Generalized Reissner–Mindlin Model for Composite Plates with No Restrictions on Constituent Materials

Abstract

Unlike previous works, the present work implements the variational-asymptotic method to develop a generalized Reissner–Mindlin model for composite plates made of inhomogeneous and anisotropic materials. From a mathematical perspective, an equivalent two-dimensional plate model is first constructed through a dimensional-reduction procedure that involves the asymptotically correct energy functional up to second order in small parameters and with no specific restrictions on constituent materials. Next, to obtain a generalized Reissner–Mindlin plate model, a hybrid energy transformation procedure is applied from an engineering perspective. During this procedure, the unnecessary mathematical complexity of partial-derivative terms in the energy functional derived herein and obscure physical interpretations of mechanical boundary conditions in the plate modeling are systematically resolved. To evaluate the accuracy and capability of these procedures, three-dimensional recovery relations are established to predict the three-dimensional fields of the original three-dimensional structure. Several examples from the literature are presented to demonstrate the consistency and efficiency of the proposed approach.