Non‐linear analysis of rectangular laminates under end shortening, using shear deformation plate theory

Abstract

AbstractConsideration is given to the prediction of the geometrically non‐linear elastic response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane. At the loaded ends lateral in‐plane expansion is either allowed freely or is prevented completely. Material properties of the laminates are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. First‐order shear deformation plate theory is used as the mathematical model of laminate behaviour and the non‐linearity is introduced in the strain‐displacement equations in the manner of the von Karman assumptions. The finite strip method is used as the main numerical analysis procedure and subsidiary use is made of the finite element method. Close comparison of results generated using the two methods is demonstrated in applications ranging from isotropic plates to unsymmetric anisotropic laminates. Further comparison with the results of an earlier‐developed finite strip method, wherein properties are based on the use of classical plate theory, shows the effect of through‐thickness shearing action in different situations.