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

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