复合材料裂纹体应力与变形通解

General Solution of Stress and Deformation in Cracked Body for Composite Materials

摘要: 复合材料力学行为研究对于新型工程结构应用更加重要，特别是各向异性材料裂纹问题已成为力学研究的讨论重点。本文主要解决复合材料中心裂纹板在混合加载下的边值问题。通过建立相关方程并利用泛复变量方法获得了弹性力学一般解答。为满足平面应力边界条件合理地选择应力函数，推导出各向异性板应力场和变形场的完全解。确定了裂纹变形场与裂纹端部奇异应力场的实函数表达式。

Abstract: The investigation of the mechanical behaviour for composite materials has even more importance to the applications in new engineering structures. Particularly, the crack problem of anisotropic materials must be discussed for the key points as in mechanical study. This paper is mainly to solve the boundary problem of the centre-cracked plate with composite materials under mixed loading. The general solution about the elastic mechanics had been achieved by way of establishing relational equations and using pan-complex variable method. The stress functions had been selected rationally to meet the needs of the plane stress boundary conditions. The whole solutions on stress field and deformation field for the anisotropic plate have been derived. The real function expressions of crack displacement fields and the singular stress fields near the crack-tip region have been determined.