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A MLPG4 (LBIE) formulation for solving axisymmetric problems. (English) Zbl 1180.74068
Sladek, Jan (ed.) et al., Advances in meshless methods. Forsyth, GA: Tech Science Press (ISBN 0-9717880-2-2/hbk). 291-316 (2006).
Summary: A Meshless Local Petrov-Galerkin Four (MLPG4) method, known as well as Local Boundary Integral Equation (LBIE) method, is proposed here for the solution of three dimensional potential and elastostatic problems characterized by axisymmetry and axisymmetric boundary conditions. Considering a typical MLPG4 (LBIE) formulation, the fields involved in the LBIEs of the problem are transformed into cylindrical coordinates while the subdomains are selected to be toroids with circular cross sections. The initial three dimensional problem is reduced to a two dimensional one where the LBIEs are defined on the axisymmetric plane of the considered problem containing only pure contour integrals. Singular integrals are avoided by considering properly distributed points located internally to the plane of symmetry. The integrals defined on the intersected parts of the surface generator of the body are simply evaluated by interpolating the global boundary parameters through line boundary elements. Three different interpolation schemes, namely the Mean Least Square (MLS) approximation, the MLS approximation with Consistent Approach (MLSCA) and the Radial Basis Point Interpolation Functions (RBPIF), are used for the representation of the unknown internal and boundary fields. Two representative examples demonstrate the accuracy of the proposed axisymmetric MLPG4 (LBIE) methodology.
For the entire collection see [Zbl 1103.74005].

74S30 Other numerical methods in solid mechanics (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)