Optimal Structural Design with Plate Finite Elements

Abstract

This paper describes a general resizing procedure applicable to structures modeled by plate (bending) finite elements. This type of finite elements when used in optimization procedures presents difficulties because of the nonlinear dependence of the stiffness matrix on the plate thickness. Assumed stress field triangular and quadrilateral elements are considered in the present work. Explicit expressions for the derivatives of the stiffness matrix with respect to the plate thickness are obtained and these are used to find derivatives of displacements and stresses. The optimization procedure is based on the Sequence of Unconstrained Minimization Technique (SUMT) with an extended interior cubic penalty function. Each unconstrained minimization is performed using Newton’s method with approximate second derivatives. Optimum design for two plate example problems are presented.