TY - GEN A1 - Zou, Zhihui A1 - Scott, Michael A. A1 - Borden, Michael J. A1 - Thomas, Derek C. A1 - Dornisch, Wolfgang A1 - Brivadis, Ericka T1 - Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry T2 - Computer Methods in Applied Mechanics and Engineering N2 - In this paper we develop the isogeometric Bézier dual mortar method. It is based on Bézier extraction and projection and is applicable to any spline space which can be represented in Bézier form (i.e., NURBS, T-splines, LR-splines, etc.). The approach weakly enforces the continuity of the solution at patch interfaces and the error can be adaptively controlled by leveraging the refineability of the underlying slave dual spline basis without introducing any additional degrees of freedom. As a consequence, optimal higher-order convergence rates can be achieved without the need for an expensive shared master/slave segmentation step. We also develop weakly continuous geometry as a particular application of isogeometric Bézier dual mortaring. Weakly continuous geometry is a geometry description where the weak continuity constraints are built into properly modified Bézier extraction operators. As a result, multi-patch models can be processed in a solver directly without having to employ a mortaring solution strategy. We demonstrate the utility of the approach on several challenging benchmark problems. KW - Mortar methods KW - Isogeometric analysis KW - Bézier extraction KW - Bézier projection Y1 - 2018 U6 - https://doi.org/10.1016/j.cma.2018.01.023 SN - 0045-7825 VL - 333 SP - 497 EP - 534 ER - TY - GEN A1 - Zou, Zhihui A1 - Scott, Michael A. A1 - Miao, Di A1 - Bischoff, Manfred A1 - Oesterle, Bastian A1 - Dornisch, Wolfgang T1 - An isogeometric Reissner–Mindlin shell element based on Bézier dual basis functions: Overcoming locking and improved coarse mesh accuracy T2 - Computer Methods in Applied Mechanics and Engineering N2 - We develop a mixed geometrically nonlinear isogeometric Reissner–Mindlin shell element for the analysis of thin-walled structures that leverages Bézier dual basis functions to address both shear and membrane locking and to improve the quality of computed stresses. The accuracy of computed solutions over coarse meshes, that have highly non-interpolatory control meshes, is achieved through the application of a continuous rotational approach. The starting point of the formulation is the modified Hellinger–Reissner variational principle with independent displacement, membrane, and shear strains as the unknown fields. To overcome locking, the strain variables are interpolated with lower-order spline bases while the variations of the strain variables are interpolated with the corresponding Bézier dual bases. Leveraging the orthogonality property of the Bézier dual basis, the strain variables are condensed out of the system with only a slight increase in the bandwidth of the resulting linear system. The condensed approach preserves the accuracy of the non-condensed mixed approach but with fewer degrees of freedom. From a practical point of view, since the Bézier dual basis is completely specified through Bézier extraction, any spline space that admits Bézier extraction can utilize the proposed approach directly. KW - Isogeometric analysis KW - Reissner–Mindlin shells KW - Dual basis functions KW - Locking Y1 - 2020 U6 - https://doi.org/10.1016/j.cma.2020.113283 SN - 0045-7825 VL - 370 ER -