A Consistent Tangent Operator Based Boundary Element Method For Design Sensitivity Analysis

Based on Perzyna's elastic-viscoplastic material constitutive relation and Von-Mises yield rule, the integrated formulae for design sensitivity analysis of elastic-viscoplastic problems are derived in this paper. A general design sensitivity analysis method and the relative numerical algorithm by the consistent tangent operator concept based boundary element method are presented. The design variables for sensitivity analysis include geometry parameters, elastic-viscoplastic material parameters and boundary condition parameters. Combining the optimization algorithm, the sensitivity analysis method by the consistent tangent operator concept based boundary element method can be used in nonlinear optimization problems further.Perzyna's elastic-viscoplastic material constitutive relation with a mixed hardening model, two flow functions and Von-Mises yield rule are considered in the sensitivity analysis. According to the implicit backward-Euler difference scheme, a 2D elastic-viscoplastic boundary element rate equation and the related iterative equation are derived. The elastic-viscoplastic radial return algorithm, the formula of elastic-viscoplastic consistent tangent operator and their limit cases are derived and discussed. Based on the direct differentiation approach, the incremental boundary integral equations and the related algorithms for both geometric and elastic-viscoplastic sensitivity analysis are developed. The design variables for sensitivity analysis include geometry parameters, elastic-viscoplastic material parameters and boundary condition parameters.The boundary and domain discretization technique and the treat of singular integral are discussed. A 2D boundary element program and the related numerical algorithm for geometry sensitivity, elastic-viscoplastic material constant sensitivity and boundary condition sensitivity have been developed. Quadratic elements are used for both boundary and domain discretization. Corners have been modeled by means of double nodes technique. Comparison...