A new solid-shell stabilization-free Virtual Element

This work introduces a framework for the construction of locking-free, three-dimensional stabilization-free Virtual Elements. The presented methodology is then used to build, for the first time in the literature, a polyhedral solid-shell element.To that end, the well-known Hu–Washizu variational approach is used to obtain an enhanced strain formulation of the linear elasticity problem. This common methodology of the shell Finite Element literature allows for the introduction of additional strain parameters to improve the element kinematics. After partitioning the space domain with a set of star-convex polyhedrons, a local coordinate system is associated to each element of the mesh using its principal axes of inertia. This allows for the construction of oriented functional spaces for the discrete strain, stress and displacement fields. In the presented analysis, those are carefully chosen to reduce transverse shear locking and improve membrane and pinching strain approximations. The proposed developments result in the construction of the ss5VE (solid-shell 5 parameter Virtual Element), a solid-shell polyhedral element designed for the analysis of thin structures. The latter is tested numerically on various test cases, proving to be a significant improvement in comparison with first-order stabilization-free Virtual Element Methods.