An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells

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

doi:10.1016/j.cma.2017.11.025

Cited by 74 publications

(81 citation statements)

References 37 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: 97%

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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: 97%

“…• 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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“…This section describes the main equations of the solid-shell FE formulation (see [ 35 ]) used to construct the discrete model. The outset is the 3D Cauchy continuum whose geometry of deformation is described by the Green–Lagrange strains.…”

Section: Solid-shell Modelmentioning

confidence: 99%

Optimal Design of CNT-Nanocomposite Nonlinear Shells

et al. 2020

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Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to accurately describe the point-wise material distribution. The sensitivity to geometrical imperfections is also investigated. The optimization is carried out making use of the Global Convergent Method of Moving Asymptotes. The extensive numerical analyses show that varying the volume fraction distribution as well as the CNTs orientation can lead to significantly enhanced performances towards the loss of elastic stability making these lightweight structures more stable. The most striking result is that for curved shells, the unstable postbuckling response of the baseline material can be turned into a globally stable response maintaining the same amount of nanostructural reinforcement but simply tailoring strategically its distribution.

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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%

“…To solve the geometrically-nonlinear deformation, the recently developed MIP (Mixed Integration Point) Newton is used, combining the advantages of a displacement formulation (a limited computational cost) with those of a mixed stressdisplacement formulation (convergence in Newton more robust). While this method was originally introduced for the Galerkin discretization [44,45], it is extended in Section 3.6 to the strong form.…”

Section: Introductionmentioning

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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An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells

Cited by 74 publications

References 37 publications

An efficient isostatic mixed shell element for coarse mesh solution

An efficient isostatic mixed shell element for coarse mesh solution

Optimal Design of CNT-Nanocomposite Nonlinear Shells

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

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