An isogeometric formulation of the Koiter’s theory for buckling and initial post-buckling analysis of composite shells

Leonetti, Leonardo; Magisano, Domenico; Liguori, Francesco S.; Garcea, Giovanni

doi:10.1016/j.cma.2018.03.037

Cited by 45 publications

(63 citation statements)

References 48 publications

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“…Moreover, Figure 13 compares the point-wise convergence obtained with MISS-8 with those obtained with the IGA  1 and IGA  2 isogeometric solutions. 40,41 For the ratio /s equal 10, MISS-8 exhibits a rate of convergence h 2 for all boundary conditions under consideration except for the SS2 condition, for which it is h 4 . For both the Clamped and SS1 boundary conditions, the performance of MISS-8 is similar to that of IGA  1 .…”

Section: Square Platementioning

confidence: 98%

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An efficient isostatic mixed shell element for coarse mesh solution

Madeo

Liguori

Zucco

et al. 2020

Numerical Meth Engineering

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A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger-Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS-8. MISS-8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking-free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick-and thin-walled beam-like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high-performance solutions. Finally, numerical results show a rate of convergence between h 2 and h 4 .

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Section: Square Platementioning

confidence: 98%

“…• Isogeometric solid-shell model, 40,41 displacement based with reduced integration (IGA). The displacement fields are interpolated by quadratic and cubic NURBS functions, with continuity  1 and  2 , respectively.…”

Section: Numerical Validationmentioning

confidence: 99%

An efficient isostatic mixed shell element for coarse mesh solution

Madeo

Liguori

Zucco

et al. 2020

Numerical Meth Engineering

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“…In [44], in the displacement formulation, it has been proposed to relax the constitutive equations at each integration point, such that one gets the advantage of the displacement formulation (almost no extra cost) with the advantage of the mixed formulation (better convergence with the Newton method). This new method is called the MIP (Mixed Integration Point) Newton, requires small implementation efforts, and has been successfully used for Reissner beams [44], isogeometric solid shells [45], isogeometric Koiters theory for buckling analysis of composite shells [54] and pantographic discrete and homogeneous lattices [36]. We emphasis that relaxing the constitutive equation at each integration point consists in setting the stress components of the weak form (N and N κ in Eq.…”

Section: The Mip Newtonmentioning

confidence: 99%

Isogeometric analysis for nonlinear planar Kirchhoff rods: Weighted residual formulation and collocation of the strong form

Maurin

Greco

Dedoncker

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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High-order shape functions used in isogeometric analysis allow the direct solution to the weighted residual formulation of the strong form, opening the door to new integration schemes (e.g. reduced Gauss-Lobatto quadrature, integration at superconvergent sites) but also to collocation approaches (e.g. using Greville or superconvergent collocation points). The goal of the present work is to compare these different methods through the application to the planar Kirchhoff rod, a fourth-order rotation-free formulation used to model slender beams under large deformations. Robustness of the geometrically-nonlinear solution is improved using the Mixed Integration Point (MIP) Newton, a method that combines the advantages of displacement and mixed formulations. Based on the observations of the convergence plots, convergence order estimates are provided for each discretization method. Advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks.

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“…Besides, the emergence of IGA has initiated a number of research studies in the area of shell buckling where the geometrically exact properties of IGA have been adopted, which naturally avoids the finite element discretization errors of curved objects. These research studies can be classified into two categories: linear buckling analysis and nonlinear buckling analysis . In particular, a Koiter‐Newton arc‐length method was proposed to study the buckling of thin‐shell structures in the works of Luo et al and Leonetti et al where the superior model quality immanent to IGA has been exploited.…”

Section: Introductionmentioning

confidence: 99%

“…These research studies can be classified into two categories: linear buckling analysis and nonlinear buckling analysis . In particular, a Koiter‐Newton arc‐length method was proposed to study the buckling of thin‐shell structures in the works of Luo et al and Leonetti et al where the superior model quality immanent to IGA has been exploited. Despite a number of research projects in the field of buckling analysis, the analyzed models are restricted to simple benchmark problems, and the original IGA paradigm referring to a tight coupling of modeling and analysis remains unconsidered due to missing concepts to handle trimming and coupling.…”

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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An isogeometric formulation of the Koiter’s theory for buckling and initial post-buckling analysis of composite shells

Cited by 45 publications

References 48 publications

An efficient isostatic mixed shell element for coarse mesh solution

An efficient isostatic mixed shell element for coarse mesh solution

Isogeometric analysis for nonlinear planar Kirchhoff rods: Weighted residual formulation and collocation of the strong form

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

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