On the mechanics of composite sandwich plates with three-dimensional stress recovery

Abstract

By using the variational-asymptotic method, a universal asymptotic model for composite sandwich plates is established to achieve a great compromise between efficiency and accuracy through the synthesis of two competing theories: equivalent single-layer theories and layer-wise theories. When each layer of a sandwich structure can be individually considered as an elastic plate, and all material constitutive constants of such plates can be assumed to be of the same order, an equivalent plate model can be constructed from the equivalent single-layer perspective. It has an asymptotically correct energy functional, capable of capturing the transverse deformations, but still limited to the zeroth-order approximation. Then, by taking into account mismatched constituent material properties, a universal model for predicting mechanical behavior of composite sandwich plates is then systematically derived from the layer-wise perspective. It has another asymptotically correct energy functional with respect to the core-layer’s plate variables and implements into a single unified representation for subsequent application to sandwich plate problems with any face-to-core-stiffness and length-to-thickness ratios. In particular, to resolve theoretical shortcomings found in published works, complementary theoretical procedures are incorporated and used into the present approach by considering the interlaminar transverse stress continuity conditions as essential conditions in conventional layer-wise theories and by providing three-dimensional recovery relations as necessary ingredients for theories based on various dimensional reduction processes. Finally, as a preliminary validation, several examples available in the literature are presented and investigated. Together with critical comparisons of the three-dimensional exact solutions, the close agreement demonstrates the capability and accuracy of this present approach.