Mlpg Methods for Discretizing Weakly Singular Bies

The general Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement & traction boundary integral equations are presented, for solids undergoing small deformations. Using the directly derived non-hyper singular integral equations for displacement gradients, simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are also presented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the present methods are very promising, especially for solving the elastic problems in which the singularities in displacemens, strains, and stresses, are of primary concern.