| The use of composite materials as structural components has inspired considerable research on the effect of flaws and imperfections on the structural strength of composites. The research usually involves two-dimensional modeling. In this dissertation, the two-dimensional crack problems in composite materials are investigated systematically by use of the hypersingular integral equation method. Some theoretical conclusions and a great deal of numerical results are obtained. The main contributions of the dissertation are as follows:1. The elasticity point-force solutions for perfectly bonded elastic half-plane in literatures are further studied. The compact formulae of displacements and stresses are given which can be used in the boundary element method.2. According to the singular stress filed, the formula of stress intensity factor at crack terminal is acquired. The nature of the unknown solutions of the hypersigular integral equations is studied by the main-part analysis method of singular integral equations, and the singular index of the unknown solutions is obtained. The finite-part integral is used to discretize the hypersingular equations as a set of linear algebraic equations, where the singular integrals of various types are specially treated and the specific calculating formula are given. Based on this, the formulae determining the stress intensity factors with the displacement discontinuities on the crack surface are proposed.3. Based on the fundamental solution of homogeneous and bimaterial plane, the hypersingular integral equation method is used to investigate the problems of an arbitrary angle crack and multiply cracks respectively .Both of the problems are reduced to a system of one-dimensional hypersingular integral equations with theory of finite-part integral. the unknown function is displacement discontinuities. and their numerical method are founded for them. the formulae of the stress intensity factors is given.4. Some examples are shown that the numerical approach is reliable. Some typical examples of planar crack problems (such as homogeneous material colinear cracks, bimaterial oblique crack, bimaterial parallel cracks etc.) are calculated, and the effect between cracks or between interface and cracks is analyzed systematically. some worthy results are obtained, part of which are not available in the literature. Therefore, a new efficient path to research plane crack problems especially composite materials plane fracture mechanicals is found. |
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