Shape design sensitivity analysis for fracture conditions

This paper deals with the shape design sensitivity analysis for quasi-brittle plane bodies and implementation of this analysis in numerical method. Special attention is devoted to basic relations of sensitivity analysis which are derived with the help of domain representation of the path-independent J-integral and introduction of adjoint system. Numerical technique for finding the sensitivity of J-integral with respect to a wide class of the boundary variations and specifically with respect to improved variations is worked out. Important aspects of shape design sensitivity analysis realization related with finite-element modelling, mesh adaptation and smoothing technique are considered. Numerical results of design sensitivity computations, performed for cracked plates loaded by in-plane forces, are presented.