A LOCAL RADIAL POINT INTERPOLATION METHOD (LRPIM) FOR FREE VIBRATION ANALYSES OF 2-D SOLIDS

A local radial point interpolation method (LRPIM) is presented to deal with boundary-value problems for free vibration analyses of two-dimensional solids. Local weak forms are developed using weighted residual method locally from the partial differential equation of free vibration. A technique to construct shape functions using radial function basis is proposed. The shape functions so formulated possess delta function property. Essential boundary conditions can be implemented with ease as in the finite-element method. Some important parameters on the performance of LRPIM are also investigated thoroughly. Numerical examples for free vibration analyses of two-dimensional solids to demonstrate the validity and efficiency of the present LRPIM are presented.