Zeroth-order shear deformation micro-mechanical model for composite plates with in-plane heterogeneity

Abstract

This article introduces a new model for investigating the mechanical behavior of heterogeneous plates, which are composed of periodically-repeated microstructures along the in-plane directions. We first formulate the original three-dimensional problem in an intrinsic form for implementation into a single unified formulation and application to geometrically nonlinear problem. Taking advantage of smallness of the plate thickness-to-length parameter and heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order plate model, which is similar to a generalized Reissner–Mindlin model (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. This present approach is incorporated into a commercial analysis package for the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level. A few examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.