Continuum-type optimality criteria methods for large finite element systems with a displacement constraint. Part II

Abstract

In Part I of this study (Rozvany et al. 1989), general aspects of iterative continuum-based optimality criteria (COC) methods were discussed and the proposed approach was applied to structural optimization problems with freely varying cross-sectional dimensions. In this paper, upper and lower limits on the cross-sectional dimensions, segmentation, allowance for the cost of supports and for selfweight, non-linear and nonseparable cost and stiffness functions and additional stress constraints are considered. The examples include beams with various geometrical properties and plates of variable thickness in plane stress. All results are compared with independently derived analytical or semi-analytical solutions and/or with solutions obtained by a mathematical programming (sequential quadratic programming, SQP) method. The number of elements in beam examples is up to one hundred thousand and in plane stress problems up to 3200 elements are used. Comparisons between computer time requirements for the COC and SQP methods are also presented. In addition, the problem of layout optimization is discussed briefly. The paper is intended to establish the power and versatility of the COC method. Notes. 1. Some less important symbols are defined where they first appear in the text. 2. Nondimensional variables are indicated by the sympbol ~. © 1990 Springer-Verlag.