Local integral equations implemented by MLS-approximation and analytical integrations

This paper is devoted to the development of advanced mesh free implementations of the governing equations and the boundary conditions for boundary value problems in elasticity. Both the strong and weak formulations are discretized by using the Moving Least Squares approximations. The weak formulation is represented by local integral equations considered on sub-domains around interior nodal points. The awkward evaluation of the shape functions and their derivatives is reduced by focusing to nodal points because of the development of analytical integrations. That results in significant saving of the computational time needed for creation of the system matrix. Furthermore, a modified differentiation scheme is developed for approximation of higher order derivatives of displacements appearing in the discretized formulations. The accuracy, convergence and computational efficiency are studied in simple numerical example.