A Simple Technique for the Minimum Mass Design of Continuous Structural Members

Abstract

A technique for determining the minimum mass design of continuous structural members is presented. The method involves formulating the minimum mass design problem as an optimal control problem, transforming the differential equations modeling the member into a penalty function, and then representing the state variables in terms of a Ritz-type expansion and discretizing to reduce the original optimal control problem to a parameter optimization problem. The technique is applied to determine the optimal design of a simply supported beam with fixed fundamental frequency of free vibration and a fixed-free column with specified Euler buckling load.