Rotation-free Bernstein-Bezier elements for thin plates and shells - development and validation

摘要

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-Bezier elements and C(1 )and G(1) 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-Bezier 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 degrees Reissner-Mindlin elements on several numerical examples. (C) 2019 Elsevier B.V. All rights reserved.