A local point interpolation method for static and dynamic analysis of thin beams

摘要: Abstract The local point interpolation method (LPIM) is a newly developed truly meshless method, based on the idea of Petrov–Galerkin (MLPG) approach. In this paper, new LPIM formulation proposed to deal with fourth-order boundary-value and initial-value problems for static dynamic analysis (stability, free vibration forced vibration) beams. Local weak forms are using weighted residual locally. order introduce derivatives field variable into scheme, technique construct polynomial Kronecker delta function property, only group arbitrarily distributed points. Because shape functions so-obtained possess essential boundary conditions can be implemented ease as in conventional finite element (FEM). validity efficiency present demonstrated through numerical examples beams under various loads conditions.