Mixed bernstein-bézier construction from unstructured mesh for higher-order finite element analysis of plates and shells

Bernstein polynomials possess several efficient and stable algorithms and have been widely used in engineering fields such as CAGD, computer graphics, and finite element analysis. In this paper, a mixed Bernstein basis function based higher-order finite element method is developed from a geometric view for the analysis and simulation of plate and shell structures represented by unstructured triangular and quadrilateral mesh. Triangular Bernstein-Bézier patches and tensor-product Bézier patches are constructed in a simple and intuitive way over triangular and quadrilateral elements, respectively. The h- and p- refinements can be easily implemented on the constructed mixed Bernstein-Bézier patches. Reissner-Mindlin theory is employed to deduce the governing equations and stiffness matrices of plates and shells. Several numerical examples including classical benchmark problems and engineering applications are studied to validate the accuracy, robustness, and convergence of the presented Bernstein-Bézier finite element method. © 2020 CAD Solutions, LLC.