A Method of Minimum Weight Design with Requirements Imposed on Stresses and Natural Frequencies

概要

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A numerical method is presented to obtain the minimum weight design of structures whose stresses caused by several alternative loads and the first few natural frequencies are required to be within certain limits. The requirements may include other types of eigen-values such as buckling loads. Thicknesses of panels and cross sectional areas of trusses are taken to be independent design variables, and geometrical configuration is assumed to be given. Finite element method is used for structural analysis. A simple procedure to obtain derivatives of eigen-values with respect to the variables is first shown. The objective function which is a sum of the weight and the penalty terms is minimized using the derivatives. Steepest descent method is modified to speed up convergence. The method is applied to obtain optimum thickness of a plate beam, a two storied truss and a simply supported beam.
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