On penalty-free formulations for multipatch isogeometric Kirchhoff–Love shells

Goyal, Anmol; Simeon, Bernd

doi:10.1016/j.matcom.2016.12.001

Cited by 18 publications

(14 citation statements)

References 15 publications

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“…In this example, the Scordelis-Lo roof [10,16,17,19,20] is investigated, demonstrating the application of the collocation method to a curved geometry with Neumann boundary conditions. The Scordelis-Lo roof is an 80 • cylinder section of length L = 50 m and radius R = 25 m, loaded by a uniform body force of −90 Nm −2 along the vertical direction (z axis, see Fig.…”

Section: Scordelis-lo Roofmentioning

confidence: 99%

“…Starting from the pioneering works of Kiendl et al [10], isogeometric Kirchhoff-Love shell formulations have been extended to non-linear material models [11,12], analysis of through-the-thickness cracks [13], damage models [14], and biological membranes [15]. Due to the rotation-free nature of these formulations, multi-patch coupling deserves special attention [12,[16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Isogeometric collocation for Kirchhoff–Love plates and shells

Maurin

Greco

Coox

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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With the emergence of isogeometric analysis (IGA), the Galerkin rotation-free discretization of Kirchhoff-Love shells is facilitated, enabling more efficient thin shell structural analysis. High-order shape functions used in IGA also allow the collocation of partial differential equations, avoiding the time-consuming numerical integration of the Galerkin technique. The goal of the present work is to apply this method to NURBS-based isogeometric Kirchhoff-Love plates and shells, under the assumption of small deformations.Since Kirchhoff-Love plate theory yields a fourth-order formulation, two boundary conditions are required at each location on the contour, generating some conflicts at the corners where there are more equations than needed. To remedy this overdetermination, we provide priority and averaging rules that cover all the possible combinations of adjacent edge boundary conditions (i.e. the clamped, simplysupported, symmetric and free supports). Greville and alternative superconvergent points are used for NURBS basis of even and odd degrees, respectively. For square, circular, and annular flat plates, convergence orders are found to be in agreement with a-priori error estimates. The proposed isogeometric collocation method is then validated and benchmarked against a Galerkin implementation by studying a set of problems involving Kirchhoff-Love shells.

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Section: Scordelis-lo Roofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Isogeometric collocation for Kirchhoff–Love plates and shells

Maurin

Greco

Coox

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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“…the small solutions to Eqs. (18)(19) or (21)(22) with λ = 6. In the cases considered, the parameters are set as follows: R = 1 m, E = 70 GPa, ν = 0.3 and ρ = 2700 kg m −3 .…”

Section: Vibrations Of a Spherical Shellmentioning

confidence: 99%

“…(18)(19) -differ from those by Junger & Feit -Eqs. (21)(22) because the effect of bending stiffness is taken into account differently. However, it is observed that neither prediction is fully consistent with the value obtained through accurate numerical simulations.…”

Section: Vibrations Of a Spherical Shellmentioning

confidence: 99%

“…The VUKIMS method proposed by Coox et al [13] also enforces interface constraints in a weak sense, but does so by explicitly making use of NURBS refinement properties. The particularly complicated problem of C 1 -coupling is discussed in [22][23][24][25][26][27]. Depending on the technique used, extra variables may be introduced, expensive additional calculations may be needed and/or the conditioning of the final system may be affected.…”

Section: Introductionmentioning

confidence: 99%

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Bézier tilings of the sphere and their applications in benchmarking multipatch isogeometric methods

Dedoncker

Coox

Maurin

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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In this work, we explore new parametric models of a sphere with rational Bézier patches. The geometry is represented as a spherical tessellation with various topologies. The tiles are degeneracy-free rational Bézier surfaces, obtained using a general composite mapping method. Five novel, topologically distinct tilings are described, four of which have conforming parameterizations. The mesh of the fifth tiling is nonconforming despite having equal interface knot vectors (intrinsic nonconformity). We apply these novel geometries in three case studies that are proposed as benchmark problems for C 0-and C 1-multipatch IGA methods.

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Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

Hirschler

Bouclier

Duval

et al. 2018

Struct Multidisc Optim

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This work explores the use of solid-shell elements in the the framework of isogeometric shape optimization of shells. The main difference of these elements with respect to pure shell ones is their volumetric nature which can provide recognized benefits to analyze, for example, structures with non-linear behaviors. From the design point of view, we show that this geometric representation of the thickness is also of great interest since it offers new possibilities: continuous sizing variations can be imposed by modifying the distance between the control points of the outer surfaces. In other words, shape and sizing optimization can be performed in an identical manner. Firstly, we carry out a range of numerical experiments in order to carefully compare the results with the commonly adopted technique based on the Kirchhoff-Love formulation. These studies reveal that both solid-shell and Kirchhoff-Love strategies lead to very similar optimal shapes. Then we apply a bi-step strategy to integrate shape and sizing optimization. We highlight the potential of the proposed approach on a stiffened cylinder where the cross-section along the stiffener is optimized leading to a final design with smooth thickness variations. Finally, we combine the benefits of both Kirchhoff-Love and solid-shell formulations by setting up a multi-model optimization process to efficiently design a roof.

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On penalty-free formulations for multipatch isogeometric Kirchhoff–Love shells

Cited by 18 publications

References 15 publications

Isogeometric collocation for Kirchhoff–Love plates and shells

Isogeometric collocation for Kirchhoff–Love plates and shells

Bézier tilings of the sphere and their applications in benchmarking multipatch isogeometric methods

Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

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