Modelling of Variable Stiffness Plates Based on Mechanics of Structure Genome

Abstract

A plate model for laminates with variable stiffness materials is constructed based on the mechanics of structure genome. The modelling aims at minimizing the difference between the potential energy of original 3D model and the equivalent plate model. In this study, a line through the thickness of the plate is chosen as the structure genome, so the the analysis of the original 3D model is separated into a 1D through the thickness analysis and a 2D global plate analysis. Energy of the 3D model is expressed in terms of 3D strains, obtained from continuum mechanics, and energy of the equivalent plate model is expressed in terms of 2D membrane strains and curvatures of the reference surface as well as the warping functions. Warping functions are solved in terms of 2D strains and are used for deriving the constitutive relation as well as recovering the local fields. Several numerical examples are studied to verify the presented theory.