A Local Hypersingular Boundary Integral Equation Method Using a Triangular Background Mesh
V. Vavourakis

doi:10.3970/cmes.2008.036.119
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 36, No. 2, pp. 119-146, 2008
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Keywords local hypersingular boundary integral equation, boundary elements, background triangles, meshless, elastostatics
Abstract In this paper, a new meshless Local Hypersingular Boundary Integral Equation method is presented for the analysis of two-dimensional elastostatic problems. The elastic domain is discretized by placing arbitrarily nodes on its boundary and interior. Given this set of nodes, the corresponding map of background triangles is constructed through a common triangulation algorithm. The local domain of each node consists of the union of triangles that this point lies, thus, creating a polygonal line of its local boundary. The local boundary integral equations of both displacements and stresses of the conventional Boundary Elements Method are taken into account. The interpolation of the unknown fields is performed by taking each face of a triangle of the local domain of a source point as a one-dimensional line element. The essential boundary conditions can be directly implemented easily because the interpolation functions possess the Kronecker delta-function property. After constructing the final linear system of equations, the only unknowns are displacements and stresses of all nodal points. Thus, leading to a banded stiffness matrix as in the Finite Element Method. The effectiveness and efficiency of the proposed method is demonstrated with three elastostatic problems in two-dimensions. Excellent agreement between the numerical results and the exact solutions is found. The numerical examples also show that the accuracy of the proposed method is as good as that of the Boundary Elements Method.
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