@misc{ZouScottBordenetal., author = {Zou, Zhihui and Scott, Michael A. and Borden, Michael J. and Thomas, Derek C. and Dornisch, Wolfgang and Brivadis, Ericka}, title = {Isogeometric B{\´e}zier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {333}, journal = {Computer Methods in Applied Mechanics and Engineering}, issn = {0045-7825}, doi = {10.1016/j.cma.2018.01.023}, pages = {497 -- 534}, abstract = {In this paper we develop the isogeometric B{\´e}zier dual mortar method. It is based on B{\´e}zier extraction and projection and is applicable to any spline space which can be represented in B{\´e}zier 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 B{\´e}zier dual mortaring. Weakly continuous geometry is a geometry description where the weak continuity constraints are built into properly modified B{\´e}zier 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.}, language = {en} } @misc{ZouScottMiaoetal., author = {Zou, Zhihui and Scott, Michael A. and Miao, Di and Bischoff, Manfred and Oesterle, Bastian and Dornisch, Wolfgang}, title = {An isogeometric Reissner-Mindlin shell element based on B{\´e}zier dual basis functions: Overcoming locking and improved coarse mesh accuracy}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {370}, journal = {Computer Methods in Applied Mechanics and Engineering}, issn = {0045-7825}, doi = {10.1016/j.cma.2020.113283}, pages = {35}, abstract = {We develop a mixed geometrically nonlinear isogeometric Reissner-Mindlin shell element for the analysis of thin-walled structures that leverages B{\´e}zier 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 B{\´e}zier dual bases. Leveraging the orthogonality property of the B{\´e}zier 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 B{\´e}zier dual basis is completely specified through B{\´e}zier extraction, any spline space that admits B{\´e}zier extraction can utilize the proposed approach directly.}, language = {en} }