Analysis of rectangular square plates by the mixed Meshless Local Petrov-Galerkin (MLPG) approach

A new mixed meshless formulation based on the interpolation of both strains and displacements has been proposed for the analysis of plate deformation responses. Kinematics of a three dimensional solid is adopted and discretization is performed by the nodes located on the upper and lower plate surfaces. The governing equations are derived by employing the local Petrov-Galerkin approach. The approximation of all unknown field variables is carried out by using the same Moving Least Squares functions in the in-plane directions, while linear polynomials are applied in the transversal direction. The shear locking effect is efficiently minimized by interpolating the strain field independently from the displacements. The Poisson's thickness locking phenomenon is eliminated by introducing a new procedure based on the modification of the nodal values for the normal transversal strain component. The numerical efficiency of the derived algorithm is demonstrated by the numerical examples.