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