Consider the application relating to critical loads for a beam from Section 1. For
Chapter 6, Problem 9(choose chapter or problem)
Consider the application relating to critical loads for a beam from Section 1. For simplicity, we will assume that the beam has length 1 and that its flexural rigidity is also 1. Following the method described in the application, if the interval [0, 1] is partitioned into n subintervals, then the problem can be translated into a matrix equation Ay = y. The critical load for the beam can be approximated by setting P = sn2, where s is the smallest eigenvalue of A. For n = 100, 200, 400, form the coefficient matrix by setting D = diag(ones(n 1, 1), 1); A = eye(n) D D_ In each case, determine the smallest eigenvalue of A by setting s = min(eig(A)) and then compute the corresponding approximation to the critical load. 1
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