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Vasilis July 30, 2009 08:00

How do I compute the normal vector to a surface with FEM
I am trying to compute the normal vector to an inclined plate with the FEM.
Based on theory, the normal vector is given by


This is the normal to the top surface. There is no variation in the y-direction. Consider it as a 2D geometry. The plate has length L, and height H, and it is inclined with a slope equal to PHI, so that it's bottom right corner is located at (a,0) and it's top left corner is located at (b,1).

If I use the FEM to compute the dz/dx derivative, I will find that it is equal to zero. Does this make sense?
The only way to compute a non-zero value for the dz/dx derivative is to solve the problem where the domain was originally a rectangular which deformed to the one I have now. Is this the only way to compute the normal vector with FEM?

Vasilis July 31, 2009 05:10

I am trying to calculate the normal on the outer surface of a circle. The circle lies in the y-z plane.

I compute the value of the derivative dz/dy (which is equal to (y-y0)/(z-z0), if the equation for the circle is (z-z0)^2+(y-y0)^2=R^2 ), and there is no good agreement between FEM and theory.
Any ideas why this is happening?

Vasilis July 31, 2009 06:37

My mistake, I can not compute the normal vectors because both x and z are independent variables.

Vasilis July 31, 2009 07:59

So, how do I calculate the normal vectors in a moving boundary domain.
If we assume that x=f(X,Z) and z=h(X,Z) taking the derivative of dx/dZ will give me the rate of deformation. But, we need to compute quantities such as dx/dz.

Does anybody has any idea about how to compute the normal vectors with FEM?
