Finite Element Modeling of Geometrically Exact Shell With Large Deformation and Rotation

Abstract

Abstract This paper developed a new geometrically exact shell element to model the relatively thin structures with large deformations and arbitrary rigid motions. The deformations were well decoupled from rigid motions by using the direct modeling approach. The rotation-free Green-Lagrange strain tensor described the large deformations together with geometrical nonlinearities. Meanwhile, the Wiener-Milenković parameter was applied to vectorial parameterize the arbitrary rotations of the fiber avoiding the singularities usually occurred in the classical shell formula. This paper also designed a new interpolating algorithm without losing objectivity to discretize the vectorial parameters, which improves the robustness of new shell element. The application of Mixed Interpolation of Tensorial Components with 9 nodes (MITC9) makes the shell element shear-locking free and with second-order accuracy. Each node contains five degrees of freedom, three for translations and two for rotations, achieving a minimal set representation of arbitrary motions. These innovations contribute to a new shell formula featuring high computational efficiency with good accuracy. Finally, two flexible multibody dynamic models are discretized by this new shell element. The numerical simulation results of the new shell element have been verified to demonstrate the capability of new shell element dealing with large deformations and arbitrary motions of thin structures.