Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

A new hyper-elastic thin shell finite element of absolute nodal coordinate formulation (ANCF) is proposed based on the Kirchhoff–Love theory. Under the condition of plane stress, a two-dimensional compressible neo-Hookean constitutive model and a two-dimensional incompressible Mooney–Rivlin constitutive model for the thin shell element of ANCF are derived. Based on the continuum mechanics, the efficient analytical formulations of the internal forces and their Jacobians of the shell element are also deduced. Then, a computation methodology for performing the nonlinear static analysis including buckling analysis of hyper-elastic thin shells is proposed. To accurately track the load–displacement equilibrium path in the analysis, the arc-length method is used to solve the nonlinear algebraic equations. The dynamics of the thin shells made of different hyper-elastic materials is also comparatively studied by using the generalized-alpha algorithm. Finally, six case studies are given to validate the proposed hyper-elastic thin shell element and computation methodology. The influence of different constitutive models on the static and dynamic responses of thin shells is revealed.