A computational method for design sensitivty analysis of elastoplastic structures Original Research Article

Design sensitivity analysis of structural systems having elastoplastic material behavior is developed using the continuum formulation and its implementation into a finite element program is described. The main idea is to develop a computational procedure for design sensitivity analysis based on the response obtained by an incremental load approach for non-linear response analysis, where the elastoplatic (time-independent) constitutive model is employed to account for the plastic material behavior; i.e. kinematic hardening and isotropic hardening. Discontinuities in the design sensitivity coefficients are investigated and a procedure is proposed to alleviate them. The control/reference domain approach is used to treat shape and non-shape design variables simultaneously. The direct variation method is adopted for this path-dependent problem to obtain the design sensitivity expression for the response variables. Analytical examples are used to demonstrate the developed sensitivity procedure and gain insights for numerical implementation. The design sensitivity expression is discretized to implement it into a computer program using the isoparametric formulation of finite element analysis. Numerical examples are presented to calculate the design sensitivity coefficients and compare them with those using the central finite difference method.