Design sensitivity coefficients for elasto‐viscoplastic problems by boundary element methods

This paper is concerned with accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with small strains and rotations, but with material non‐linearities present (elasto‐plastic or elasto‐viscoplastic problems). This approach is based on direct differentiation (DDA) of the relevant derivative boundary element method (DBEM) formulation of the problem. Analytical differentiation of the DBEM equations leads to singular integral equations for the DSCs with weakly (logarithmically for 2‐D) singular kernels which are easy to deal with. Also, stress components and their sensitivities are obtained on the boundary of a body with great accuracy. These quantities are typically difficult to obtain accurately from finite element methods (FEM). A computer program for general two‐dimensional (plane strain and plane stress) problems has been developed based on the above formulation. Numerical results are presented for some sample problems and these are compared against direct solutions. The agreement between the DBEM and direct solutions is excellent for these examples.