Local integral equation method for viscoelastic Reissner–Mindlin plates

摘要

A meshless local Petrov-Galerkin (MLPG) method is applied to solve static and dynamic bending problems of linear viscoelastic plates described by the Reissner–Mindlin theory. To this end, the correspondence principle is applied. 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 mean surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied. A meshless approximation based on the moving least-squares (MLS) method is employed in the numerical implementation.