A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids

TLDR: The meshless local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants and local weak forms.

Abstract: The meshless local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the free vibration analysis, the essential boundary conditions are implemented through the direct interpolation form and imposed using orthogonal transformation techniques. In the forced vibration analysis, the penalty method is used in implementation essential boundary conditions. Two different time integration methods are used and compared in the forced vibration analyses using the present MLPG method. The validity and efficiency of the present MLPG method are demonstrated through a number of examples of two-dimensional solids.