Meshless Local Petrov-GalerkinMethod 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 anisotropicmedium. The Heavisidestep function is used as the test functions in the local weak form. It is lead- ing to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace trans- for technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is cov- ered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local inte- gral equations has a pure contour character only in elas- tostatics. In elastodynamics an additional domain inte- gral is involved due to inertia terms. The moving least square (MLS) method is used for approximation ofphys- ical quantities in LBIEs.