Axiomatic/asymptotic analysis of refined layer-wise theories for composite and sandwich plates

Abstract

This article deals with layer-wise (LW) models for composite and sandwich plates. Refined layer-wise models are built according to the Carrera Unified Formulation (CUF), which has been developed over the last decade for beams, plate, and shell theories. CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. In this article, displacement variables are expanded along the layer thickness through Legendre polynomials. Comparisons with previous analysis based on equivalent single layer (ESL) approaches are given. The effect of each term of the expansion on the accuracy of stress/displacement components for the static response of composite and sandwich plates is analyzed. Ineffective terms are discarded from the expansion in order to save computational cost. The reduced models obtained, which are denoted as mixed axiomatic/asymptotic models, are as accurate as full expansion models. Numerical analysis is restricted to closed-form solutions via Navier-type solutions. A number of problems related to laminated and sandwich structures are solved and related reduced models are built by varying geometrical, lay-up, and mechanical parameters. Results show that in some cases (in particular those related to sandwich plates) reduced layer-wise models can save up to 50% of the degrees-of-freedom of the full models without significant accuracy losses. It is found that the significant terms related to reduced models are very much subordinated to the problems considered and that from that point of view the use of a framework that can generate any theory, such as CUF, appears very suitable to build reduced models for plates.