تجزیه و تحلیل حساسیت طراحی شکل برای شرایط شکستگی

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.

A lot of papers have been devoted to the shape design sensitivity analysis (SDSA) and optimization problems with integral and local functionals (see for example [1] and [2]). Expressions for shape design sensitivity have been expressed as boundary integrals or as domain integrals and evaluated using finite element analysis and boundary-element analysis. Fewer studies have been devoted to the special class of problems for finding relations connecting strengths characteristics with variations of geometrical parameters of the considered bodies. Effective relations connecting the stress intensity factors and the energy release rate with the variations of geometric and material parameters of quasi-brittle bodies and their implementation in FEM are of significant interest in fracture mechanics and in the theory of optimal structural design. These relations give us the possibility to evaluate the sensitivity of fracture criterion with respect to imperfect structural shape and nonideal manufacture and to estimate structural parameters influence of crack propagation. Application of these relations is useful for determination of structural solutions which increase the strength and help to solve the problems of optimal design. SDSA gives also important relevant information. Note the paper [3], where the growth of an initial crack was treated as a change in shape and it was shown how SDSA leads to a well known expression of Rice’s path-independent integral and how this integral can be computed through domain integration, which gives much more accurate results when using FEM (see also [4]). This paper deals with the shape design sensitivity analysis for quasi-brittle elastic plates. We apply the approach, based on using J-integral and on introduction of adjoint system, to derive the design sensitivity analysis relations. Special attention is devoted to basic relations of sensitivity analysis which are derived with the help of well known domain representation of the J-integral.