana Raimo project and if it started by then how it's going other than that I will see you next time bye