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Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems. (English) Zbl 1147.74047
Summary: We discuss the moving least-square approximation (MLS) method. In some cases, the MLS may form an ill-conditioned system of equations, so that the solution cannot be correctly obtained. Hence, in this paper we propose an improved moving least-square approximation (IMLS) method. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and accuracy than the MLS, and will not lead to ill-conditioned systems of equations. Combining the boundary integral equation (BIE) method and the IMLS approximation method, a direct meshless BIE method, the boundary element-free method (BEFM), is presented for two-dimensional elasticity. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution for nodal variables, and boundary conditions can be applied easily; hence, it has higher computational accuracy. For demonstration purpose, we give selected numerical examples.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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