Reissner–Mindlin shell implementation and energy conserving isogeometric multi‐patch coupling

Sommerwerk, Kay; Woidt, Malte; Haupt, Matthias; Horst, Peter

doi:10.1002/nme.5316

Cited by 19 publications

(8 citation statements)

References 56 publications

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“…Second, IGA offers a rigorous framework for simulating the mechanics of masonry and the equilibrium state of the surface, which is a distinct advantage over the network-based TNA methods. Simulation of shell structures with IGA has been widely investigated to calculate the inner stress state of shells under outer loads [22][23][24]. Cazzani et al applied a NURBS based isogeometric beam model to simulate the historical masonry arches [25].…”

Section: Related Workmentioning

confidence: 99%

Design of self-supporting surfaces with isogeometric analysis

Xia

Mantzaflaris

Jüttler

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Self-supporting surfaces are widely used in contemporary architecture, but their design remains a challenging problem. This paper aims to provide a heuristic strategy for the design of complex selfsupporting surfaces. In our method, non-uniform rational B-spline (NURBS) surfaces are used to describe the smooth geometry of the self-supporting surface. The equilibrium state of the surface is derived with membrane shell theory and Airy stresses within the surfaces are used as tunable variables for the proposed heuristic design strategy. The corresponding self-supporting shapes to the given stress states are calculated by the nonlinear isogeometric analysis (IGA) method. Our validation using analytic catenary surfaces shows that the proposed method finds the correct selfsupporting shape with a convergence rate one order higher than the degree of the applied NURBS basis function. Tests on boundary conditions show that the boundary's influence propagates along the main stress directions in the surface. Various self-supporting masonry structures, including models with complex topology, are constructed using the presented method. Compared with existing methods such as thrust network analysis and dynamic relaxation, the proposed method benefits from the advantages of NURBS-based IGA, featuring smooth geometric description, good adaption to complex shapes and increased efficiency of computation.

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Section: Related Workmentioning

confidence: 99%

Design of self-supporting surfaces with isogeometric analysis

Xia

Mantzaflaris

Jüttler

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…In case of arbitrary non-conforming interfaces, the coupling conditions are imposed in a weak sense. There are different approaches that can be employed; namely penalty methods [34][35][36], mortar methods [34,[37][38][39][40][41][42][43], and Nitsche methods [44][45][46][47][48]. Because stiffened structures are built with thin shells, we seek to consider isogeometric Kirchhoff-Love shell formulation.…”

Section: Introductionmentioning

confidence: 99%

The embedded isogeometric Kirchhoff–Love shell: From design to shape optimization of non-conforming stiffened multipatch structures

Hirschler

Bouclier

Duval

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Isogeometric shape optimization uses a unique model for the geometric description and for the analysis. The benefits are multiple: in particular, it avoids tedious procedures related to mesh updates. However, although the analysis of complex multipatch structures now becomes tractable with advanced numerical tools, isogeometric shape optimization has not yet been proven to be applicable for designing such structures. Based on the initial concept of integrating design and analysis, we develop a new approach that deals with the shape optimization of non-conforming multipatch structures. The model is built by employing the Free-Form Deformation principle. Introducing NURBS composition drastically simplifies the imposition of the shape updates in case of a non-conforming multipatch configuration. In the case of stiffened structures, the use of embedded surfaces enables to tackle the geometric constraint of connecting interfaces between the panel and the stiffeners during shape modifications. For the analysis, we introduce the embedded Kirchhoff-Love shell formulation. The NURBS composition defines the geometry of the shell while the displacement field is approximated using the same spline functions as for the embedded surface. We also formulate a new mortar method to couple non-conforming Kirchhoff-Love shells which intersect with any angle. We apply the developed method on different examples to demonstrate its efficiency and its potential to optimize complex industrial structures in a smooth manner.

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“…Despite the superior modeling capabilities of trimming, engineering‐related geometric models often contain multiple trimmed objects that need to be consolidated as a single model. To enforce coupling constraints between shell patches, a number of approaches have been proposed, for example, penalty‐type methods, Nitsche‐type methods, as well as other methods, cf the works of Coox et al and Sommerwerk et al, to name only a few. Compared to penalty‐type methods, the variationally consistent Nitsche method can preserve optimal convergence rates and well‐conditioned discrete equations and thus received considerable attention in the community.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric stability analysis of thin shells: From simple geometries to engineering models

Guo

Ruess

2019

Numerical Meth Engineering

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The buckling properties of thin-walled structures are sensitive to different sources of imperfections, among which the geometric imperfections are of paramount importance. This work contributes to the methodology of shell buckling analysis with respect to the following aspects: first, we propose an isogeometric analysis framework for the buckling analysis of shell structures which naturally eliminates the geometric discretization errors; second, we introduce a parameter-free Nitsche-type formulation for thin shells at large deformations that weakly enforces coupling constraints along trimmed boundaries. In combination with the finite cell method, the proposed conceptual modeling and analysis framework is able to handle engineering-related shell structures; and third, we introduce a NURBS modeling of measured geometric imperfection fields, which is much closer to the true imperfection shape compared to the classically used faceted FE models. We demonstrate with a number of benchmark problems and engineering models that our proposed framework is able to fully compete with established and highly sophisticated finite element formulations but at a significant higher level of accuracy and reliability of the analysis results. KEYWORDSfinite cell method, geometric imperfections, isogeometric analysis, parameter-free variational coupling, shell buckling Int J Numer Methods Eng. 2019;118:433-458. wileyonlinelibrary.com/journal/nme

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Reissner–Mindlin shell implementation and energy conserving isogeometric multi‐patch coupling

Cited by 19 publications

References 56 publications

Design of self-supporting surfaces with isogeometric analysis

Design of self-supporting surfaces with isogeometric analysis

The embedded isogeometric Kirchhoff–Love shell: From design to shape optimization of non-conforming stiffened multipatch structures

Isogeometric stability analysis of thin shells: From simple geometries to engineering models

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