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Rotation-free Bernstein–Bézier elements for thin plates and shells — development and validation

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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–Bezier elements and C 1… Click to show full abstract

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–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°Reissner–Mindlin elements on several numerical examples.

Keywords: thin plates; free bernstein; rotation free; plates shells

Journal Title: Computer Methods in Applied Mechanics and Engineering
Year Published: 2019

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