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- (b) For the configuration shown below. Write the finite difference equation under steady state conditions for node (m, n). Ax- m, n + 1 Material A KA Ay Ay m, n Material B m, n-1 Ax m-1, n m+ 1, n(3) For the given boundary value problem, the exact solution is given as = 3x - 7y. (a) Based on the exact solution, find the values on all sides, (b) discretize the domain into 16 elements and 15 evenly spaced nodes. Run poisson.m and check if the finite element approximation and exact solution matches, (c) plot the D values from step (b) using topo.m. y Side 3 Side 1 8.0 (4) The temperature distribution in a flat slab needs to be studied under the conditions shown i the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I all cases assume the upper and lower boundaries are insulated. Assume that the units of length energy, and temperature for the values shown are consistent with a unit value for the coefficier of thermal conductivity. Boundary Temperatures 6 Case A C D. D. 00 LEGION Side 4 z episProblem 3 There are 520 nodes and 800 brick finite elements in a model. 40 nodes are completely fixed and other 50 are fixed from displacement along x-axis. There are 3 degrees of freedom in a node. What is the number of unknowns in the FE model?
- Suppose that the stiffness matrices of the above question (as shown below) are as follows: b -b a a K1 =108 x K2 =108 x -b -a a b 0.1 m 0.05 m 0.5 m 0.5 m where a= 1.8 N/m and b=2.9 N/m. Find the assembled stiffness matrix of the system using the following connectivity table. Element Node i Node j (1) 2 (2) 2 What is the summation of all terms located on the main diagonal of the assembled [a bc] stiffness matrix? (Hint: if the assembled stiffness matrix is b de then you e f need to find the value of a + d+ f). Your Answer: Answer The shape function value ) is zero at the centre of the element. O is always higher than 1. O is equal 1 at its own node and zero at other nodes. O is always less than 1.A square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. 1.0 4. 1.0 3. X- 1.0 1.0 2. 2.****USE MATLAB TO SOLVE THIS QUESTION**** 5. A composite cantilever beam, made of High Strength (HS) carbon/epoxy material with [04/304], plies, has uniformly applied load go. When qo=50N/m, length of the beam, L=0.1m, and width of the beam, b=0.05m. Find the maximum deflection of the beam. (for the HS carbon fiber/epoxy, E₁1 =131 GPa, E₂2= 11.2 GPa, V12 = 0.28, G12 = 6.55 GPa and ply thickness t=0.2mm) 90-50N/m L
- 3. Jacobian Matrix: a) Derive the equation for Joint Force of the given planar 1R robot. As it's a planar robot, forces at the end-effector are Ex and Ex. b) Find the force (FX) when the link length is 0.5 m, Joint force is 1 Nm, Joint variable, 0 = 60 and Fx = 0 N. T P₂ y r F -F₂ ee 0,0 F Р. X 7 ४1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…Explain the term ‘shape function’. Why polynomial terms are preferred for shape functions in finite element method? Note: Please I need soultion without palagrism and not handwrite
- Fig Q3 shows a uniform cantilever beam of length L which is loaded by a linearly varying load: w(x)= wo where w is the load per unit length at the fixed end (x =0). w(x) Fig Q3: A uniform cantilever beam (a) Using Ritz method, derive a two-term polynomial function to approximate the transverse displacement (u) of the beam. Total potential energy (TPE) for a beam under bending load is: TPE= EI du 2 dr² -w(x)udx where E is Young's modulus and I is second moment of area.200 OOOD O Subject Date: Q1/Find the domain P the function 2. Y3DIn(2x+X-6-6)1 - Explain Van-Neumann stability by finite difference schemes for this equations a- Laplace equation. J²u dyz (x, y) = 0 J²u dx2(x, y) + b- poison equation. J²u J²u { (x, y) + əy² (x, y) = f (x, y) əx²