Numerical optimum design of elastic annular plates with respect to buckling

Abstract

Annular plates of fixed volume, under uniform radial edge compression are considered. The plate is divided into N segments of linearly variable or constant thickness. Geometrical constrains for the segment thickness and for the effective stress are assumed. Two types of objective functions are explored: (I) maximum value of critical load at the fixed number of circumferential buckling half-waves j, (II) unimodal optimum design for such a number j that buckling load equals max ▪. The shooting method is applied to compute the distribution of axial forces in the prebuckling state and the basic buckling load for the plate of variable thickness. The optimal distribution of segment thicknesses Xk for k = 1, …, N are computed by means of Rosenbrock's method with internal penalty function. Results of numerical analysis are reported for the both optimum design problems I and II.