On the development of NURBS-based isogeometric solid shell elements: 2D problems and preliminary extension to 3D

Bouclier, Robin; Elguedj, Thomas; Combescure, Alain

doi:10.1007/s00466-013-0865-4

Cited by 34 publications

(27 citation statements)

References 42 publications

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“…It can be seen that the convergence of the displacement toward the reference solution is very fast and almost not influenced by the slenderness ratio. Note also that such a problem could be solved by means of conforming high‐order elements or isogeometric elements …”

Section: Numerical Examplesmentioning

confidence: 99%

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Legrain

Moës

2018

Numerical Meth Engineering

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Summary A novel integration scheme is proposed for fictitious domain finite element methods. It relies on the use of a surface tracking strategy based on anisotropic mesh adaptation. Thanks to an error estimator, the method builds iteratively an adapted anisotropic mesh that is refined near the geometrical interface and elongated in the direction of a small curvature. This strategy allows to decrease the integration cost, which can be problematic for high‐order fictitious domain methods. In addition, it opens the possibility for the creation of unfitted solid shell strategies that can be used for the treatment of thin structures. Numerical studies show that the method leads to promising results for both integration cost and behavior with respect to locking.

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Section: Numerical Examplesmentioning

confidence: 99%

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Legrain

Moës

2018

Numerical Meth Engineering

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“…We want to solve this problem using the recent concept of IGA along with the solid‐shell element approach . In order to do that, we will discretize the shell using a single layer of solid 3D NURBS elements through the thickness.…”

Section: The Mixed Solid‐shell Nurbs Element For Elasticity Under Smamentioning

confidence: 99%

“…The concept was first introduced in Hughes et al and, more recently, was formalized in the book by Cottrell et al , where a detailed description can be found. In recent years, this has led to a series of many publications (see, for instance, , ).…”

Section: The Mixed Solid‐shell Nurbs Element For Elasticity Under Smamentioning

confidence: 99%

“…Closer to the solid‐shell context, one can mention the work of Hosseini et al , who developed a solid‐like Bézier shell element. However, only Bouclier et al , using a mixed approach, and more recently Caseiro et al , using an Assumed Natural Strain method, seem to have applied the pure solid‐shell approach to the NURBS context. Up until now, these works were limited to linear elastic structural analysis.…”

Section: Introductionmentioning

confidence: 99%

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An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis

Bouclier

Elguedj

Combescure

2014

Int. J. Numer. Meth. Engng

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SUMMARYIn this work, we develop an isogeometric non-uniform rational B-spline (NURBS)-based solid-shell element for the geometrically nonlinear static analysis of elastic shell structures. A single layer of continuous 3D elements through the thickness of the shell is considered, and the order of approximation in that direction is chosen to be equal to two. A complete 3D constitutive relation is assumed. The objective is to develop a highly accurate low-order element for coarse meshes. We propose an extension of the mixed method of Bouclier et al.[11] to deal with locking in the context of large rotations and large displacements. The main idea is to modify the interpolation of the average through the thickness of the stress components. It is also necessary to stabilize the element in order to avoid the occurrence of spurious zero-energy modes. This was achieved, for the quadratic version, through the adjunction of artificial elementary stabilization stiffnesses. The result is an element of order 2, which is at least as accurate as standard NURBS shell elements of order 4. Linear and nonlinear test calculations have been carried out along with comparisons with other published NURBS and classical techniques in order to assess the performance of the element.

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“…Higher-order solid elements have been shown to be able to efficiently analyze thin-walled structures in the context of the p-version of the finite element method [116,117] and isogeometric analysis [63,64,118,119]. In many situations, there are potential advantages of higher-order solid elements over dimensionally reduced plate and shell elements: Solid elements are able to seamlessly discretize thin structures of variable thickness that consist of thin-walled, thick-walled and truly solid parts.…”

Section: Scordelis-lo Roofmentioning

confidence: 99%

A collocated C⁰ finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics

Schillinger

Evans

Frischmann

et al. 2014

Numerical Meth Engineering

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We demonstrate the potential of collocation methods for efficient higher-order analysis on standard nodal finite element meshes. We focus on a collocation method that is variationally consistent and geometrically flexible, converges optimally, embraces concepts of reduced quadrature, and leads to symmetric stiffness and diagonal consistent mass matrices. At the same time, it minimizes the evaluation cost per quadrature point, thus reducing formation and assembly effort significantly with respect to standard Galerkin finite element methods. We provide a detailed review of all components of the technology in the context of elastodynamics, that is, weighted residual formulation, nodal basis functions on Gauss-Lobatto quadrature points, and symmetrization by averaging with the ultra-weak formulation. We quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings. Our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort, such as higher-order elastostatic analysis. Furthermore, we illustrate the potential of collocation for efficient higher-order explicit dynamics. Throughout this work, we advocate a straightforward implementation based on simple modifications of standard finite element codes. We also point out the close connection to spectral element methods, where many of the key ideas are already established. AbstractWe demonstrate the potential of collocation methods for efficient higher-order analysis on standard nodal finite element meshes. We focus on a collocation method that is variationally consistent and geometrically flexible, converges optimally, embraces concepts of reduced quadrature, and leads to symmetric stiffness and diagonal consistent mass matrices. At the same time, it minimizes the evaluation cost per quadrature point, thus reducing formation and assembly effort significantly with respect to standard Galerkin finite element methods. We provide a detailed review of all components of the technology in the context of elastodynamics, i.e. weighted residual formulation, nodal basis functions on Gauss-Lobatto quadrature points, and symmetrization by averaging with the ultra-weak formulation. We quantify potential gains by comparing the computational efficiency of collocation and standard finite elements in terms of basic operation counts and timings. Our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort, such as higher-order elastostatic analysis. Furthermore we illustrate the potential of collocation for efficient higher-order explicit dynamics. Throughout this work, we advocate a straightforward implementation based on simple modifications of standard finite element codes. We also point out the close connection to spectral element methods, where many of the key ideas are already established.

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On the development of NURBS-based isogeometric solid shell elements: 2D problems and preliminary extension to 3D

Cited by 34 publications

References 42 publications

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis

A collocated C⁰ finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics

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On the development of NURBS-based isogeometric solid shell elements: 2D problems and preliminary extension to 3D

Cited by 34 publications

References 42 publications

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis

A collocated C0 finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics

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A collocated C⁰ finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics