DESIGN SENSITIVITY ANALYSIS FOR RATE-INDEPENDENT ELASTOPLASTICITY

A new incremental, direct differentiation method for design sensitivit y analysis of structures with rate-independent elastoplastic behavior is presented. We formulate analytical sensitivity expressions that are consistent with numerical algorithms for elastoplasticity that use im plicit methods to integrate the constitutive equations and return mapp ings to enforce the consistency conditions. The sensitivity expression s can be evaluated with only a modest increase in computational expens e beyond the cost of simulation. Combined with the inherent advantages of implicit integration strategies, this represents a significant imp rovement over previous sensitivity formulations for history-dependent materials. First-order sensitivity expressions involving the complete set of design variables, including shape design variables, are derived for a generic response functional. The reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load ste p in the finite element procedure is used to update the response sensi tivities for that time step. No iterations are needed in the sensitivi ty computations. A numerical example demonstrates the accuracy and eff iciency of the new sensitivity analysis method for an elastoplastic an alysis problem. Explicit sensitivities from the new method are confirm ed by finite difference estimates.