A local point interpolation method for stress analysis of two-dimensional solids

A local point interpolation method (LPIM) is presented for the stress analy sis of two-dimensional solids. A local weak form is developed using the wei ghted residual method locally in two-dimensional solids. The polynomial int erpolation, which is based only on a group of arbitrarily distributed nodes , is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions p ossess the Kronecker delta function property, the essential boundary condit ion can be implemented with ease as in the conventional finite element meth od (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background in tegration. The implementation procedure is as simple as strong form formula tion methods. The LPIM has been coded in FORTRAN. The validity and efficien cy of the present LPIM formulation are demonstrated through example problem s. It is found that the present LPIM is very easy to implement, and very ro bust for obtaining displacements and stresses of desired accuracy in solids .