Finite-rotation theories for composite laminates

Abstract

For the finite-element analysis of arbitrary composite laminates various finite-rotation theories are presented in a single formulation. First a refined theory is derived which allows a quadratic shear deformation distribution across the thickness. The so-called difference vector appearing in the kinematic relations is expressed in terms of rotational degrees of freedom permitting a clear determination of the deformed normal vector in every nonlinear range. The constitutive relations derived are applicable to orthotropic material properties varying arbitrarily across the thickness and to curvilinear laminate coordinates as well. This refined theory is then transformed into simplified theories of Kirchhoff-Love and Mindlin-Reissner types. Finally, the last formulation is used to formulate a layer-wise theory able to grasp the shear deformations very accurately. Kinematic relations and the corresponding constraints are presented in two alternative forms suitable for the application of isoparametric and classical finite-element formulations.