@misc{StammenDornisch, author = {Stammen, Lisa and Dornisch, Wolfgang}, title = {Eine konvektive isogeometrische Elementformulierung mit angepassten Interpolationsordnungen}, series = {Forschungskolloquium 2021 in 2022 : Baustatik-Baupraxis : Kloster Steinfeld}, journal = {Forschungskolloquium 2021 in 2022 : Baustatik-Baupraxis : Kloster Steinfeld}, editor = {Klinkel, Sven and Klarmann, Simon}, publisher = {RWTH Aachen, Lehrstuhl f{\"u}r Baustatik und Baudynamik}, address = {Aachen}, isbn = {978-3-946090-15-1}, pages = {51 -- 52}, language = {de} } @misc{StammenDornisch, author = {Stammen, Lisa and Dornisch, Wolfgang}, title = {Investigations on the use of adapted approximation orders for a convective IGA formulation}, series = {11th European Solid Mechanics Conference}, journal = {11th European Solid Mechanics Conference}, address = {Galway, Irland}, pages = {1}, abstract = {In isogeometric analysis (IGA), which was founded by Hughes et al. [1], the geometry representation is used for the analysis as well. Hence, due to the exact description of the geometry, analysis results can be improved [1, 2]. Therefore, different kinds of splines, like non-uniform rational B-splines (NURBS) [3], are used as shape functions for the discretizations. In linear elasticity problems, for standard formulations, shear locking phenomena can occur due to the different orders of the derivatives in the unbalanced strain-displacement relation. This effect can be reduced using shape functions of higher order, causing an increased computational effort. For low-order formulations, the degrees of shape functions can be adapted accordingly in order to counteract this effect. For an isogeometric displacement-stress mixed Reissner-Mindlin shell formulation such adapted approximation spaces were investigated in [4], for instance. In [5], additionally to a proper choice of shape function spaces, convective coordinates are employed in the derivation of isogeometric shell formulations. In this contribution, a convective displacement-based isogeometric formulation is introduced, wherein the displacements in the different surface directions are approximated independently using appropriate approximation orders. Therefore, two different meshes are generated from the NURBSdescribed geometry representation, employing order elevation solely for one of the two surface directions. Thus, the order is elevated in opposite directions for these two meshes. The two different possibilities of order elevation are investigated. Furthermore, the use of different convective basis systems is studied. This comprises convective basis systems in each control point, computed according to [6], as well as convective basis systems determined from the local geometry direction in each integration point. The achieved results are compared to whose of a two-dimensional displacementstress mixed formulation presented in [7].}, language = {en} } @misc{StammenDornisch, author = {Stammen, Lisa and Dornisch, Wolfgang}, title = {A mixed isogeometric plane stress and plane strain formulation with different continuities for the alleviation of locking}, series = {Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference}, journal = {Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference}, editor = {Soriano, Enrique Nadal and Cardiel, Carmen Rodrigo and Casas, Jos{\´e} Martinez}, publisher = {Editorial Universitat Polit{\`e}cnica de Val{\`e}ncia,}, address = {Valencia, Spanien}, isbn = {978-84-9048-969-7}, pages = {114}, abstract = {Isogeometric analysis and mixed finite element methods offer promising opportunities to enhance analysis results for complex problems like incompressible elasticity and are able to cope with different locking phenomena. In this contribution, a mixed two-field isogeometric formulation with independent approximations for displacements and stresses is derived, and its ability to counteract different types of locking is investigated using two examples. Furthermore, the influence of the continuity of the stress shape functions on the accurancy of results and convergence behaviour is shown.}, language = {en} } @misc{StammenDornisch, author = {Stammen, Lisa and Dornisch, Wolfgang}, title = {Investigations on adapted interpolation orders for a mixed isogeometric plate formulation}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {23}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {4}, issn = {1617-7061}, doi = {10.1002/pamm.202300170}, abstract = {In order to overcome locking effects that especially occur for lower order finite element formulations, different methods can be employed. This can be conducted using mixed formulations or adapted approximation orders, for instance. Hence, in order to tackle shear locking that is caused by non-matching interpolation degrees in the shear strain equation, an irreducible and a mixed Reissner-Mindlin plate formulation with accordingly adapted conforming discretizations are derived within the scope of this contribution. In addition, non-uniform rational B-splines (NURBS) are employed therefore, in order to benefit from the properties and refinement strategies offered by isogeometric analysis (IGA) and to achieve more accurate results. The effect of various combinations of interpolation orders on the convergence behavior and the ability to alleviate locking is investigated for both the irreducible and the mixed isogeometric plate formulation and examined for a benchmark example. This is also supplemented by investigations on the stability of the considered variants, tested by the existence of the correct number of zero-energy modes.}, language = {en} } @misc{StammenDornisch, author = {Stammen, Lisa and Dornisch, Wolfgang}, title = {A convective isogeometric element formulation with mixed basis function degrees}, series = {Isogeometric Analysis 2022 (IGA 2022) - Book of Abstracts}, journal = {Isogeometric Analysis 2022 (IGA 2022) - Book of Abstracts}, editor = {Korobenko, Artem and Evans, John and Hsu, Ming-Chen}, pages = {103}, abstract = {Employing isogeometric analysis (IGA), the geometry of structures is discretized by non-uniform rational B-splines (NURBS), which simultaneously provide the basis functions for the corresponding analysis as well. Due to the high continuity within patches, a unique local convective basis system, which corresponds to the local geometry directions of the mesh, can be defined in every point. Locking Phenomena, which strongly affect purely displacement-based low order elements, can be counteracted by employing particular methods or higher polynomial degrees; both options increase the resulting computational effort significantly. Using order elevation only in specific directions has the potential to optimize the ratio between locking counteraction and computational costs. In this contribution, the use of directed deformations based on convective basis systems in each control point is proposed for a displacement-based isogeometric formulation with specifically adapted orders. Therefore, distinct meshes for the interpolation of the displacements in each direction are generated based on the initial geometry. Subsequently, the order of every mesh is elevated in only one direction. Consequently, different possibilities for the combination of order elevations have to be examined. This procedure is conducted for a two-dimensional linear elasticity problem. The benefit of a convective formulation with direction dependent degrees is shown by a comparison to a standard isogeometric formulation. Furthermore, the impact of the directions selected for order elevation on the accuracy of the results is investigated.}, language = {en} } @misc{DornischAzizi, author = {Dornisch, Wolfgang and Azizi, Nima}, title = {Vergleich zwischen isogeometrischen und spektralen Reissner-Mindlin Schalenelementen}, series = {15. Fachtagung Baustatik - Baupraxis, 4.-5. M{\"a}rz 2024, Hamburg}, journal = {15. Fachtagung Baustatik - Baupraxis, 4.-5. M{\"a}rz 2024, Hamburg}, pages = {8}, abstract = {Der Beitrag vergleicht die Genauigkeit von Reissner-Mindlin-Schalenelementen zwischen der isogeometrischen Methode und der spektralen Elemente-Methode. W{\"a}hrend die erste durch die hohe Kontinuit{\"a}t zwischen den Elementen eine sehr hohe Genauigkeit in Bezug auf Anzahl der Freiheitsgrade aufweist, besticht die letztere durch eine einfachere Formulierung und eine bessere Konditionierung auch f{\"u}r sehr hohe Ansatzordnungen.}, language = {de} }