A local point interpolation method for static and dynamic analysis of thinbeams

The local point interpolation method (LPIM) is a newly developed truly mesh less method, based on the idea of meshless local Petrov-Galerkin (MLPG) app roach. In this paper, a new LPIM formulation is proposed to deal with fourt h-order boundary-value and initial-value problems for static and dynamic an alysis (stability, free vibration and forced vibration) of beams. Local wea k forms are developed using weighted residual method locally. In order to i ntroduce the derivatives of the field variable into the interpolation schem e, a technique is proposed to construct polynomial interpolation with Krone cker delta function property, based only on a group of arbitrarily distribu ted points. Because the shape functions so-obtained possess delta function property, the essential boundary conditions can be implemented with ease as in the conventional finite element method (FEM). The validity and efficien cy of the present LPIM formulation are demonstrated through numerical examp les of beams under various loads and boundary conditions. (C) 2001 Elsevier Science B.V. All rights reserved.