Invariant-based formulation of a triangular finite element for geometrically nonlinear thermal analysis of composite shells

Abstract

The paper describes an invariant-based formulation of a triangular finite element for geometrically nonlinear analysis of shear flexible composite shells subjected to thermal loads. Transverse shear deformation is taken into account using the first order shear deformation theory. The focus is on the representation of the strain energy of the shell in terms of invariant quantities which depend on the components of the strain tensor and elastic constants of the material. Based on the invariant expression for the strain energy density, algorithmic relations are derived for computing the stiffness matrix of the shell finite element. The finite element formulation is used to study stability of equilibrium configurations in the region of large thermal displacements. A positive definite second variation of the total energy is used as a sufficient criterion for stability of equilibrium configurations. A series of numerical examples are given to estimate performance of the finite element in solving nonlinear problems of composite plates and shells under uniform temperature rise. Solution of some classical problems of laminated plates and shells shows that there exist equilibrium configurations not previously reported in the literature.