TY - GEN A1 - Stammen, Lisa A1 - Dornisch, Wolfgang ED - Korobenko, Artem ED - Evans, John ED - Hsu, Ming-Chen T1 - A convective isogeometric element formulation with mixed basis function degrees T2 - Isogeometric Analysis 2022 (IGA 2022) - Book of Abstracts N2 - 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. Y1 - 2022 UR - https://drive.google.com/file/d/1CYA-jTeVREnLcY2XIY1HuYiYutElGxXE/view SP - 103 ER - TY - GEN A1 - Stammen, Lisa A1 - Dornisch, Wolfgang T1 - On the use of mixed basis function degrees within a convective isogeometric element formulation T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - Solving linear elasticity problems using standard finite element methods, different locking phenomena can occur. In order to counteract these effects, mixed methods or formulations using higher approximation orders can be employed, for instance. As a consequence, this leads to an increased computational effort. Hence, a selective elevation of orders in decisive directions within a purely displacement-based element formulation is proposed in this contribution. Within isogeometric analysis (IGA), the geometry is discretized using non-uniform rational B-splines (NURBS), which simultaneously represent the basis functions for the analysis. Due to the fact that the geometry can be preserved exactly during analysis, this can increase the accuracy of results. In this contribution, convective basis systems that are aligned with the local geometry are employed combined with selective order elevation. The required convective basis systems are interpolated from those determined in each control point. Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202200159 SN - 1617-7061 N1 - 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) VL - 23 IS - 1 ER - TY - GEN A1 - Stammen, Lisa A1 - Dornisch, Wolfgang ED - Klinkel, Sven ED - Klarmann, Simon T1 - Eine konvektive isogeometrische Elementformulierung mit angepassten Interpolationsordnungen T2 - Forschungskolloquium 2021 in 2022 : Baustatik-Baupraxis : Kloster Steinfeld Y1 - 2022 SN - 978-3-946090-15-1 SP - 51 EP - 52 PB - RWTH Aachen, Lehrstuhl für Baustatik und Baudynamik CY - Aachen ER - TY - GEN A1 - Marker, Paul A1 - Stammen, Lisa A1 - Bleicher, Achim T1 - Energy-efficient actuator placement for a convertible bending-active structure T2 - IASS Annual Symposium 2019 – Structural Membranes 2019, Form and Force, 7–10 October 2019, Barcelona, Spain Y1 - 2019 UR - https://congress.cimne.com/Formandforce2019/admin/files/fileabstract/a328.pdf SP - 1717 EP - 1724 CY - Barcelona, Spain ER - TY - GEN A1 - Stammen, Lisa A1 - Dornisch, Wolfgang T1 - Investigations on the use of adapted approximation orders for a convective IGA formulation T2 - 11th European Solid Mechanics Conference N2 - 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]. KW - Isogeometric analysis KW - adapted approximation orders KW - convective basis systems Y1 - 2022 UR - https://az659834.vo.msecnd.net/eventsairwesteuprod/production-abbey-public/cab20a58733c4d95bc33e1b330b064a2 CY - Galway, Irland ER - TY - GEN A1 - Stammen, Lisa T1 - A two-field isogeometric formulation with different continuities T2 - Virtual International Conference on Isogeometric Analysis / Solids and structures, 26.-29. Sept. 2021, Lyon (France) N2 - Isogeometric Analysis (IGA), which was founded by Hughes et al. [1], tries to unify Computer-aided design (CAD) and finite element analysis (FEA) by using the same model for geometry representation and analysis. Therefore, in contrast to common finite element analysis, non-uniform rational B-splines (NURBS) and other kinds of splines are used as shape functions instead of the usual polynomials. Due to the exact representation of the geometry, analysis results can be improved [1, 2]. For mixed formulations, stresses and/or strains or pressures are approximated independently and in addition to the usual displacement approximation. Using, this kind of method is more robust and offers more accurate results. Hence, such formulations can be employed to solve incompressible elasticity problems, for instance [3]. Recent investigations, e.g. [4], have already combined isogeometric analysis and mixed formulations in order to benefit from the advantages of both methods. In this contribution, a mixed isogeometric method is proposed in order to improve the analysis results and counteract different locking phenomena. Therefore, spline basis functions are used and the displacement shape functions of a two-dimensional isogeometric plane stress and plane strain element are supplemented by independent stress shape functions. These additional stress shape functions are chosen to be of one order lower compared to the displacement shape functions, but with adapted continuity. Evaluating the errors of the calculated displacements and stresses for a plane stress and an incompressible elasticity plane strain problem, it is shown that the proposed method can lead to an improved accuracy of results compared to a standard isogeometric formulation. Furthermore, the influence of different continuities on the convergence behavior and the accuracy of the results is investigated. Y1 - 2021 UR - https://iga2021.sciencesconf.org/program/graphic/date/2021-09-27 ER - TY - GEN A1 - Stammen, Lisa A1 - Dornisch, Wolfgang ED - Soriano, Enrique Nadal ED - Cardiel, Carmen Rodrigo ED - Casas, José Martinez T1 - A mixed isogeometric plane stress and plane strain formulation with different continuities for the alleviation of locking T2 - Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference N2 - 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. KW - Isogeometric Analysis KW - Mixed Formulations KW - Spline Basis Functions KW - Continuity KW - Locking Y1 - 2022 UR - https://yic2021.upv.es/book-of-abstracts/ SN - 978-84-9048-969-7 SP - 114 PB - Editorial Universitat Politècnica de València, CY - Valencia, Spanien ER - TY - GEN A1 - Stammen, Lisa A1 - Dornisch, Wolfgang T1 - Investigations on adapted interpolation orders for a mixed isogeometric plate formulation T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202300170 SN - 1617-7061 N1 - 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), December 2023 VL - 23 IS - 4 ER -