Regularized formulation for optimal design of axisymmetric plates

Abstract

This paper presents a regularized mathematical formulation, necessary conditions of optimality and solutions of problems of optimal design of solid, elastic, axisymmetric plates of prescribed total material volume. Single-purpose design criteria of minimum static compliance (maximum stiffness) and maximum frequency of free, transverse vibrations, are considered.The regularization, which alleviates some anomalies and difficulties encountered earlier in plate optimization problems, is based on a new compound plate model with two simultaneous design variables, namely, variable thickness of a solid part of the plate and variable concentration of a dense system of thin, integral stiffeners attached to the solid plate part. A numerical, optimality-criterion-based method of solution is developed for the problem, and several optimal designs are presented. The results are compared with results obtained from optimal design formulations applied heretofore, and substantiate the superiority of the new, regularized formulation.