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MidTermExamS11

# MidTermExamS11 - MCE 561 Computational Methods in Solid...

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MCE 561 Computational Methods in Solid Mechanics Mid-Term Exam – March 28, 2011 1. Using appropriate variables heat transfer in a one-dimensional fin is governed by the equation 0 2 2 = + - mT dx T d where T ( x ) is the temperature distribution (primary variable) and m is a constant. a.) Develop the weak form over a typical element e = ( x a , x b ). b.) Next using the usual Ritz-Galerkin scheme, develop the finite element equation and clearly identify each term. It is not necessary to introduce a specific interpolation scheme (e.g. linear, quadratic, . . . ) at this step. c.) What type of interpolation functions can be used for T ? Explain your reasoning. 2. An elastic beam with uniform properties EI and length L is fixed at both ends and carries a uniformly distributed loading of q o as shown. a.) Using two equal-sized beam elements, formulate and solve this problem. There is no need to re- derive any of the previously developed element equations for this problem type. Your solution

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MidTermExamS11 - MCE 561 Computational Methods in Solid...

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