Research in Engineering and Aviation

A Meshless Integral Method Based on Regularized Boundary Integral Equation

September 2006

Author(s): A. Bodin,J. Ma, X. Xin., and P. Krishnaswami

Journal: Computer Methods in Applied Mechanics and Engineering, v195, n44-47, p6258-6286. DOI: 10.1016/j.cma.2005.12.005


A meshless integral method based on the regularized boundary integral equation is developed and applied to two-dimensional linear elasticity. The governing integral equation is obtained from the weak form of elasticity over a local sub-domain, and the moving least-squares approximation is used for meshless function approximation. The method is built on the LBIE method proposed by Atluri and co-workers, and several key improvements are introduced in this work that significantly enhance the accuracy and robustness of the method. The most critical improvement is the use of the subtraction technique to remove the strong singularity that results in a regularized governing integral equation. The technique is straightforward and efficient, and is much simpler and easier compared to other singularity removal techniques. A special numerical integration is employed for the calculation of integrals with weak singularity which further improves accuracy. The collocation method is employed to enforce the essential boundary conditions exactly, which is simple and computationally efficient. The natural boundary conditions are incorporated in the system governing equation and require no special handling. Numerical tests show that the meshless integral method is accurate and robust. The effects of weight function, support domain, sub-domain, and monomial basis are investigated and discussed.