Meshless local Petrov–Galerkin (MLPG) method for Reissner–Mindlin plates under dynamic load

A meshless local Petrov–Galerkin (MLPG) method is applied to solve dynamic plate bending problems described by the Reissner–Mindlin theory. Both harmonic and impact loads are considered. The Laplace-transform is used to eliminate the time dependence of the variables for transient problems. A weak formulation for the set of governing equations in the Reissner–Mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate. Nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. Unknown Laplace-transformed quantities are computed from the local boundary integral equations. The time-dependent values are obtained by the Stehfest’s inversion technique.