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针对含不同孔型复合材料板,根据非均质各向异性弹性理论和复变函数理论,提出了积分方程法求解方案。建立了相应的数学模型,对含不同孔型复合材料板进行了孔边应力分析,通过保角映射方法建立精确的边界条件,解决了复杂孔型的边界条件问题,借助仿射变换能同时并且同方法的处理这两个应力函数在边界上的问题。建立了基于准确的边界条件的边界积分方程分析体系,最终得到开口结构的应力分布。给出了含矩形和八边形孔复合材料板的精确解析解。并针对不同的荷载状况,以及它们对矩形和八边形孔边应力集中系数的影响进行探讨。
According to the heterogeneity anisotropy elasticity theory and complex variable function theory, a solution scheme of integral equation method is proposed for composite plates with different holes. The corresponding mathematical model is set up to analyze the stress of the hole edge of composite plate with different holes. By means of the conformal mapping method, the accurate boundary conditions are established to solve the boundary condition problem of complex holes. By means of affine transformation, The same method deals with the problem of the two stress functions at the boundary. The boundary integral equation analysis system based on accurate boundary conditions is established, and finally the stress distribution of the open structure is obtained. The exact analytic solutions of composite plates with rectangular and octagonal holes are given. The influences of different load conditions and their stress concentration factors on rectangular and octagonal holes are discussed.