NEW MODELS FOR OPTIMAL TRUSS TOPOLOGY IN LIMIT DESIGN BASED ON UNIFIED ELASTIC PLASTIC ANALYSIS/

This paper presents several equivalent formulations for a structural d esign problem where the load-carrying capacity is maximized for a pres cribed volume subject to bounds on complementary energy and stresses. This limit design model covers the full range of strictly elastic, ela stic/plastic and strictly plastic designs and is based on the unified analysis model of Ben-Tal and Taylor [1]. While this design model is c onvex, it is nonlinearly constrained and is of a very high dimension f or topology design problems. Application of duality principles leads t o several simpler but nonsmooth equivalent models. In particular, for the case when the design variables do not have explicit bounds, the du al models reduce to a minimization, subject to a single linear constra int, of a pointwise maximum of a finite number of convex functions. Mo re importantly, these simpler design models are of greatly reduced siz e, since they contain only nodal variables. Further, the two cases of strictly plastic as well as strictly elastic limit design models can b e reduced to linear programs both of which, unexpectedly, are shown to be equivalent to the more widely studied model for minimum compliance topology design of elastic trusses. Several numerical examples illust rate the usefulness of these new dual formulations.