Meshless Local Petrov-Galerkin Method in Anisotropic Elasticity

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a pure contour character only in elastostatics. In elastodynamics an additional domain integral is involved due to inertia terms. The moving least square (MLS) method is used for approximation of physical quantities in LBIEs. keyword: meshless method, local weak form, Heaviside step function, moving least squares interpolation, Laplace transform