Nonlinear displacement-based finite-element analyses of composite shells—A new total Lagrangian formulation

Abstract

Presented here is a new total Lagrangian finite-element formulation for general laminated composite shells undergoing large-displacement, large-rotation, and large-strain motion. The theory fully accounts for geometric nonlinearities (large rotations), large in-plane strains, general initial curvatures, transverse shear deformations, and interlaminar normal stresses by using Jaumann stress and strain measures, an exact coordinate transformation, and a new concept of orthogonal virtual rotations. In addition, with the inclusion of transverse normal and shear stresses, the theory accounts for three-dimensional stress effects and gives accurate effective structural stiffnesses. Because of the inclusion of all possible initial curvatures, the developed strain-displacement expressions can be used for any surface structures and are fully nonlinear, which contain von Karman strains as a special case. Moreover, the theory accounts for the continuity of interlaminar shear and peeling stresses and the normal and shear stress conditions on the bonding surfaces by using a new layer-wise local displacement field, which results in a higher-order shear theory that contains most shear deformation theories as special cases. In this paper, we develop a fully nonlinear displacement-based finite-element formulation based on the derived shell theory. The verification and accuracy of the theory will be presented in a subsequent paper by comparing obtained numerical results with some exact solutions.