Analysis of Shear Locking Effect on Reissner Plates Using Meshless Local Petrov-Galerkin Method

Resumo

The shear locking is an interesting numerical phenomenon which can be found in several formulations,
such as those based on Finite Element Method (FEM) and Meshless Local Petrov-Galerkin (MLPG) Method, when
they are directly applied to thin plates analyzed through Reissner's theory. It is known that the shear locking effect
is caused by using the same interpolation functions for all generalized displacement fields, producing inconsistent
results in case of thin plates. In order to avoid this phenomenon, the rotations must be built from the first derivative
of the transversal displacement field. In the FEM formulation, this problem is overcome by using reduced-selective

integration schemes. However, this alternative can hardly be extended to Meshless Methods due to the non-
polynomial characteristic of the approximations. More complex numerical formulations can be considered,

however in this paper the variable changing technique is applied, by solving the shear locking effect in a simple
and efficient way, without increasing the number of degrees of freedom in plate’s problems.