A novel hybrid boundary element is developed for polygonal holes in finite anisotropic elastic plates based on two different special fundamental solutions for holes. Since these special fundamental solutions satisfy traction-free condition along the hole's boundary, there is no mesh required on the boundary of polygonal holes. Various types of polygonal holes with rounded corners, such as triangles, rhombuses, ovals, pentagons, are considered by adding proper perturbation to an elliptical hole. The developed hybrid element is a mixture of two special boundary elements: one is based on the special fundamental solution derived through nonconformal mapping and the other is based on the solution derived through perturbation technique with conformal mapping. The special boundary element methods are combined through submodeling technique. First, the global model is solved using the perturbation solution. Then, using the displacements obtained from global model, an auxiliary submodel is set up and the results are evaluated with the nonconformal solution. The present method is compared and validated with conventional boundary element method and finite element method. The effect of hole curvature, material anisotropy, and loading condition on the stress distribution around the hole is presented.

中文翻译：

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二维各向异性弹性固体中圆角多边形孔的新型混合边界元


基于孔的两种不同的特殊基本解，针对有限各向异性弹性板中的多边形孔开发了一种新型混合边界元。由于这些特殊的基本解满足沿孔边界的无牵引条件，因此多边形孔的边界上不需要网格。通过对椭圆孔添加适当的扰动来考虑各种类型的具有圆角的多边形孔，例如三角形、菱形、椭圆形、五边形。所开发的混合单元是两种特殊边界单元的混合：一种基于通过非共形映射导出的特殊基本解，另一种基于通过共形映射的摄动技术导出的解。通过子模型技术将特殊的边界元方法结合起来。首先，使用扰动解来求解全局模型。然后，利用从全局模型获得的位移，建立辅助子模型，并用非共形解来评估结果。该方法与传统边界元法和有限元法进行了比较和验证。介绍了孔曲率、材料各向异性和加载条件对孔周围应力分布的影响。