Modeling of composite plates based on Reissner's Mixed Variational Theorem with variables separation

Abstract

a b s t r a c tIn this work, the modeling of laminated composite plates is performed through a variables separation approach based on a Reissner's Variational Mixed Theorem (RMVT). Both the displacement and transverse stress fields are approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z. This choice yields to a non-linear problem that can be solved by an iterative process. That consists of solving a 2D and 1D problem successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used.Numerical examples involving several representative laminates are addressed to show the accuracy of the present LayerWise (LW) method. It is shown that it can provide quasi-3D results less costly than classical LW computations. In particular, the estimation of the transverse stresses which are of major importance for damage analysis is very good.

Modeling of cylindrical composite shell structures based on the Reissner’s Mixed Variational Theorem with a variable separation method

“…The first one is solved on S, while the second one is solved on z . As in [80], the fixed point algorithm is stopped when the distance between two consecutive solutions is smaller than a fixed value ε 0 .…”

“…This is particularly suitable for the modeling of composite structures. Note that this method has been successfully applied to displacement-based plate/shell models in [76][77][78][79] and also to RMVT plate models in [80].…”