Three-dimensional static analysis of rectangular thick plates by using the meshless local Petrov-Galerkin method

In this article, a meshless local Petrov-Galerkin (MLPG) approach is developed for three-dimensional (3D) analysis of thick plates. Two different MLPG methods including MLPG1 and MLPG5 are employed to solve the elasto-static problems of thick plates. In MLPG1, a namely fourth-order spline function is considered as test function, while the Heaviside step function is employed as test function in MLPG5. Considering 3D equilibrium equations, the local symmetric weak forms are derived. The moving least-squares approximation is used to interpolate the solution variables and the penalty method is applied to impose the essential boundary conditions. In the present study, brick-shaped domains are chosen as local subdomains and support domains. The integrals appearing in the weak formulation are easily evaluated over brick-shaped subdomains and their boundaries. Considering the present approach, elasto-static deformations and stresses are analysed for thick rectangular plates with various boundary conditions and different aspect ratios. Excellent agreement is seen comparing the present results with the known analytical and numerical solutions in the literature.