ИСТИНА

Questions discussed are related to an important class of problems concerning modeling of brittle or quasi-brittle elastic bodies with cracks. The stress intensity factors and the energy release rate are of significant interest in fracture mechanics. These relations give us the possibility 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. It is considered that the problems are described by linear differential equations in partial derivatives. The integro-differential formulations are reduced to finding the minimum of a quadratic functional characterizing the state of the elastic system under specific differential constraints. The main attention is paying to computational aspects of finding the energy release rate (J-integral) for elastic plates with cracks and adaptive methods for construction of adequate finite element meshes.