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

A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional<br />solids. A local weak form is developed using the weighted residual method locally in two-dimensional<br />solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed<br />nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form<br />and point interpolation. Since the shape functions possess the Kronecker delta function property, the<br />essential boundary condition can be implemented with ease as in the conventional finite element method<br />(FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh<br />for both field interpolation and background integration. The implementation procedure is as simple as<br />strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency<br />of the present LPIM formulation are demonstrated through example problems. It is found that the present<br />LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired<br />accuracy in solids.