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A new singular/hypersingular MLPG (LBIE) method for 2D elastostatics. (English) Zbl 1179.74179
Summary: A new meshless local Petrov-Galerkin (MLPG) type method based on local boundary integral equation (LBIE) considerations is proposed for the solution of elastostatic problems. It is called singular/hypersingular MLPG (LBIE) method since the representation of the displacement field at the internal points of the considered structure is accomplished with the aid of the displacement local boundary integral equation, while for the boundary nodes both the displacement and the corresponding traction local boundary integral equations are employed. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and boundary variables is employed. The essential boundary conditions are satisfied via the free terms of the singular and hypersingular LBIEs, respectively. This means that, for any distribution of nodal points, displacements and tractions can be treated as independed variables, avoiding thus derivatives of the MLS shape functions. On the local boundaries of the hypersingular LBIEs, tractions are avoided with the aid of an auxiliary local integral equation explicitly derived in the present work. Strongly singular and hypersingular integrals are evaluated directly and with high accuracy by means of advanced integration techniques. Two representative numerical examples that demostrate the achieved accuracy of the proposed singular/hypersingular MLPG (LBIE) method are provided.

74S30 Other numerical methods in solid mechanics (MSC2010)
74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity