A boundary-domain integral formulation inevitably arises when the boundary element method (BEM) is applied for solving the differential equation that governs linear elastostatic problems with body forces. Although the domain integrals introduced by the body forces can be evaluated using internal cells this destroys the boundary-only meshing feature of BEM and makes the integration processes inefficient. This paper shows that these problems can be solved more efficiently without using internal cells by the Radial Basis Integration Method (RBIM) which employs a meshless quadrature obtained by performing boundary-only offline computations. Using RBIM, weakly singular domain integrals can be computed via a simple selective quadrature procedure, whereas, strong singular domain integrals may be computed using two schemes: The first, is based on the same selective quadrature procedure, and the second is based on the singularity separation scheme. The present method, unlike classical radial integration method (RIM), does not have problems in calculating integrals in concave or multiple-connected domains. The results obtained in some 2D linear elastostatic problems with arbitrary body forces show that this method can be as accurate as RIM but less time-consuming than the latter. This method could be applied to other engineering problems involving source terms.

中文翻译：

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将径向基积分法与边界元耦合，解决二维弹性中的任意体力问题

当应用边界元法 (BEM) 求解控制体力线性弹性静力学问题的微分方程时，不可避免地会出现边界域积分公式。尽管可以使用内部单元来评估由体力引入的域积分，但这破坏了边界元法的仅边界网格划分特征，并使积分过程效率低下。本文表明，通过径向基积分方法（RBIM），可以在不使用内部单元的情况下更有效地解决这些问题，该方法采用通过执行仅边界离线计算获得的无网格求积。使用 RBIM，可以通过简单的选择性求积过程来计算弱奇异域积分，而可以使用两种方案来计算强奇异域积分：第一个基于相同的选择性求积过程，第二个基于奇异性分离方案。与经典径向积分方法（RIM）不同，本方法在计算凹域或多重连通域中的积分时不存在问题。在一些具有任意体力的二维线性弹性静力问题中获得的结果表明，该方法可以与RIM一样准确，但比后者耗时更少。该方法可以应用于涉及源项的其他工程问题。