A MLPG(LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems

摘要

A new meshless local Petrov-Galerkin (MLPG) method, based on local boundary integral equation (LBIE) considerations, is proposed here for the solution of 2D, incompressible and nearly incompressible elastostatic problems. The method utilizes, for its meshless implementation, nodal points spread over the analysed domain and employs the moving least squares (MLS) approximation for the interpolation of the interior and boundary variables. On the local and global boundaries, traction vectors are treated in a way so that no derivatives of the utilized MLS shape functions are required. Both displacement and hydrostatic pressure, at all the considered nodal points, are evaluated with the aid of local integral representations valid for incompressible and nearly incompressible solids. Since displacements and stresses are treated as independed variables, the boundary conditions are imposed directly without any problem via the integrals defined on the global boundary of the analysed body. Singular and hypersingular integrals are evaluated directly with high accuracy through advanced integration techniques. Three numerical examples illustrate the proposed methodology and demonstrates its accuracy.