On plane stress and plane strain in classical lamination theory

Abstract

Classical Lamination Theory combines the specially orthotropic nature of unidirectional composite plies with the assumptions of Kirchhoff plate theory to arrive at the in-plane properties of the laminate. Traditionally, the derivation assumes a plane stress state in each lamina prior to performing the rotational transformation from the lamina coordinates to the laminate coordinates, resulting in an incomplete formulation of the out-of-plane properties. In this work the rotational transformation of each lamina is performed prior to applying the plane stress or strain simplifications, resulting in an accurate formulation of the out-of-plane properties. Both plane stress and plane strain are considered. To illustrate the new formulation's ability to accurately predict out-of-plane properties, an optimization is performed to find laminates that exhibit the extrema of the out-of-plane Poisson's ratios. Verification of nearly optimal laminates with finite element analysis and experimental testing demonstrates improved accuracy of the new formulation.