Phenomenological invariant-based finite-element model for geometrically nonlinear analysis of thin shells

A Kirchhoff–Love type curved triangular finite element is proposed for geometrically nonlinear analysis of elastic isotropic shells undergoing small strains but large displacements. The finite-element formulation is based on the expression of the strain energy in terms of invariants of the strain and curvature-change tensors of the shell middle surface. The element sides are chosen as three independent directions for determining the strains and curvature changes. The emphasis is put on improvement of the bending behavior of the element so that the element is able to undergo finite curvature changes. Recursive relations are obtained for exactly calculating the coefficients of the first- and second-order variations of the strain energy of the finite element which are necessary to formulate the equilibrium and stability conditions of the discrete model of a shell. A shell finite element with 15 degrees of freedom is developed and tested. Numerical examples are presented to demonstrate the accuracy and mesh convergence of the finite-element solutions.