An efficiency assessment of selected unconstrained minimization techniques as applied to nonlinear structure analyses

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Virginia Polytechnic Institute and State University


This thesis seeks to identify the potential for the unconstrained minimization algorithms of mathematical programming to be cost-effective with the conventional techniques of nonlinear structural analysis. With this in mind, the author has attempted to critically evaluate a few of the more commonly used algorithms for their effectiveness in solving structural problems involving geometric and/or material nonlinearities. The algorithms have been categorized as being zeroth order requiring only function evaluations, first order requiring evaluation of both the function and the gradient or second order requiring in addition a variable metric. The sensitivity of the first and second order algorithms to the accuracy of derivatives derived on the basis of finite difference operations clearly suggests using analytically derived derivatives in order to obtain better control of the computational effort required for convergence to the exact solution. The thesis concludes by attempting to identify the algorithm which promises to be most effective in predicting nonlinear structural response and suggests improvements that could be made to make it even more cost-effective when compared with other well known techniques of nonlinear structural analysis.