HW10 - dx du u dx d Evaluate the stiffness matrix for the...

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MCE 561 Computational Methods in Solid Mechanics Homework Assignment 10 Due May 2, 2011 1. Using both the Direct Iteration and the Newton-Raphson methods solve the one degree of freedom problem Ku = F , where K = 50(1 + e 2 u ) and F = 100 (assume consistent units). Do this problem using two different initial guesses of 0.0 and 0.4. Use MATLAB or a similar software and make plots your results similar to those shown in the example on the course web site. First make a plot of Ku vs u. Compare the solutions and the computational effort required for each method. 2. Using the usual Ritz-Galerkin method, determine the finite element matrices for the one- dimensional nonlinear equation 0 1 = +
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Unformatted text preview: dx du u dx d Evaluate the stiffness matrix for the two-noded linear element. Partial Ans. ∑ ∫ = --+ = ψ ψ ψ = N k x x e e e e j e i e k e k e ij b a h u u dx dx d dx d u K 1 2 1 1 1 1 1 2 3. For the previous one-dimensional second order equation, determine the Jacobian (tangential stiffness) matrix associated with the Newton-Raphson method given by equation (15) in the on-line notes. Evaluate the general relation for the two-noded linear element case. Note the lack of symmetry of the matrix. Ans. ---+ --+ = 1 1 1 1 2 1 1 1 1 2 ] [ 1 2 2 1 e e e e e e h u u h u u J...
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