Geometrically nonlinear analysis of composite plates through asymptotically accurate isoenergetic theory

Abstract

This study introduces a novel approach for analyzing composite plates. The methodology employs the Variational Asymptotic Method (VAM) in an innovative and mathematically rigorous manner to dimensionally reduce the plate using its three-dimensional ($3D$) model energy. The VAM decouples the $3D$ plate problem into a $1D$ through-the-thickness analysis and a $2D$ planar problem. The Through-the-thickness $1D$ analysis is done ensuring the continuity of displacements and transverse stresses. This elegantly reduces the dimension of the plate by expressing the $3D$ variables in terms of $2D$ variables. However, the obtained reduced-order model, while accurate, is not directly suitable for $2D$ extremization to solve for the remaining $2D$ variables. To address this challenge, Concept of isoenergetics is introduced, which eliminates higher-order derivatives, thereby facilitating efficient extremization and reducing computational complexities. The validity and versatility of our proposed methodology are demonstrated through comparisons with benchmark problems from the literature and $3D$ finite element analysis.