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New models for optimal truss topology in limit design based on unified elastic/plastic analysis. (English) Zbl 0898.73046
We present 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 a unified analysis. 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. Several numerical examples illustrate the usefulness of these new dual formulations.

MSC:
74P99 Optimization problems in solid mechanics
74R20 Anelastic fracture and damage
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