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Could someone please help me with writing the MATLAB code for this problem? there is no way to upload text files (for the nodes lists)
Could someone please help me with writing the MATLAB code for this problem? there is no way to upload text files (for the nodes lists) on Chegg, as far as i am aware. If you know of a way to do this, please let me know.
Stress Concentration in a Plate with 2D Finite Element Triangles A plate in plane-stress has a 0.0lmeter diameter hole in it. In this homework, you wil be using 2D finite elements to calculate the maximum | stress in the plate (where x is 'to-the- right' and y s up'). The plate is 0.05meters wide and 0.05meters tall, as shown in the below picture. The plate has a thickness of 0.00lmeters (into the paper). The picture also shows the simple triangle-mesh that you will be using. The plate is loaded with a uniform horizontal pressure/traction (to-the-right) on its right edge with a total load of 1000N The boundary condition is 0 on the left edge of the plate. The plate is made of steel with E-210x10N/m2 and Poisson's ratio v#0.3 You have been provided with the list of 5314 triangle elements and the associated list of 2773 nodes in the below ASCII text files: elems.out nodes.out You have also been provided a list of the left-edge nodes in the below ASCII file leftlist.out and a list of the right-edge nodes in the below ASCII file: rightlist.out Use the 3node triangle-element (Constant-Strain-Triangle [CST] to find the maximum stress in the plate. Compare it to the theoretical value from Figure A-15-1 below, which of 6.25x107 N/m2 . (You will find the FEM agrees within 0.6% even with these gives a simple CST's.) For the nodal-loads, it is adequate to simply apply the total 1000N equally to each of the nodes on the right edge (the nodes in file rightlist.out), i.e., 1000/51 Newtons to each node. The associated reduced-stiffness matrix solves in bseconds or 2.35seconds in MATLAB on my desk PC, e.g., depending on what command you use: >> tic; disp-reduced-inv( Kreduced) * n0dalload reduced Elapsed time is 6.082989 seconds. >tic; disp reduced-K_ reduced nodal load reduced, toc Elapsed time is 2.356513 seconds. even using plain dense computations and no sparsity-exploitation. Make sure your computer will store about a 5494x5494 matrix of floating-point values before you begin. A 5500x5500 matrix in double precision is only 242MB; my desk PC has 8GB of RAM (8e9/ 242e6 33); so, unless you have a very, very tiny computer, you should not have any memory problems on this hw even using dense-matrix methods. You are not allowed to use a canned FEM software for this homework. You must write the for-loops and tun in at least a hardcopy of the files [MATLAB, C, Fortran, whatever] that you used to solve this homework problem HINT: You will need to constrain a single node to have zero y-displacement, otherwise, your reduced stiffness matrix will be singular and your Ax-b solver may give complaints. Stress Concentration in a Plate with 2D Finite Element Triangles A plate in plane-stress has a 0.0lmeter diameter hole in it. In this homework, you wil be using 2D finite elements to calculate the maximum | stress in the plate (where x is 'to-the- right' and y s up'). The plate is 0.05meters wide and 0.05meters tall, as shown in the below picture. The plate has a thickness of 0.00lmeters (into the paper). The picture also shows the simple triangle-mesh that you will be using. The plate is loaded with a uniform horizontal pressure/traction (to-the-right) on its right edge with a total load of 1000N The boundary condition is 0 on the left edge of the plate. The plate is made of steel with E-210x10N/m2 and Poisson's ratio v#0.3 You have been provided with the list of 5314 triangle elements and the associated list of 2773 nodes in the below ASCII text files: elems.out nodes.out You have also been provided a list of the left-edge nodes in the below ASCII file leftlist.out and a list of the right-edge nodes in the below ASCII file: rightlist.out Use the 3node triangle-element (Constant-Strain-Triangle [CST] to find the maximum stress in the plate. Compare it to the theoretical value from Figure A-15-1 below, which of 6.25x107 N/m2 . (You will find the FEM agrees within 0.6% even with these gives a simple CST's.) For the nodal-loads, it is adequate to simply apply the total 1000N equally to each of the nodes on the right edge (the nodes in file rightlist.out), i.e., 1000/51 Newtons to each node. The associated reduced-stiffness matrix solves in bseconds or 2.35seconds in MATLAB on my desk PC, e.g., depending on what command you use: >> tic; disp-reduced-inv( Kreduced) * n0dalload reduced Elapsed time is 6.082989 seconds. >tic; disp reduced-K_ reduced nodal load reduced, toc Elapsed time is 2.356513 seconds. even using plain dense computations and no sparsity-exploitation. Make sure your computer will store about a 5494x5494 matrix of floating-point values before you begin. A 5500x5500 matrix in double precision is only 242MB; my desk PC has 8GB of RAM (8e9/ 242e6 33); so, unless you have a very, very tiny computer, you should not have any memory problems on this hw even using dense-matrix methods. You are not allowed to use a canned FEM software for this homework. You must write the for-loops and tun in at least a hardcopy of the files [MATLAB, C, Fortran, whatever] that you used to solve this homework problem HINT: You will need to constrain a single node to have zero y-displacement, otherwise, your reduced stiffness matrix will be singular and your Ax-b solver may give complaints
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