Rotation-Free Bernstein-Bézier Elements for Thin Plates and Shells - Development and Validation

Abstract

A new finite element procedure for thin plates and shells is presented. It combines a geometrically non-linear, rotation-free Kirchhoff–Love formulation with triangular and quadrilateral Bernstein–Bézier elements and C1 and G1 inter-element continuity conditions, as well as boundary conditions for clamping and for symmetry. The formulation is free from transverse-shear locking and relies on a high polynomial degree to mitigate membrane locking. Bernstein–Bézier elements are, as opposed to NURBS, suitable for arbitrary triangulations. Unlike with Hermite elements, no stress concentrations occur if the boundary is partially clamped and the formulation can be potentially extended to stiffened plates and shells and to step-wise changes of thickness and material properties. The convergence behaviour is demonstrated and the computational efficiency is compared with that of C° Reissner–Mindlin elements on several numerical examples.