Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions

Infinitesimal deformations of a homogeneous and isotropic thick elastic plate have been analyzed by using a meshless local Petrov–Galerkin (MLPG) method and a higher-order shear and normal deformable plate theory (HONSDPT). Radial basis functions (RBF) are employed for constructing trial solutions, while a spline function is used as the weight function over a local subdomain. The present method uses a number of randomly distributed nodes in the domain and is truly meshless. Two types of RBFs, i.e. multiquadrics (MQ) and thin plate splines (TPS), are employed and effects of their shape parameters on the quality of the computed solution are examined for deformations of thick plates under different boundary conditions. It is found that the present MLPG formulations give results very close to those obtained by other researchers. A benefit of using RBFs is that no special treatment is needed to impose the essential boundary conditions, which substantially reduces the computational cost.