%0 Conference Paper %1 oesterle2016hierarchic %A Oesterle, Bastian %A Bischoff, Manfred %A Ramm, Ekkehard %B M. Kleiber, T. Burczynski, K. Wilde, J. Gorski, K. Winkelmann, L. Smakosz (Eds.) "Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues". Proceedings of the 3rd Polish Congress of Mechanics (PCM) & 21st International Conference on Computer Methods in Mechanics (CMM), Gdansk, Poland, 8-11 September 2015 %D 2016 %K IGA_SHELL ibb from:maltevonscheven inproceedings %P 41-46 %T Hierarchic isogeometric analyses of beams and shells %X The higher inter-element continuity of the Isogeometric Analysis (IGA) applying NURBS functions for geometry as well as mechanics opens up new possibilities in the analysis of thin-walled structures, i.e. beams, plates and shells. The contribution addresses the straightforward implementation of classical theories requiring C1-continuity, such as the Euler-Bernoulli beam and Kirchhoff-Love shell theory. Based on these “simplest” models shear deformable theories, introducing Timoshenko and Reissner-Mindlin kinematics, are formulated in a hierarchic manner. In contrast to the usual Finite Element concept using total rotations the present model picks up traditional formulations introducing incremental rotations as primary variables. Furthermore an alternative version is discussed with a split of the displacements into bending and transverse shear parts. Both hierarchic concepts can be easily extended to 3D–shell models. The key aspect of this alternative parameterization is the complete a-priori removal of the transverse shear locking and curvature thickness locking (in the case of 3D-shells).

@inproceedings{oesterle2016hierarchic, abstract = {The higher inter-element continuity of the Isogeometric Analysis (IGA) applying NURBS functions for geometry as well as mechanics opens up new possibilities in the analysis of thin-walled structures, i.e. beams, plates and shells. The contribution addresses the straightforward implementation of classical theories requiring C1-continuity, such as the Euler-Bernoulli beam and Kirchhoff-Love shell theory. Based on these “simplest” models shear deformable theories, introducing Timoshenko and Reissner-Mindlin kinematics, are formulated in a hierarchic manner. In contrast to the usual Finite Element concept using total rotations the present model picks up traditional formulations introducing incremental rotations as primary variables. Furthermore an alternative version is discussed with a split of the displacements into bending and transverse shear parts. Both hierarchic concepts can be easily extended to 3D–shell models. The key aspect of this alternative parameterization is the complete a-priori removal of the transverse shear locking and curvature thickness locking (in the case of 3D-shells).}, added-at = {2021-03-09T13:40:59.000+0100}, author = {Oesterle, Bastian and Bischoff, Manfred and Ramm, Ekkehard}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2435a6ba5525db61de5bdfabac248a2c4/ibb-publication}, booktitle = {M. Kleiber, T. Burczynski, K. Wilde, J. Gorski, K. Winkelmann, L. Smakosz (Eds.) "Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues". Proceedings of the 3rd Polish Congress of Mechanics (PCM) & 21st International Conference on Computer Methods in Mechanics (CMM), Gdansk, Poland, 8-11 September 2015}, interhash = {8149db04f379ad101af84c92ae8b7c3d}, intrahash = {435a6ba5525db61de5bdfabac248a2c4}, keywords = {IGA_SHELL ibb from:maltevonscheven inproceedings}, pages = {41-46}, timestamp = {2021-03-09T12:40:59.000+0100}, title = {Hierarchic isogeometric analyses of beams and shells}, year = 2016 }