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

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.

A Shell Description of Beams Incorporating Transverse Thickness Strain Energies for Receding Contact

The geometrically exact nonlinear deflection of a beamshell is considered here as an extension of the formulation derived by Libai and Simmonds (1998, The Nonlinear Theory of Elastic Shells, Cambridge University Press, Cambridge, UK) to include deformation through the thickness of the beam, as might arise from transverse squeezing loads. In particular, this effect can lead to receding contact for a uniform beamshell resting on a smooth, flat, rigid surface; traditional shell theory cannot adequately such behavior. The formulation is developed from the weak form of the local equations for linear momentum balance, weighted by an appropriate tensor. Different choices for this tensor lead to both the traditional shell equations corresponding to linear and angular momentum balance, as well as the additional higher-order representation for the squeezing deformation. In addition, conjugate strains for the shell forces are derived from the deformation power, as presented by Libai and Simmonds. Finally, the predictions from this approach are compared against predictions from the finite element code abaqus for a uniform beam subject to transverse applied loads. The current geometrically exact shell model correctly predicts the transverse shell force through the thickness of the beamshell and is able to describe problems that admit receding contact.

Shear Effects on Energy Dissipation From an Elastic Beam on a Rigid Foundation

This work describes the energy dissipation arising from microslip for an elastic shell incorporating shear and longitudinal deformation resting on a rough-rigid foundation. This phenomenon is investigated using finite element (FE) analysis and nonlinear geometrically exact shell theory. Both approaches illustrate the effect of shear within the shell and observe a reduction in the energy dissipated from microslip as compared to a similar system neglecting shear deformation. In particular, it is found that the shear deformation allows for load to be transmitted beyond the region of slip so that the entire interface contributes to the load carrying capability of the shell. The energy dissipation resulting from the shell model is shown to agree well with that arising from the FE model, and this representation can be used as a basis for reduced order models that capture the microslip phenomenon.