as howling winds echo across the snow-covered reaches of the wild northwest, the Quaker Elk Company, makers of Quaker Pop Wheat, and Quaker Pop Rice, the delicious cereal shot from guns, in cooperation with the Mutual Broadcasting System, present by special recording Sergeant Preston of the Yukon. It's Yukon King, swift as his strongest lead dog of the northwest, breaking his trail for Sergeant Preston of the northwest mounted police in his relentless pursuit of lawbreakers. Gold, gold discovered in the Yukon, a stampede to the crime site in the wild race for riches, back to the days of the Gold Rush, and the adventures of Sergeant Preston and his wondered of Yukon King as they meet the challenge of the Yukon. Do you believe in people? Do you believe that a man living in a mud hut in some dark far-off corner of the world is still a man for all of that? If you do, this message is for you. It's the story of that man and his neighbors in a primitive village in the Orient, the Middle East, Africa, South America. There are thousands of such villages, all seeking something better than they've had before. Enough food to go around, a clean well, a school for the children. These are the freedom villages of our world today, and they're coming into the 20th century primarily by their own bootstraps. They need just a little help. A contribution in any amount will help swell the fund, and village by village, the free world will be strengthened. Send your contribution today to Freedom Village, Care, New York 16, to any local care office. This message is brought to you as a public service. Sergeant Preston and his great dog Yukon King were in Dawson to report to the inspector at the end of a patrol. They were walking down the town's main street, but an old friend whom the sergeant hadn't seen for some time came out of the cafe. Jim Harper! Oh, well, as I live and breathe, it's Sergeant Preston. Glad to see you, Sergeant. Glad to see you, Jim. You too, King. How's your daughter, Fanny? She's fine. How long have you been in Dawson? Just got in this morning. You'll finally give up the search for gold at Baldrack? Nope. Oh, sorry. I'm starting back there this afternoon. Fanny's been there alone since yesterday. I just came in to transact a little business with Andy Janks. He runs the cafe, you know. Yes, I know. I can see him in there exhaling a heavy gold watch and chain. By the way, Jim, what time is it? All right, you guessed it. It's my watch he's got. I've watched a lot to you, Jim. The last time I saw you, you said you'd serve before you'd part with it. Well, I didn't sell it permanent, Sergeant Preston. Andy's just holding it in security for the cash flow. I'll be able to pay him back inside of a few months. Well, you'll get the money to repay him at Baldrack. Well, the gold mine up there has played out, isn't it? Well, well, yes, you might say so. I got to get going, Sergeant. Fanny's home alone. I promised her I'd start back right away. Just a minute, Jim. What's going on at Baldrack? All right, you. What do you mean? I've been in Dawson less than an hour, and I've already heard about two men from Baldrack who came here to raise cash, and you're the third. I've got to get going. Besides, I promised I wouldn't say anything. Hold on, Sergeant Preston. Goodbye, Sam. Hold on, James. James, there's something going on at Baldrack, all right? I wonder if the inspector said anything. A few minutes later, Sergeant Preston was in the office of his superior. When he had finished the report of his recent patrol, he spoke of Jim Harper and the others from Baldrack who had come to town to raise cash. You heard about the inspector? Yes, I have, Sergeant. Well, Baldrack isn't on my patrol, sir. I don't know much about the community. Well, a lot of the people went there when gold was found in the mountains. They stayed claims and started work. They soon learned that the ore was of very low grade and practically worthless. Well, I don't explain why they're risking their most tertiary possessions to raise money. No, it doesn't, Sergeant, and I'm curious. I have a week before I'm supposed to start out on the trail again. That time I could go to Baldrack and look around, sir. I'd appreciate that, sir. I'll overhaul my gear and start out in the morning, sir. Jim Harper left Dawson that evening, and it was the following morning when Sergeant Preston sat out on the trail along the rim of Willowaw Canyon toward Baldrack. The Mounties dogs were big and strong, and paced by the Great Dog King, they covered ground much faster than Jim Harper's aged team. Late afternoon found Sergeant Preston within sight of Baldrack when Jim Harper reached his home. Jim took the dogs out of harness, and when inside, agreed his 18-year-old daughter. Glad you're back, Hopper. You made good time. Well, not bad considering the age of my dog. I'll have to make out. That's fair, Penny. Fair to me. Then, of course, the dogs aren't used to working much. I don't mean the dogs. Then I got the cash I wanted. I told you Andy'd let me have it. Oh, well, Andy drinks his almighty shrewd mess. If he longs to cast his best in Mr. Martin, then he could, it must be all right. Yeah, yeah. Yeah, Martin's got a good thing there. You hope Mr. Martin's on the level. Of course he is. He's a fine man. What's more, he knows gold mining, had a lot of experience in California. Why, you said yourself you liked the janta. Well, yes, I did. You don't sound sure of it. What's wrong with Martin? Well, it's not Mr. Martin. Popper said, Curly Larson. Well, what's wrong with him? I don't know. He said he'd done anything wrong. Not that I know of it.  They're, well, they're shifting. Well, it takes a life. You can't go on. The door. I'll open it. Oh, well, Mr. Martin. Howdy, Miss Penny. All right, Jim. Come in, Martin. Come on in. Thank you. It's just got back from Dawson. Yes, I saw you coming into town. I'm all ready for you, Martin. Got the cash for that stock right here in my pocket. Fine. I'll make out a certificate for you. Here, Martin, sit right at this table. There's a pen and ink. Thank you. Mr. Martin, are you sure there's gold in the mom? Sure. Why, Miss Penny, everyone knows there's gold there. Yes, but it's never been worthwhile to work this town. Because of shipping costs, my dear. Because of shipping costs. You see, it's not worth the while to ship a ton of ore all the way to the states for the 50 or $75,000 worth of gold it holds. But if that ore is refined right here in Bald Rock, now, that's a different story. If I didn't think it's worthwhile, my dear, I wouldn't be here. Hey, Jim, there's your stock certificate. Yeah, and here's your cash. Well, how come you're going to begin building the refines? Very soon, Miss Penny. Very soon. You have to buy up a few parcels of land, then we'll be all ready to go. Oh, yes. Cool. Internation is hammering on the door like that. Mr. Martin, yes. Hey, what's the excitement, Martin? Mr. Martin. What is it, honey? I've got to see you right away. You better come with me. Is something wrong? I've got to see Martin, that's all. It must be urgent. It is. Will you come with me, Martin? Yes, we're through here. I'll see you later, Jim. Yeah, yeah. Open up and call. I'm sure there's nothing serious. Martin is an excitable man, you know. I'll see you later. Trouble us. Money of trouble. Come with me. I'll tell you while we're walking to the car. We've got to get out of here as fast as we can. We've got to travel fast and find a track. Why? Sergeant Preston owns a mountain. He's just came into town. Preston, I've heard of him. What's he doing here? This is office patrol. I don't know why he's here, but that's beside the point. Point is, it won't take him long to learn that we're selling stocks on the promise of building a gold refinery. Soon find out that we have no intention of setting up any machinery or giving these people any return on their case. How can we know our intentions? After all, listen, Martin, I had trouble with the law in Whitehorse. What? I'm wanted for a couple of robberies in the shooting. You never told me that. It didn't matter until now. Preston sees me. I'm a going goose. And if he knows you're working with me, he'll find reason to hold you until he can check up. Then he'll learn that you haven't ordered any machinery. Well, we've collected a tidy bundle of cash. It's pretty near time to leave town anyway. Won't take as long to throw a gear together and get moving? First, we've got to take care of Preston's dog. See? Yeah. I've never gotten away from Whitehorse if King hadn't been wounded. He can track down any man who ever lived. What do we do? Shoot the gun? No, no, no. It's gunshots that bring Preston on the run. He's taking along with us. Then he can't follow us then. Talk sense, Curly. King's a one-man dog. He'd never go along with us. He's locked in a wooden crate. He won't have much choice. Just put the crate on our sled. Very smart, Curly. How do you get the dog inside a crate? Sergeant Preston works as official police with him on a cord, around his neck. In an emergency, he uses it to call for help. King knows that whistle. He'll come when he hears it. Yes, but I... He doesn't know you, does he? No. Then you can get closer on the crowd. Maybe in the cafe. The sharp knife won't be hard to cut the cord and take the whistle. If Preston goes to the cafe... He'll go there. But that's the best place to get information. And you get the whistle. Don't waste any time. Bring it to me with the cab. Curly's reasoning was logical and accurate. Sergeant Preston had gone to the crowded cafe for information, leaving King to watch the dog team behind the building. When Martin arrived, he saw the sergeant. Notice particularly the cord around his neck. Directly surmised that it was attached to a whistle in a pocket of Preston's tunic. He waited for over half an hour before he had an opportunity in the jostling crowd to cut the cord, but definitely removed the whistle with a skilled touch of a pickpocket. Then he hurried to rejoin Curly in the shack. You ready, Curly? Yes. I'm just waiting on the bag. I just finished the crate. You got the whistle cash? Yes. Have any problems? No, but I had to wait for a good chance to steal it. Is the money still in the cafe? It was when I left a minute ago. His dogs are around in the back. Open that door and he's so... Right. Now, the crate over close. That ought to do it. How are you going to get the dog inside? That's easy.  I watch him through this crack in the door. When he gets close, I'll get the door shut. Lucky it opens out. The swing out wide, the dog will come bounding through the opening and be right inside the crate. Then you drop his gate and we'll have him. You know, raise an awful commotion when he finds these traps. It won't matter once we're clear out of town. I blow the whistle. We'll continue our adventure in just a moment. Boy, oh boy, that was a curved pitch of a pool any better. Hey kid, wouldn't you like to be in the ballpark and see how a star pitcher makes the ball curved right over home plate? Golly, everything about a major or minor league game is exciting. The crowds, the goodies. Get in on that excitement. Come out to the ball game as guests of a major or minor league team. Walk right through the gate free if you're 12 years or younger and have mom or pop with you or another paying a doubt. It is easy to get a free baseball ticket as going to the grocery store. Get it right inside packages of Quaker Puff Tweet and Quaker Puff Rice and Muffet Tread-A-Tweet. You get two free tickets inside Quaker Packo 10. Names of teams and dates are on every ticket. Golly, why wait? Get a free baseball ticket package of Quaker Puff Tweet-A-Rice, Muffet Tread-A-Tweet or Quaker Packo 10. If your store doesn't have the special packages yet, send a box out from the regular package to baseball box 5205 Chicago 77 Illinois. To continue, King was with the other dogs of the team behind the cafe when he heard the whistle of his master. He couldn't understand it. He thought Sergeant Preston was still inside the cafe. The whistle sounded from a shack, a hundred yards or so away. King had been taught to obey that whistle. After only a brief hesitation, he bounded through the snow toward the door of Curly Shacks. As he came close, the door swung open and the whistle sounded again inside the building. King saw a crate in the doorway. Instinct warned him of a trap, but it was too late to check his leaf. He knew instantly that something was wrong. Stop it. As he turned in the small space, a board dropped into a slot, blocked his exit. He got it. All right, now let's get out of here. That side of the crate. Take it out the back. That's all right. The team is hitched. You have the cash? Yes, right here. Where do we go? Down. The route through the canyon alongside the river. That's the shortest. Soft snow in the canyon might get stuck. And these tracks take the longer route. It's safer. Fails like ice won't show tracks of our sled. I grabbed that crate. It was not until some time later that Sergeant Fustin discovered the loss of his whistle. He mentioned it to the owner of the cafe. What do you suppose happened to the sergeant? I can't imagine. I'll investigate the loss of the whistle later. First, I want to talk to those men who told me about Martin and Curly. I saw Martin here a little while ago, but he left. That was before I knew you were checking up on his proposition. What did he live? Come with me. I'll show you. All right. And we'll go out the back door. From there I can point out the shack where Martin and Curly are living. It's an old place that's a prospect you'll build some time ago. Who's your dog, Sergeant? I don't know whether it's Sergeant. Hello, boys. Quiet down. Take it easy. Ting. Why are you off? I don't see your late dog. That was a lie. Ting. Ting. That shack right over yonder where Martin and Curly live. The door is open. Yes. Curious. I'll go see if they're there. During the walk across the hard-packed snow, Sergeant Preston was bothered by the loss of his whistle and the disappearance of King. But it didn't occur to him that the two were connected. He found both the front and back door of the cabin wide open. There was no sign of either Curly or Martin. Behind the shack, no tracks were visible on the icy snow. Meanwhile, Martin and Curly maintained a steady pace through gathering darkness. King had worked ceaselessly on the slack of the crate that impressive. The wood was gouged and splintered from his strong pranks. When the sled reached the rim of a canyon, Curly called a haul.  Why are we stopping? The dog has been looking on the crate. If he sees there's any chance he's getting free, he can take the crate off the sled and stab for the one side. All right. Everybody, don't get your fingers inside. Get it down at the edge of the wood beam. Right here. Now we can leave it here. By the time the dog gets free, we'll be miles away. And take chances on that dog. What are you going to do? When they kill them much. No, no. They'll shove the crate over the edge of the ravine. All rivers down below. Fast and deep. I don't take any kings.  I'll handle this. Curly, you did it. You all right, did it. The dog had killed me if he got the chance. Now while we're here, get rid of Preston's whistle. I don't want anyone to find you carrying the police whistle. Here it is. You toss it into the canyon. Now there's one more thing, Martin. Curly, what's the gun mean? About time I carried our money.  Cross that money to me. See here, Curly, if this is something... Oh, it's the money. There you are. That's better. I'm sorry, Martin, but there isn't enough cash for both of them. What are you going to do? Curly, Curly, wait. Don't shoot me. Curly picked up the money pouch, stepped on the runners of his sled, and shouted to the dog. Curly didn't suspect that King had escaped from his recent prisons. The crate weakened by the powerful fangs of the great dog had broken on impact with the water. King was free and swimming toward shore when Martin struck the water. King's instincts and training directed that he save human lives wherever possible. He knew that Martin's weak struggles were futile. He knew that the nearly unconscious man was drowned. The dog swam to Martin. His strong teeth found a grip on Martin's pocket. Then he set out for the ice-clothed shore. Martin hung desperately to a slender thread of consciousness. For the aid of King pulling on the shore of his pocket, he was able to crawl to the narrow strip of shore between the river's edge and the face of the sheer cliff. In the cliff, he saw a shallow cave that offered some protection and shelter. King left Martin and started upstream on the narrow beach at top speed. Sergeant Preston spent hours questioning the various people of Bald Rock without finding any trace of Martin or Curly or his great dog King. He was with Jim Harper and his daughter. They could tell him nothing about King, but they went into great detail about the plans of Martin. And here's the fact that he never gets Sergeant Preston. Doesn't the idea sound like a good word? Yeah, yes it does. There is gold in the mountains. It's there. Only trouble is it's low grade over. If the orc would be refined here, those mines could operate as a profit. I think it's a... I hear a dog. It's King. Boy, where in the world have you been, fella? You've all wet. What happened to you? What a beautiful dog. Yeah, boy. There he now. What's the trouble? He's tugging at your legs. I'll need to go somewhere, right? That's what he wants. Go ahead, King. I'm following. King led the way to the rest of the dog team, sleeping in the snow behind the cafe. Without awaiting orders, he routed the team and put them in line. Sergeant Preston asked no questions. He strapped on the harness, raced the tow line to his sled, knowing he could travel faster on the runners than he could by following King on foot. All right, King. I'm coming. I'm your king. We'll continue our adventure in just a moment. Golly, kid. Wait for a game for a lot of fun, aren't they? He smashed that ball right out of the ballpark. And that put our team ahead. Gee, I wouldn't miss seeing this game for anything. Say, are you fellas and girls getting in on the fun? Well, come on. Come out to the ballgame as guests of a major or minor league team. Get your free baseball tickets right inside packages of Quaker Puff Wheat, Quaker Puff Rice, or Muffet Shredded Wheat. And two free tickets are inside Quaker Packo 10. Names of teams and dates are on every ticket. If you are 12 years or younger, just bring mom or dad or another paying adult. And see major or minor league baseball games free. So rush to the grocery store. Get free baseball ticket packages of Quaker Puff Wheat or Rice, Muffet Shredded Wheat, or Quaker Packo 10. If your store doesn't have the special packages yet, send a box top and the regular package to baseball box 5205 Chicago 77 Illinois. Go to the ballgame free. See home run hitters in person. Now to continue. King followed his own back trail into the ravine and along the river bank. Instead of taking the course followed by Chloe's flair, which has led to the rim of the canyon. Suddenly Sergeant Preston saw a green of yellow flames and a moment later realized that it was a campfire burning in a shallow cave on the side of the canyon. Preston leaped on the runners and hurried to the side of Martin who laid close to the fire. One today. Yes, that's impressive. Yes, I might know who you are, but don't talk too much about that. I'm Martin. Huh? Who shot you? Curly. That dirty double crossing crook. I'll have to cut away your clothes. Look at that wound. Ah, how did you find me? My dog got me, huh? Doggy saved my life, pulled me out of the river in spite of what I did. What did you do? Curly and I, we knew you'd learn about our swindler. Figured we'd better get away while we had the chance. While Sergeant Preston dressed the wound, which was not serious, Martin told about the theft, the Mounties' whistles, and the capture of King and the attempted murder. I don't deserve to live after what I did. I've heard about you and Martin. You're supposed to be a top-notch engineer. Ah, I used to be good. I know my business, but got off on the wrong foot. Ah, your wound's best. Thanks.  He's heading for Connors Creek. You go straight on to the canyon. You'll save a lot of time. I hope you get that crook. I'll try. Come on, King. Oh! Light him up, boy, and line the path. Curly had stayed on the canyon's rim, where the trails were hard packed and would show no tracks. But Sergeant Preston, by going through the canyon, cut miles on the route. He didn't realize how close he was to Curly until King suddenly barked. Then the mouth he saw, vague shape in the darkness ahead. Get him, King! King was off like an arrow from a bow, streaking ahead of the team. Curly heard his snout, and burned. He saw the furry shape charging with leaps and bounds. No, it can't be! He hesitated, unable to believe that King was still alive. He went for his gun, but he'd waited too long. King was in the air in a final mighty leap. He thought there would be killer in the chest and venom crawling. And a ghost on the other side! All right, Curly. It's the end of your trail. I'll take over, King.  He's a ghost on it! No ghost, Curly, but that's not your fault. It's right hard enough to kill him. I'll get to your feet. I'll pick up Martin and go back to Bald Rocks. Martin! Yes, he's alive, and he'll be a witness for the crown against you. It was the following morning, when Sergeant Preston brought his prisoners into Bald Rock. Word of the swindle quickly spread throughout the community. Also the word that Sergeant Preston wanted everyone who had bought stock to assemble in the cafe. Jim Harper and his daughter and many others were there with their stocks jivided. Disappointment was stamped on their faces. When Sergeant Preston arrived, he was accompanied by Martin. A hush swept the assembly. All of you people would have thought it. You know that by this time. I have your money here intact. I can redeem all the stock certificates.  Martin had a plan, and it's a good one. He intended to swindle you and so did Curly. However, Martin has the know-how and there's cash enough to do exactly as he promised. Well, that's folks. Folks, I want a chance to redeem myself. I want to build a refinery and go ahead just as we planned. A few people can see your way clear to give me another chance. What about Curly? Curly's in jail and he'll stay there. He's wanted for a number of crimes in addition to the attempted murder of Martin. Martin, however, has made just one mistake and he regrets it. Do you think we should give him another chance? Yes, I do. Just to safeguard your interest, Jim, you handle the money. I'd rather have it that way. One of you men handle the money. Just let me work. Sounds fair enough. What do you say, boys? Then that settles. We'll build a refinery. It was some time after the affair in Bald Rock when Sergeant Preston reported to the inspector after a regular patrol. There was a curious expression on the inspector's face. You lost your official whistle in Bald Rock. Yes, sir. Try this one. What? Well, this looks like gold. It is, Sergeant. All but the card. That's made of silk. But that's my name engraved on it. That's right. It's made of the first gold to be refined in Bald Rock. It's a duplicate of our official whistle, except that it's made of gold. It's a gift to you and the people of Bald Rock. You were a little premature when you said that the Bald Rock situation had been concluded when you put Curly into jail. Yes, sir. I seemed to have been premature. I didn't suspect anything like this when the Bald Rock case was closed. We'll return in just a moment for the word about our next exciting adventure. There's roaring adventure on Mutual. Tales that will take your breath away and transport you into lands where danger is your constant companion. First, we take you far up into the barren Yukon territory of yesterday where icy winds and howling wolves are an opted drive a man wild and civilized ways are gone and never present lust for gold. Now let's go to another lawless world, the West of early frontier days, not so cold but which makes up for the freezing temperatures with trigger tense tempers where the gun is a man's lease on life. This is a country which abounds with cattle rustlers and where miles and miles go by before you see any signs of life. The West beautiful but wild, a land which cries out for the hand of the law. You will never lack for adventure on Mutual whether it freezes you with fear in the wild northwest territory or singes you with the accurate heat of the western plains. It's all on Mutual every week over most of these stations. The Masked Government strikes without warning and no one knows his identity. Unless Sergeant Preston can capture him before the gold shipment is sent out the Sergeant is almost certain to be heading into a deadly ambush. These Sergeant Preston of the Yukon Adventures are brought to you every Monday through Friday at this time by the Quaker Boats Company, makers of Quaker Pop Wheat and Quaker Pop Rice, the delicious cereals shot from guns. By special recording in cooperation with the Mutual Broadcasting System they are a copyrighted feature of Sergeant Preston of the Yukon Incorporated created by George W. Trenble, produced by Trenble Campbell Mule Incorporated and directed by Fred Flower Day. The part of Sergeant Preston is played by Paul Sutton. This is Jay Michael wishing you goodbye, good luck and good health from Quaker Pop Wheat and Quaker Pop Rice. So long. This is Mutual, radio network for all America.


So we have been discussing modeling of plate bending elements, so we'll continue with that, so just to recapitulate this is the problem that we are considering, we are considering plate element carrying transverse loads, so the plate undergoes bending in 2 direction and twisting, so this is what we have been studying for the last couple of classes. So we have considered 2 models, one model where we assume the plate to be thin, in which case the strain energy and kinetic energy expressions are of this form, where chi is the vector of these curvatures, dou square W by dou X square dou square W by dou Y square and dou square W by dou X dou Y, and so consequently if you look at the field variable that is present it is W, and then the order of highest derivative present in the Lagrangian is 2, because we are seeing here dou square W by dou X square, so the degrees of freedom should include the field variables and all its derivatives up to order 2-1 which is W dou W by dou X and dou W by dou Y, so at every node therefore there should be 3 degrees of freedom, so the interpolation functions must consist of complete polynomials of at least order 2, in a thick plate on the other hand the strain energy and kinetic energy are as shown here, in addition to this definition of chi and gamma we need to take into account, now we define in addition to W we also define the rotation of the plane that is normal to the middle plane after deformation the angle through which it rotates that we are considering there are theta X and theta Y and the field variables therefore if you look at it will be W, theta X and theta Y, and the highest derivative in the field variable is 1, therefore at every node we should have W, theta X and theta Y as the degrees of freedom, so this is the basis for formulating thick plate elements, so we started with thin plates, we assumed we considered a rectangular thin plate and there are 4 nodes, 4-noded rectangular element and each node there are 3 degrees of freedom therefore there should be 12 terms that is 12 generalized coordinates are needed in the representation of the field variable, so we use a 12-term expansion as shown here up to cubic all the terms in the Pascal triangle are included, the last 2 terms X cube Y and X Y cube are selected so as to retain geometric invariance, this element we showed that across the element boundaries theta Y won't be continuous therefore it is a non-conforming element. Then by considering the shape functions to be made up of products of beam shape functions cubic polynomials we developed a conforming rectangular element and in this model we showed that we need to include dou square W by dou X dou Y also as a degree of freedom, so as to ensure that if it is not done what happens is dou square W by dou X dou Y becomes 0 at all the nodes and consequently as the element size becomes small the plate will behave like there won't be any twist and to remedy that we introduced an additional degree of freedom. Then we consider thick rectangular plate elements and we showed that it is a conforming element and we used these polynomials, quadratics and we developed the stiffness and mass matrices and showed that this element is conforming. We have considered rectangular geometry, now we will consider triangular geometry, we will start by considering a thin triangular non-conforming element, we consider element with 3 degrees of freedom 1, 2, 3 as shown here triangular element and we need 3 degrees of freedom at every node therefore this element will have 9 degrees of freedom, so we need to include 9 terms in the representation for the displacement. So what we do is we select a local coordinate system where X axis is taken to coincide with the edge 1, 2 and this Y axis is in the plane of the plate orthogonal to this X axis and Z axis is out of plane, so this is local coordinates and we also have a global coordinates and we indicate the variables X theta X and theta Y, W theta X theta Y using upper case letters. So we have to select now 9 terms, so what we do is we start with 1, then X and Y then these 3 terms get selected, next when it comes to cubic terms to get a complete cubic we need to have 10 terms, but we need only 9 terms in our representation, so what is being done in this element is this X square Y and XY square are multiplied by a common generalized coordinate, so as we will see shortly that this will lead to, this will make the element a non-conforming element. So let's consider this, so W is represented as this polynomial and we can rewrite this by defining this row vector consisting of 1, XY, X square, etc. and the alpha is the vector of generalized coordinates alpha 1 to alpha 9 as shown here, we call this matrix as P of X, Y and this is written as P into X, Y, so this has 1 row and 9 columns and this is 9, this is 1 cross 9 and this is 9 cross 1. Now we need W theta X and theta Y, so I have dow W by dow Y, dow W by dow X we differentiating this I formulate this matrix. Now what we do is we use this equation at node 1 coordinate is 0, 0 and 2 X2, 0 and node X3, Y3 and determine alpha, so we have to first determine the shape functions, so this leads to equation of the form the element degrees of freedom, nodal degrees of freedom in terms of these generalized coordinates is related to each other through this matrix A, which is a function of nodal coordinates, so alpha can be obtained as inverse of this, so this determines the relationship between generalized coordinates and the nodal degrees of freedom, so we can write W as P alpha becomes now PAE inverse WE, now a comment needs to be made at this juncture this matrix AE becomes singular whenever this condition is satisfied, X2-2, X3-Y3 equal to 0, so elements which have the geometric property satisfying this condition the A matrix will become singular, so if you encounter this situation you have to move the nodes, you remesh and move the nodes, so you have to check that. Now the evaluation of, now let us consider what happens to this along Y equal to 0, so you consider this equation along Y equal to 0, so I get this equation and it turns out that W will be a cubic polynomial, theta X will be a quadratic, theta Y also is quadratic and we can show that, that W and theta Y depends upon W1, theta Y1, W2 and theta 2, so which is the edge that Y equal to 0 represents, so it is along edge 1, 2, so this is 0, 0 and 0, X2, so we have this equation, now along edge 1, 2 the nodes are 1 and 2, so W and theta Y are depends upon the nodal degrees of freedom at 1 and 2, so consequently we can show that W and theta Y will be continuous across element boundaries, but if you look at theta X you can show that it depends on nodal values at node 3 also, so therefore it means that we cannot achieve continuity of theta X across element edges, and therefore this element is a non-conforming element. Now we can, I leave it as a question is the geometric invariance property satisfied in this element, you can think about that, notwithstanding this limitation as we have been doing earlier we will proceed with the formulation, so W now is given by PAE inverse WE, the expression for kinetic energy is half area integral rho HW dot square your volume element, now for W dot I will put this, so it will be W dot transpose W dot if you write in that manner we get the expression for kinetic energy to be this, and the term inside this bracket we call it as the element mass matrix in the local coordinate system, you see we should keep track of the coordinate system also, this is the mass matrix in the local coordinate system, the integrals that appear here are product of polynomials so they can be evaluated in closed form, so we don't need any special tools to evaluate this it can be evaluated exactly or a suitable Gauss quadrature can also be used. Now how about strain energy, again let's start with W equal to PAE inverse WE, and strain energy is given by this HQ by 12 chi transport D chi DA, and this KE inverse, KE bar which is a element stiffness matrix in the local coordinates is given by this, this B bar is the strain matrix you can show that it is given by this matrix, so you have to differentiate the shape function through the matrix of partial derivatives that define strain displacement relations, so again these elements of this matrix can be evaluated exactly in this element, so there is no problem, so KE can be evaluated, so what we have done right now is we have analyzed this element in its local coordinate system, so for assembling process to be implemented we have shown we should transform it to global coordinates, so how do we do that? So these are the structural matrices that we have derived till now in the local coordinate system, this is the element stiffness matrix a bar indicates that it is in local coordinates this is element mass matrix. Now transformation to global coordinate system you can see here the degree of freedom W theta X, theta Y in the local coordinates can be shown to be related to the values in the global coordinate system through this transformation matrix, this we have discussed earlier on many occasions so we will not get into the details, so we get this, I call this matrix as L2, so it is L2 into the nodal values in global coordinates, so equipped with this now we can go ahead this is our L2 into this, so WE is the collection of all nodal degrees of freedom 9 cross 1 in local coordinates and this is similar quantity in global coordinates, so this is the transformation matrix 9 by 9 and this is REW, so this is WET that is this transpose of that this is the local degrees of freedom, degrees of freedom in the local coordinate system and these are the degrees of freedom in global coordinate system. So now TE which is the elements kinetic energy in the global coordinate system is you can reduce it to be this, where M bar E is the local mass matrix in the local coordinate system, so this is the element mass matrix, this is the element stiffness matrix in the global coordinate system, before we start discussion on thick plates and other issues we will revert back to a basic notion that in dealing with triangular geometries we can introduce instead of Cartesian coordinate system we can also follow what is known as area coordinate system, so to explain that you consider this triangle 1, 2, 3 and we for any point within the domain I construct these 3 triangles and the triangle opposing node 1 is called A1, this is now we consider the point P this point is said to have the area coordinate L1, L2, L3 where L1 is A1 by A, L2 is A2 by A, L3 is A3 by A, clearly total area is A1 plus A2 plus A3, which is equal to A, now therefore if you add L1 plus L2 plus L3 it will be 1, so now you consider this node 1, suppose this point P coincides with this node 1 then clearly A1 will be the entire area of this triangle, so the coordinate at the vertices this coordinate will be 1, 0, 0, so if I come here it will be 0, 1, 0, so similarly it is 0, 0, 1, so vertices are having this property, so this is advantageous in representing triangular geometry even in 3 dimensions, we can also define L1 which is the area coordinate at node 1 to be the distance of point P to the side 2, 3, this distance divided by distance from 1 to side 2, 3, so that means you find the distance of 1, 2, this line 2, 3 and this to this, that ratio is also equal to L1, so equation of side 2, 3 is L1 equal to 0, right, on this edge L1 is 0, so if you draw a line parallel to this line it will be a line having L1 equal to constant, so let XI, YI, I equal to 1, 2, 3 be the coordinates of vertices 1, 2, 3 in Cartesian coordinate system, we can show that any point in the domain with coordinates L1, L2, L3 is the X coordinate can be obtained by using this formula and Y can be obtained using this formula, so now we have L1 plus L2 plus L3 equal to 1 and these two relations, so we can solve for L1, L2, L3 in terms of X and Y by using those three equations which are put together here, so this matrix I call it as A, A transpose and this is the vector of L1, L2, L3, so from this the relationship between area coordinates and Cartesian coordinates can be computed and with A inverse being given by this. Now it turns out that the formulary for finding L1, L2, L3 are as given here, now if you recall when we discuss triangular element the shape functions were exactly the same as this, so Ni and Li are identical for this case, an useful result which will be helpful in evaluating elements of mass and stiffness matrices is shown here, integral over area of L1 to the power of M, L2 to the power of N, L3 to the power of P is given by this, so with 0 factorial being 1, okay, so with 0 you can compute by putting MN or P equal to 0 you can you know get various combinations, so now equipped with this basic notion we will now consider thick triangular plate, now in a thick plate the expression for strain energy and kinetic energy already we have discussed they are given by these expressions and the field variables here will be W theta X and theta Y and the highest order of the derivative is 1, therefore at any node the degree of freedom, the field variables are W theta X, theta Y, highest order of the field variable is 1, therefore degrees of freedom are W theta X, theta Y at the nodes, so I need now to represent any of these field variables say for example W, there are 3 nodes I need a 3 term expansion, so I write it as Li Wi where Li are the functions that we discussed a while before, so this is theta X, this is theta Y, so now we will assemble these 3 field variables and put it in a single equation, so W theta X, theta Y is given by this. Now W E is the element nodal degrees of freedom at the 3 nodes 1, 2, 3 which are W 1, theta X 1, theta Y 1 and similar quantities at the other 2 nodes, so this N we can show that using these representations you can show that N will be having this form, we can go to the mass matrix and stiffness matrix they can be evaluated exactly, I will not get into all the details, once you evaluate the mass matrix you can evaluate it as sum of 2 square matrices with M1 being given by this and M2 given by this. Now how about strain energy, so we have this representation W is N into W E and chi is this, so we can using these relations we can derive the strain the matrix B for flexure and for shear separately, let's consider flexure first this is this and this is a constitutive law which relates sigma X X, sigma Y Y and sigma XY to the corresponding strains and the stiffness matrix due to flexure is given by this, now similarly the shear by considering gamma is this we compute the B matrix associated with shear and this is given by this, so it has 2 rows and 8 columns, so this can be used to construct a contribution to the stiffness matrix from shearing action, so based on that there is a dispute details of evaluation the KS is a contribution to the element stiffness matrix from shear components and this itself is determined in terms of these quantities which are shown here, okay, so the various elements are shown here it requires some manipulation, so if you do that you will get this. Now KE after evaluating this contribution is taken as sum of flexure contribution and shear contribution, so then the constant force suppose the element is carrying constant force the equivalent nodal forces can be evaluated as shown here using principle of virtual void, so we can show that this element a conforming element as you can see the variation of the field variables along the edges or straight lines, so it will ensure the required continuity conditions to be satisfied by the all the 3 variables, that was for a thick element, thick triangular element. Now the thin triangular element that we formulated was nonconforming, so is there any way we can develop a thin triangular conforming element, now the idea here is the way we develop this is we will ensure that normal slope along the edges vary linearly, it was the normal slope along the edge which was not satisfying the required continuity conditions in the earlier model, so we want to address that by doing this, so what we do is we consider this triangle element 1, 2, 3, then introduce another node within the element at the centroid for example and construct 3 elements written as 1, 2, 3, so if you consider element 1 we will analyze these 3 elements separately, for element 1 there will be a global coordinate system and for each one of these element there will be a local coordinate system, so this is as shown here, this X axis is taken to be parallel to edge 2, 3, so that this Y axis is normal to the line edge 2, 3, so the idea here is we divide this plate into, this triangular plate into, plate element into 3 sub triangles, 1, 1, 2, 3, the numbering is opposing node 1 I have element 1, opposing node 3 I have element 3 and similarly opposing node 2 I have element 2. So if you now consider these 3 elements separately, the basic idea is we will perform the analysis of these 3 elements separately and establish compatibility conditions, so obviously the nodal degrees of freedom at 1, 2 and 3 must match, so these 3 must be same as this 3, this 1 must be same as this 1, 2 must be same as this, similarly O, 0 at the 3 places should be the same. Now each element will have 9 degrees of freedom, please note that 4 and 6 are not nodes, they are certain intermediate points, the nodes are 1, 0 and 3 here and 1, 0 and 2 here and 2, 0 and 3 here, so each one will have 9 degrees of freedom, so when we assemble this there will be 27 degrees of freedom. Now by establishing the compatibility conditions at 1, 2, 3 and at 0 we will be able to derive 15 equations, now from 27 equations we should arrive at 9 equations, so 18 equations need to be eliminated, 15 are obtained by considering compatibility at 1, 2, 3 and 0, the remaining 3 are obtained by demanding that the normal slope along edge 0, 1 at 0.4 matches with the normal slope along edge 0, 1 at 4 for element 3 and 2, and similarly the normal slope at 5 matches for elements 1 and 3, and normal slope at 6 matches for elements 1 and 2, so that 18 equations will derive and eliminate from the 27 degrees of freedom, 18 degrees of freedom and get a 9 by 9 stiffness and mass matrices. Now one of the detail, matter of detail that we need to consider is when we study each of these elements we will be considering a local coordinate system which is specific to each of the individuals, and whatever answer we get for each of the element before we can establish this compatibility we should transform them to the global coordinate system, then only we will be able to do this. So now we will consider one of these elements, so the element 1 which has edges 0, 2, 3 and this is X axis and this is the Y axis. Now what we do is we need 9 terms in our expansion, so here what we do is we take, if we go back to the Pascal's triangle we need 9 terms, so 1, 2, 3, 4, 5, 6, then what we do is 7, 8 and 9, we will eliminate, we will not include this term, okay, Y is that is done, so we have to see that. The term we include is 1 X, Y, X square, XY, Y square, X cube, XY square and Y cube, the X square Y term is not included, we will come to the reason for that. We can now rewrite this in the form P into alpha where P is this matrix of these functions, and alpha is the vector of these 9 generalized coordinates. Now W is given by this I want to compute and now dow W by dow Y, this is given by this function, so along edge 2, 3, see you should see the way the coordinate system is configured, we are having X axis along, X axis here is parallel to edge 2, 3, so Y equal to constant will be lines parallel to this edge, so if you consider Y equal to constant we will get wherever there is Y I will get this which is dow W by dow Y, I am looking at the normal slope to the edge, so I get this as a linear function, so dow W by dow Y varies linearly in X, so that ensures that the continuity conditions on normal slope will be satisfied, right, in a linear thing there will be 2 unknowns and we have 2 nodes, so that will depend on that so it is quite satisfying. Now that is the reason why we are taking function in this form, so the strategy is to ensure that the normal slope varies linearly along the edge, which enables us to achieve conformity, now we will now consider elements 1 by 1, for the first element I will now add a superscript W1 is given by this, kinetic energy is given by this, and mass matrix we evaluate using this, this can be done exactly, in an exact manner because these are integrants are simple polynomials we can evaluate that. Now we can repeat this for the other 2 elements also in its own local coordinates, okay, each time I get mass matrix the bar indicates the mass matrix in its own local coordinates, now so the element on the other hand the element kinetic energy is given by this, now this M bar I will simply assemble in this form I will have to put now constraints before I do that I am simply defining M bar in this manner, this alpha, alpha is the generalized coordinates for each element there are 9 of them, so this will be a 27 cross 1 matrix and this will be a 27 cross 27 matrix, each one being a 3 cross 9 matrix. So now here for the element level alpha has 27 elements, the element 1, 2, 3 what I mean is the element that is a finite element 0, 2, 3 not 1, 2, 3 itself would have 9 degrees of freedom, we need to apply 18 constraints to ensure internal compatibility between the triangles, this needs to be done such that the resulting degrees of freedom would be made up of nodal displacements at nodes 1, 2, and 3, okay, so that is how we have first that means we are now talking in the language of alpha that has to be translated into the language of nodal degrees of freedom and the elimination should be done such that in the end what remains are the nodal degrees of freedom at nodes 1, 2, and 3. So now for subtrangle 1 the relationship between nodal degrees of freedom and alphas are given by this, that means for this is at node 2 that is at X2, Y2 in the local coordinate system we have W theta X, theta Y at X2, Y2 is given as W bar of 1 at node 2 I write in this form, where this A bar 1 subscript 2 is this matrix. In the global coordinate system now we have to use the transformation matrix L2 that we just now saw in the development of the previous element we need not get into that again the same transformation matrix is used and we get W for the first element at node 2 is related to the nodal degrees of freedom through this matrix for the first element, so where L2 of 1 is the coordinate transformation matrix for element 1. Now at the common nodes of the 3 triangles, W3 at 1 must be W2 of 1, so that is W3 viewed from element 1 must be W2 of this, okay, that is 1. So similarly I get these conditions by demanding at 1, 2, 3 the nodes 1, 2, 3 viewed from elements 1, 2, 3 there is a compatibility of deformation, and similarly at 0 there should be elemental compatibility and this would force these vectors to be equal, now this provides 15 constraint equations, so from 27 we can eliminate 15, we are still we need as I already said 3 more need to be eliminated, so compatibility of normal slopes along the interior edges of the 3 sub triangles provides the additional 3 equations, these are established by equating the normal slope at midpoints 4, 5, and 6, so now consider sub triangle 1 and midpoint 5, let S be the direction from 0 to the node 2, so dow W by dow N for the first element evaluated at node 5, we can show that this is given in terms of this transformation, so this for W1 of 5 I can use in terms of this A bar matrix that we have shown just now in terms of generalized coordinates I get this as this, so this dow W by dow N for element 1 at node 5 is given by this, now similar quantities can be computed for other 2 elements also, and at 1, 2, 3 for elements 1, 2, 3 at nodes 4, 5, 6, see I am talking about nodes 4, 5, and 6 and the normal slopes viewed from element 2, element 3 this way and this way and this way and this way, so this slope, this slope and this slope, now by equating that we get 3 more constant equations, so now we have to assemble all of this and achieve the reduction from 27 degrees of freedom to 9 degrees of freedom, so we will now be left with 9 independent values in alpha 1, alpha 2, alpha 3, out of this 27 variables 9 will be left, so these can be determined in terms of nodal degrees of freedom by using the relations W for 1, 2, 3 this is for the element 1, 2, 3 whereas these are for the subt triangles, so these numbering equivalence is needed, so once that is done we can assemble now all the required information W at node 1, W at node 2, W at node 3 for the triangular element 1, 2, 3 in which we are primarily interested is related to these alphas through these matrices, so we are now basically putting all these equations together, this, this and these equations, so they assume this somewhat involved form it is straight forward you have to pay attention and you know get to the details, if you sit with pen and paper you will be able to follow this, now after getting this relation we partition this matrix as shown through these red lines here and rewrite these set of equations in this form, from this we can eliminate alpha of 0 and alpha of 0 is a combination of this alpha 2 and alpha 3, that we can write in terms of alpha 1 through this relation, so this is where the elimination is now taking place and consequently I get alpha 0 to be this and WE therefore will be from the first equation A11 alpha 1 plus A10 alpha 0, for alpha 0 I will use a second equation I get this, so the element degrees of freedom and the alphas are now related through this, W is related to this through this equation, so this is this alpha 1 therefore in terms of nodal degrees of freedom is given by this, so going back to the transformation that relates alphas to WE we derive this matrix that relates these two quantities and that is the one that we are looking for, so that I call it as A double bar WE, so now when I evaluate the mass matrix I have to use this transformation, okay, essentially we are eliminating the, enforcing those compatibility relations in the nodal degrees of freedom and the slopes normal to the edges and assembling, correctly assembling all the relations and this is how we get the mass matrix. How about stiffness matrix, the same transformation works, so KE is given by A double bar transpose into this matrix into this and the elements of this can be evaluated for the shape functions that we have used that is given by this where this strain matrix B is can be shown to be given by this. Now similarly using the virtual work principle and we can again show that the equivalent nodal forces are given by this, so this I leave it as an exercise, so the main idea here is basically captured in this view graph, so what we are doing is this element we are dividing into three sub triangles as shown here and analyzing these three sub-triangles separately and while analyzing each of these triangles we are enforcing, we are making a particular choice for this representation so that the slope Dow W by Dow Y along the edges will be linear function, so that is one important issue, and then what we do is when we analyze these three triangles separately there will be 27 degrees of freedom and by enforcing compatibility at nodes 1, 3, 0 among these elements we get 18 equations and 15 equations and we generate three more equations by considering equivalence of normal slope at 0.4 between elements 3 and 4, at 0.5 between elements 3 and 1 and 3, and at 0.6 between elements 1 and 2, so that gives 18 equations and the remaining manipulations are aimed towards implementing this elimination process and deriving the correct mass stiffness, mass and stiffness matrices. So this is a three-noded triangular conforming element, so in summary we have now developed elements for rectangular geometry and for triangular geometry, we have considered thin plate and thick plate, and for each one we have developed a non-conforming element and a conforming element, so in the rectangular geometry we started by taking four-noded rectangle and therefore the element had 12 degrees of freedom and we selected this as the trial function and we showed that here the normal slopes along the edges won't match therefore this becomes a non-conforming element. Now to get a conforming thin rectangular element this is for thin, the next strategy we used was we constructed the shape functions by as products of beam trial functions, there as I pointed out at the beginning of the lecture there was a need to introduce an additional degree of freedom namely dou square W by dou X dou Y at every node, so that although the element becomes conforming because of that introduction of that additional degree of freedom the use of this element in conjunction with other structural elements becomes unwieldy, so that is one problem with this element, but as I already, as I happen to mention in the previous class that can be eliminated by approximating dou square W dou X dou Y in terms of theta X and theta Y, but if you do that the element again becomes a non-conforming element. Now when we came to thick rectangular conforming elements the field variables were in the variational equation W theta X and theta Y highest derivative was 1, so in a rectangular element with 4 nodes these were the representation that we used where these trial functions were quadratic they had cross terms XI and eta, so this element we developed and showed that it is a conforming element. Now in a thin triangular non-conforming element we started by considering this trial function, actually a complete cubic polynomial would have 10 terms but we need only 9 terms, so what we did was we combined this X square Y and XY square terms and associated with those terms a common generalized coordinate, this again had this problem of being non-conforming because of incompatibility of normal slope along edges. Next the thick triangular conforming element we use area coordinate system to represent this like in rectangular conforming element this was also shown to be a conforming element. Finally we developed a thin triangular conforming element by enforcing linear variation of normal slope along edges and dividing the triangular element into 3 subtriangles and analyzing them separately and enforcing compatibility of nodal deformations and normal slope at the midpoints of the edges of the subtriangles, so this is what we have done. Now then way forward now is we have to consider problems of stiffened plates, so these arise in bridge decks, so this is the slab and these are the girders, and the girders can, so if we take a planar view the girders, cross girders can be like this and the longitudinal girders can be like this, so this rectangular element itself is a plate element, so we can see that the plate element gets stiffened by the presence of these beams, so the centroidal axis of the beam will be here, the midplane of the slab will be here, so the deformation of the beam and slab should conform to each other, so when we are developing for example a thin plate theory we will have W as a variable here, and in a beam equation we will have V, and this V and W we should ensure that they are constrained by the fact that the way the beam deforms along this line is compatible with the way W deforms, so we will see this in one of the future classes. Next what we will consider is this plate bending element we have been considering only the action due to transverse loads, now in problems of shells there can be simultaneous presence of axial loads as well as transverse loads, so the shell structures the element need not be flat initially, that is one of the assumptions if you recall we made when we were dealing with plates, but if we agree that a curved surface can be represented by using flat flat elements like this we can still use this theory that we have developed, these are called facet elements, so there the issue would be we should consider the in plane action in conjunction with the transverse action, so assuming that the deformations resulting from each one of them is small they can be treated separately, and we can consider this membrane action and the so called bending action, plate action separately, and we can analyze this using plane stress model and this using one of the plate bending models that we have discussed. Now obviously there will be many questions about conformity and issues like that, so when we combine we have to ensure that the required desirable features are imparted into the built up element, so we combine the plane stress element where we have along X and Y, U and V are the field variables, and in plate bending we have for example in the thin plate theory we have W, theta X and theta Y we deal with that. So there will be additional questions on treatment of this theta Z it's called drilling degree of freedom that needs to be studied separately, so we will try to see how to combine these two for flat elements and maybe if time permits we will also consider curved elements subsequently. So in the next class what we will do is we will try to work out few numerical examples, so certain class of problems like rectangular plates which are all round simply supported have exact solutions, so we can check the accuracy of some of these formulations against the exact solutions, and then we can see the influence of boundaries and so on and so forth, so we can solve a set of examples to illustrate the various features of this triangular and rectangular elements, and I will also develop the theory for the stiffen plates and illustrate them with some examples, so with that our discussion on plate and shell elements would be completed, so with that we will conclude the present lecture.


The study aims to investigate the relationship between physical activity in healthy community dwelling older adults and outcomes related to functional limitations, disability, or loss of independence. The study found that greater physical activity of an aerobic nature was associated with higher functional status, while moderate and high levels of physical activity were effective in reducing the risk of functional limitations or disability. Exercise training interventions also showed improvement in physiological and functional measures, suggesting a long-term reduction in incidence of mobility disability. The study suggests that regular aerobic activity and short-term exercise programs may be effective in maintaining functional independence in older age, with moderate to higher levels of activity being effective. However, a precise characterization of an effective physical activity dose is difficult. This article was authored by Patterson Donald H. and Warburton Darren E.R. We are article.tv, links in the description below.


What's up everybody, Jason here for jazzymskatespricks.com. We're going away with the last four flawless random number of block spots Away in this 2020 Panini Mosaic football one box blaster break random teams number three So again the way this works guys is first everybody gets a random team 32 spots old and then it fell random team We just ship the hits out of the blaster box number no veteran common ship Then at the end of the break will take out 32 customer names and more randomizer again in a separate dice for the randomizer And the top four out of the 32 will win a spot in the high-end pick a team number two flawless college football random number block So good luck guys, let's do the break first. Let's roll it and we got ourselves a six and a sig the full 12 times one two three four five six seven eight nine ten eleven Dave down to king. All right. Come on, bro Geez, I don't know what's taking so long anyway There it is 12 times Here as well one two three four five six seven eight nine ten eleven twelve And again stick with what you got guys No trace just a quick little blaster, but let me show you the the bigger teams of course to be chasing here So We got jayce with the chargers Where's everybody else bangles alex? miami, where's miami? steve lock Little bit quarterback teams and of course there's a lot of a lot of really good teams, but Just those three really quick All right, now let me just copy this right here Into the sheets. All right, so stick with what you got. Let's print out this sheet Chase Claypool NFL debut a rookie and Tony Gibson green Patrick Queen rookie Sound Arnold green Touchdown matches Antonio Or sorry Tony Gonzalez to the ridgewater green Henry rugs rookie Tom Brady base and a Len Dawson prism silver All right, sweet Now let's see who's gonna get into the r&b guys. Good luck Let's roll the dice and we got ourselves a one out of four five times Good luck five times top four get in One two three four five Boom top four mark Dario Foud and Michael Hansen So there you go after five times Top four get in congratulations guys now coming up next is this video here randomizer for the r&b For the bangles cowboys packers to use chargers dolphins 49ers and then the break itself pretty to number two Pretty sure you guys jaskiescasebreaks.com


So, in the news now in all the parts of Africa, a mission ECOS will hold on, or will on Thursday rather, visit Guinea, which has been dripped by a military coup, according to a communique issued late Wednesday. The communique was issued after a virtual meeting of the organization. The meeting was convened by ECOS Chairman Nanna Kufo-Addo to discuss the political developments in Guinea. The communique, he said, the visit of ECOS mission would be led by Ghanaian Foreign Minister Shelly Ayoko Bochue. There will also be representatives from Nigeria, Burkina Faso and the ECOS Commission. The bloc also decided to suspend the membership of Guinea and called for the immediate restoration of civil rule in the country. The heads of states expressed their strong consent. As I told you and required President Al-Fakande's physical integrity to be respected, the same for all people arrested and immediate release of President Al-Fakande and all people arrested. A high level mission should be sent by ECOS to Guinea as of tomorrow in order to speak with the new authorities. And after this mission, ECOS should be able to re-examine their positions. But for now, ECOS has decided to suspend Guinea from all the decision-making instances of ECOS. We ask that this decision be in dust by the African Union and the United Nations.


Welcome back. Hi. Hello. I posted a video on Wednesday. I basically returned to YouTube. I took a two week break and the very simple reason being one, depressed, two, busy, three, moved flat and there was going to be a moving vlog coming out soon and I started on Lomotrogene. Now I was on 25 milligrams and today is the first day that I'm taking 50 and I want to talk bigger today. So to anyone who didn't see my last life update video, I spoke to my consultant and my consultant has started me on Lomotrogene and we are decreasing the puttyping down to 150 at night. I'm taking the Lomotrogene up to 100 in the morning. Basically I stopped my morning puttyping and I'm currently still on 200 milligrams a night of puttyping. That's going to come down in the next two weeks to 150 and then my Lomotrogene dose is going up to 100. So we do this over a set period of six weeks which is what my consultant said. So I'm on two weeks of 25, two weeks of 50 and then I'm on 100 until my next week to my consultant which I believe is the sixth of eight weeks of all. This is Lomotrogene. Start in these now. Now this is my life's way from where and I'm actually terrified of it. So last week I came out in a rash. I have only had my hamster for two weeks and this is important to the story. I'm allergic to hamsters and I'm allergic to sawdust. This is Nibbles. He's currently enjoying spinning a Nibble. Nibbles, Nibbles, Nibbles. But I also started Lomotrogene at the same time and as most of you probably know or you can find by simply typing in Lomotrogene to Google, the Lomotrogene rash is something and a few months huge rash I panicked for my GP. My GP took me off Lomotrogene for a few days to see if anti-estimulants could help get rid of it and that's how we determine whether it was the Lomotrogene or my allergen was the allergen. So I got started back on Lomotrogene and things have been okay. I did say I'm scared about increasing the dose because from what? When the dose gets inquiry that's when the rash shows and I am already overly paranoid anyway.  Like I've literally stopped hacking over it and I'm looking at the big picture with it. I've noticed you know when you start any psychiatric medication it takes six to eight weeks for it to actually start to do anything. So I'm not actually expecting any changes as of yet and wait, I'm expecting that around week seven, week eight. I can tell now that it hasn't done anything yet. I know that because I'm really depressed recently and I still am. So like I'm actually, I have been like struggling to actually do anything. The fact that this flat is about half unpacked, I think that shows where I'm at. There's not really a lot to say about starting Lomotrogene because this is week three for me, but I am definitely anxious about it. But I'm hoping, like I said, looking at the big picture that it will have the positive results that it has had on countless other people. I asked on Twitter and a lot of you guys said it's really great and it really helps and anyone who's followed Lomotrogene for a long time knows that I struggle with the cotypian and the weight gain associated with it. I can safely say that stopping the molyndo has 100% made me a lot less hungry, like I'm not as bingey, which is good. When I bingey, I bingey. And overall my thoughts on Lomotrogene, based on what I've read, it is a very helpful medication and it's not got as many, it's not sedating, which I said there's a lot, a lot of my medications are very much so, especially my nightmares. I do have insomnia and I literally cannot sleep. I could stay awake for a few days and I'd really crash. And that's why I was doing early this year, which is why I was in and out of hospital and yeah, it just wasn't good, it wasn't healthy. So I can say that the fact that I do take medication at night, that makes me really sleepy is 100% help with my mental health, like I'm actually sleeping at night and I'm waking up in the morning, which is, and Lomotrogene, as my castle said, it's going to make me feel more alert. I'm not entirely sure it has yet, but I do definitely feel quite alert, but I think that's because I'm anxious about medication. But yeah, that's my experience so far. I haven't had any, really, I've had a ledger action in my hamster, but apart from that, I scored. I don't really have much to say about it.  I didn't know if it was the hamster, I was wrapped up with the medication, so it was my G.P. and it was the hamster. Thank you, Nibbles. Love my little Nibbles. Nibble, Nibble. You like stuff like your carpet, do you? Just floofs on it. Don't you put them on it all morning. Don't. You like stuff like your carpet. You're doing menace in that wheel though. Squeaky, squeaky, squeaky, squeaky. But yeah, that's my experience so far. I will be doing another one of these when I am on 100 milligrams to talk about that. That will be in a few weeks time. The next few days are going to be videos that I did plan on making when I got my two week break, but I never actually made. They are all mental health based because that's what I do. And there is going to be a moving vlog at some point when I have the time to sit and go through my phone, all my SD cards, my computer, everything. Like I've got so much for it, it's ridiculous. If you're new, subscribe and if you have any questions or video requests or anything you want to know or even just say hi, comment down below, make sure you leave a thumbs up and I will see you guys tomorrow. Sit on the notification bell and tell everyone about the video and also if you want to support the channel a little bit more, head over to Patreon and make a pledge. Thank you to the people who are going to be on the screen after this and I will see you guys soon with another video. Bye!


Occasionally when you're reading the book you stumble upon a line or a paragraph that we really resonate with One that plays through your head throughout the day that you always go back to reflect on now recently I finished Eckhart Tolle's book and New Earth this one here, which I think is pretty good and There was one line that I Had to share for this video because it really highlights the stuff we're going to be talking about so I quote The great arises out of small things that are on it and careful Everybody's life really consists of small things Greatness is a mental abstraction in the favorite fantasy of the ego The paradox is that the foundation for greatness is honoring the small things of the present moment instead of pursuing the idea of greatness Now what does that mean? I'm sure we've all heard about it before Practice makes perfect Malcolm Gladwell talks about how you require or you need 10,000 hours of consistent practice of Consistent effort to become a master of your craft This is the accepted amount by many experts, but many people believe you need more than 10,000 hours You heard of the book of mastery Success is not a linear path It has ups and downs. It's got these weird trials and tribulations that you have to go through That's why it takes time Because it's not linear. You don't just grow at the same rate. It always changes But what people don't understand about success is that it's not just an event It's a process doesn't just happen And this is partly because the media and how the media manipulates people into thinking, you know Shit just happens to lucky people assess few people things just magically happen, which is a great falsehood It's a fallacy Things don't just happen is always the background events that precede them that you don't usually see right Think of when they're building a skyscraper like the one in Dubai You don't see them building it up. You just hear about the news about when it's finished They say the tallest skyscraper in the world has just been built boom. Look at that I just came out nowhere Now, but you didn't see the previous four years of consistent effort that was required over the five years wherever long it took Just like someone in the gym when you see them looking big and juicy and swole You're like, oh, they probably just were born like that or they hit the gym for one year But no, they started when they were 11 It always takes some extended amount of time to really be a master of what you do I like to show the guys a story of me I used to be a skateboarder, right? I skated for five years and when I started off It was actually pretty difficult. It took me six weeks to learn the initial most basic fundamental skateboard We were just cold and all the just kind of like this bam You pretty much have the board going to the air with you. It's just like a jump Took another six weeks to learn how to pop shove it Another maybe 10 weeks to learn how kick flip It just took a long time to get the fundamental baseline set up But once you have the foundation you can build on those tricks and do some more complicated tricks a very heel flip Tray flip 360 switch 360 flip, etc. You just kept going on and going on but it was through consistent effort I used to skateboard every single day for hours and I did that for five years after five years I still wasn't great. I was decent, but I wasn't great That's the same with anything else in life. I'm sure if you played guitar for an extended mouth Yes, you know about this You know about your friends that try learn how to play guitar They think they can get it in three weeks or four weeks through watching a few YouTube videos Doesn't happen that way. You have to honor the process. You have to enjoy the daily grind Forget about the end outcome It will happen if you are not the daily grind the daily grind is what's important It's what really matters is or that you have control over Focus on your circle of influence some things of course you won't have control over but the things you can do is what you need to focus on It's kind of like how people always say things like how do you eat an elephant or something like that?  One bite at a time The journey of a hundred miles or was that thousand miles starts with a single step We hear it over and over again, but how many of us actually have it embedded in our heads How many of us actually adhere to the philosophies? Not many You need to know this stuff and to buy in if you want to be great Enjoy the process and you will inevitably reach the end outcome Hope you guys enjoyed that video and be great