Development of Invariant-Based Triangular Element for Nonlinear Thermoelastic Analysis of Laminated Shells

A finite element formulation is proposed for geometrically nonlinear analysis of thermally loaded composite laminated shells taking into account temperature-dependent properties of the material. The laminated shell is modeled by an equivalent single layer under the assumptions of the first-order shear deformation theory. A three-node triangular element is formulated using three natural coordinates directed along the element sides. The study focuses on representation of the total potential thermoelastic energy of anisotropic shell in terms of combined invariants which depend on the natural components of the strain tensor and those of the tensors describing mechanical and physical properties of the material. Based on the resulting expression for the energy, compact and algorithmic relations are derived for computing coefficients of the first and second variations of the strain energy of the finite element which are necessary to formulate the equations for finding equilibrium states and to examine their stability. Some examples are presented to demonstrate the ability of the finite element to deal with postbuckling behavior of thermally loaded laminated shells.