Invariant-Based Geometrically Nonlinear Formulation of a Triangular Finite Element of Laminated Shells

A non-standard approach is proposed to develop a simple and computationally effective triangular finite element applicable to geometrically nonlinear analysis of composite shells. The approach is based on the natural components of the stress and strain tensors and their invariants which allow one to express the strain energy of the shell in a compact form without coordinate transformations. The natural components of the tensors are referred to fibers oriented along the triangle edges. An advantage of using the natural strains is that it suffices to approximate one-dimensional functions rather than two-dimensional strain fields over the elemental area. To this end, analytical solutions of auxiliary beam bending problems are used. The validity and accuracy of the approach proposed are verified using benchmark solutions and numerical data available in the literature.