Nonlinear finite element treatment of unsymmetric laminated composite shells

Abstract

The concentration of the current contribution is on the geometrically nonlinear analysis of laminated composite shells employing the finite element method. For this purpose, the use is made of a higher-order shell model with extensible directors possessing twelve parameters, then the exact Green–Lagrange strains and the three-dimensional second Piola–Kirchhoff stress tensor are extracted based on the base vectors of the shell mid-surface. The principle of virtual work is adopted to derive the weak form of governing equations. A computationally efficient four-node shell element is designed and to remedy the locking problems involving transverse shear, membrane and curvature–thickness ones, the ANS (assumed natural strain) approach and the assumed strain scheme are used. Finally, standard benchmarks are solved for isotropic materials allowing geometric nonlinearity to examine the performance of the proposed shell element and then results of thin and thick layered composite structures are presented. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023.