Geometrically nonlinear formulation of a 48 D.O.F. quadrilateral shell element with rational B‐spline geometry

Abstract

Abstract A geometrically nonlinear formulation for a 48 degrees‐of‐freedom (d.o.f.) quadrilateral shell element is presented. Each of the three displacement functions of u , v and w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized ratronal B‐spline functions which may be linked to the geometric data bases generated by the computer‐aided design system. The displacement functions and the 48 d.o.f. are expressed in both curvilinear and Cartesian forms, whereas the strain‐displacement equations are expressed in curvilinear co‐ordinates. The use of Cartesian displacement functions and degrees‐of‐freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap‐through buckling of a spherical cap and large deflection of a semi‐toroidal bellows shell. Results compare well with alternative solutions.