Multipatch isogeometric analysis for geometrically exact shell elements using B-bar method and Bézier extraction

Abstract

In the present study, a multipatch isogeometric analysis method for geometrically exact shell problems is proposed. Generalized curvilinear coordinates are used for the first-order shear-deformable geometrically exact shell elements. This general tensor-based shell formulation can be directly linked to a computer-aided design system such as nonuniform rational basis spline (NURBS), which is represented by two parameters. Nitsche’s method for patch-to-patch connections in conforming or nonconforming meshes is adopted. The compatibility conditions between NURBS patches in Nitsche’s coupling are weakly imposed using the continuity of displacements, rotations, and stress resultants. The final algebraic equation for the solution fields has a simple symmetric form with previously derived strain–displacement relation matrices and material modulus for membrane, bending, and transverse shear terms. To alleviate the locking phenomenon, the B-bar method, which utilizes the strain projected onto a lower-order field, is used in the isogeometric shell element. Reduced-order B-splines for strain fields are constructed based on tying points, which eased the locking phenomenon compared with the classical B-bar method. To further alleviate additional shell locking by a higher-order regularity, the Bézier extraction method is adopted to reduce the element regularity. The proposed combination of Nitsche’s coupling and B-bar projection demonstrates the superior accuracy and robustness in the multipatch isogeometric shell examples with a high convergence rate.