Shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell element for linear and geometrically nonlinear analyses

Abstract

AbstractA high‐performance shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell finite element method is proposed for linear and geometrically nonlinear analyses of shells. First, an arbitrary polygonal Mindlin–Reissner plate element and an arbitrary polygonal membrane element with drilling degrees of freedom are constructed based on hybrid displacement‐function and hybrid stress‐function methods, respectively. Both elements have only two corner nodes along each edge. Second, by assembling the plate and the membrane elements, an arbitrary polygonal flat shell element is constructed. Third, based on the corotational method, a proper best‐fit corotated frame for geometrically nonlinear polygonal elements is designed. By updating the analytical trial functions of shell element in each increment step, the original linear flat shell element is generalized to a geometrically nonlinear model. Numerical examples show that the new element possesses excellent performance for both linear and geometrically nonlinear analyses, and possesses outstanding flexibility in dealing with complex loading distributions and mesh shapes.