Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method
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摘要: 提出了一种求解三维线弹性问题的奇异杂交边界点方法．将修正变分原理与移动最小二乘法结合起来，利用了前者的降维优势和后者的无网格特性．使用刚体位移法处理方法中的强奇异积分，提出了一种自适应的积分方案，解决了原有的杂交边界点方法中存在的“边界层效应”．在该方法中，将基本解的源点直接布在边界上，避免了在正则化杂交边界点法中不确定参数的选取．三维弹性力学问题算例体现了这些特点．结果表明该方法与已知的精确解符合较好，同时研究了影响该方法精度的一些参数．Abstract: The singular hybrid boundary node method (SHBNM) is proposed for solving threedimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ‘boundary layer effect', which is the main drawback of the original hybrid BNM, was overcomed by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3-D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
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