A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff–Love shells

Hirschler, Thibaut; Bouclier, Robin; Dureisseix, David; Duval, Arnaud; Elguedj, Thomas; Morlier, Joseph

doi:10.1016/j.cma.2019.112578

Cited by 27 publications

(14 citation statements)

References 66 publications

(146 reference statements)

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“…Multipatch flux discontinuities can be then solved by mortar methods. 44 Another property is the efficient construction of adaptive procedures due to properties of spline basis functions to describe variables with different resolution levels enabling the multiresolution approach. 13 F I G U R E 1 Nonoverlapping control volume scheme for one-dimensional case Classical IGA 10,11 usually employs Galerkin weak formulation (8) using B-splines or NURBS as basis and test functions.…”

Section: Control Volume Isogeometric Analysismentioning

confidence: 99%

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Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

Kamber

Gotovac

Kozulić

et al. 2020

Numerical Methods in Fluids

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Summary A novel adaptive algorithm that is based on new hierarchical Fup (HF) basis functions and a control volume formulation is presented. Because of its similarity to the concept of isogeometric analysis (IGA), we refer to it as control volume isogeometric analysis (CV‐IGA). Among other interesting properties, the IGA introduced k‐refinement as advanced version of hp‐refinement, where every basis function of the nth order from one resolution level are replaced by a linear combination of more basis functions of the n+1th order at the next resolution level. However, k‐refinement can be performed only on whole domain, while local adaptive k‐refinement is not possible with classical B‐spline basis functions. HF basis functions (infinitely differentiable splines) satisfy partition of unity, and they are linearly independent and locally refinable. Their main feature is execution of the adaptive local hp‐refinement because any basis function of the nth order from one resolution level can be replaced by a linear combination of more basis functions of the n+1th order at the next resolution level providing spectral convergence order. The comparison between uniform vs hierarchical adaptive solutions is demonstrated, and it is shown that our adaptive algorithm returns the desired accuracy while strongly improving the efficiency and controlling the numerical error. In addition to the adaptive methodology, a stabilization procedure is applied for advection‐dominated problems whose numerical solutions “suffer” from spurious oscillations. Stabilization is added only on lower resolution levels, while higher resolution levels ensure an accurate solution and produce a higher convergence order. Since the focus of this article is on developing HF basis functions and adaptive CV‐IGA, verification is performed on the stationary one‐dimensional boundary value problems.

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Section: Control Volume Isogeometric Analysismentioning

confidence: 99%

“…In Figure 6, the corresponding CVs are presented above basis functions for better visualization. Then, the coefficients j are calculated from the system of equations (44) so that the Fup approximation (f ) satisfies the mean function values over all CVs.…”

Section: Adaptive Algorithm For Function Approximationmentioning

confidence: 99%

Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

Kamber

Gotovac

Kozulić

et al. 2020

Numerical Methods in Fluids

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“…In the literature, three methods are predominantly used to achieve the latter coupling in a weak sense and they are summarized in the following. High-order mortar methods have been studied in [18,20] in the context of Kirchhoff plates and Kirchhoff-Love shells, respectively, and have been extended to a general C ncoupling in [11]. For a detailed review in the context of isogeometric analysis, we refer to the review article [17].…”

Section: Introductionmentioning

confidence: 99%

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

2021

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This work focuses on the development of a super-penalty strategy based on the $$L^2$$ L 2 -projection of suitable coupling terms to achieve $$C^1$$ C 1 -continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from boundary locking, especially on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters.

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“…In the literature, three methods are predominantly employed to achieve displacement and rotational continuity in a weak sense and they are briefly outlined in the following. Mortar-type methods have been presented for patch coupling in [31,29] in the scope of Kirchhoff plates and Kirchhoff-Love shells, respectively, and have been generalized to arbitrary smoothness in [23]. It is well-known that mortar methods introduce additional artificial unknowns into the underlying system of equations to enforce the corresponding constraints, where the choice of discretization space for these Lagrange multipliers plays a pivotal role for the robustness of the method.…”

Section: Introductionmentioning

confidence: 99%

Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach

Coradello,

Kiendl,

Buffa

2021

Preprint

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Penalty methods have proven to be particularly effective for achieving the required C 1 -continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily applicable to the displacement and rotational coupling of trimmed, non-conforming surfaces. However, the accuracy of the resulting solution depends heavily on the choice of penalty parameters. Furthermore, the selection of these coefficients is generally problemdependent and is based on a heuristic approach. Moreover, developing a penalty-like procedure that avoids interface locking while retaining optimal accuracy is still an open question. This work focuses on these challenges. In particular, we devise a penalty-like strategy based on the L 2 -projection of displacement and rotational coupling terms onto a degree-reduced spline space defined on the corresponding interface. Additionally, the penalty factors are completely defined by the problem setup and are constructed to ensure optimality of the method. To demonstrate this, we asses the performance of the proposed numerical framework on a series of non-trimmed and trimmed multipatch benchmarks discretized by non-conforming meshes. We systematically observe a significant gain of accuracy per degree-of-freedom and no interface locking phenomena compared to other penalty-like approaches. Lastly, we perform a static shell analysis of a complex engineering structure, namely the blade of a wind turbine.

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A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff–Love shells

Cited by 27 publications

References 66 publications

Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach

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