New models for optimal truss topology in limit design based on unified elastic/plastic analysis Original Research Article

This paper presents several equivalent formulations for a structural design problem where the load-carrying capacity is maximized for a prescribed volume subject to bounds on complementary energy and stresses. This limit design model covers the full range of strictly elastic, elastic/plastic and strictly plastic designs and is based on the unified analysis model of Ben-Tal and Taylor [1]. While this design model is convex, it is nonlinearly constrained and is of a very high dimension for topology design problems. Application of duality principles leads to several simpler but nonsmooth equivalent models. In particular, for the case when the design variables do not have explicit bounds, the dual models reduce to a minimization, subject to a single linear constraint, of a pointwise maximum of a finite number of convex functions. More importantly, these simpler design models are of greatly reduced size, since they contain only nodal variables. Further, the two cases of strictly plastic as well as strictly elastic limit design models can be 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 illustrate the usefulness of these new dual formulations.