A locking-free meshless local Petrov–Galerkin formulation for thick and thin plates

In this paper, a locking-free meshless local Petrov–Galerkin formulation is presented for shear flexible thick plates, which remains theoretically valid in the thin-plate limit. The kinematics of a three-dimensional solid is used, instead of the conventional plate assumption. The local symmetric weak form is derived for cylindrical shaped local sub-domains. The numerical characteristics of the local symmetric weak form, in the thin plate limit, are discussed. Based on this discussion, the shear locking is theoretically eliminated by changing the two dependent variables in the governing equations. The moving least square interpolation is utilized in the in-plane numerical discretization for all the three displacement components. In the thickness direction, on the other hand, a linear interpolation is used for in-plane displacements, while a hierarchical quadratic interpolation is utilized for the transverse displacement, in order to eliminate the thickness locking. Numerical examples in both the thin plate limit and the thick plate limit are presented, and the results are compared with available analytical solutions.