Galerkin formulations of isogeometric shell analysis: alleviating locking with Greville quadratures and higher-order elements
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Publication:2236912
DOI10.1016/j.cma.2021.113757zbMath1506.74463OpenAlexW3141300353MaRDI QIDQ2236912
Roger A. Sauer, Z. Zou, E. J. Savitha, Thomas J. R. Hughes, Michael A. Scott
Publication date: 26 October 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2021.113757
isogeometric analysisGreville abscissaeReissner-Mindlin shell theoryKirchhoff-love shell theorymembrane and shear locking
Numerical computation using splines (65D07) Finite element methods applied to problems in solid mechanics (74S05) Shells (74K25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Isogeometric methods applied to problems in solid mechanics (74S22)
Related Items (23)
Galerkin Formulations with Greville Quadrature Rules for Isogeometric Shell Analysis: Higher Order Elements and Locking ⋮ Efficient and robust quadratures for isogeometric analysis: reduced Gauss and Gauss-Greville rules ⋮ Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements ⋮ Reduced quadrature for finite element and isogeometric methods in nonlinear solids ⋮ Extending CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane Timoshenko rods ⋮ Machine learning discovery of optimal quadrature rules for isogeometric analysis ⋮ A general isogeometric finite element formulation for rotation‐free shells with in‐plane bending of embedded fibers ⋮ High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation ⋮ Non-uniform \(C^1\) patches around extraordinary points with applications to analysis-suitable unstructured T-splines ⋮ Fourier analysis of membrane locking and unlocking ⋮ A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors ⋮ Learned Gaussian quadrature for enriched solid finite elements ⋮ Numerical methods for fourth-order PDEs on overlapping grids with application to Kirchhoff-Love plates ⋮ Overcoming membrane locking in quadratic NURBS-based discretizations of linear Kirchhoff-Love shells: CAS elements ⋮ Isogeometric multi-patch analyses for mixed thin shells in the framework of non-linear elasticity ⋮ Isogeometric Bézier dual mortaring: the Kirchhoff-Love shell problem ⋮ An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors ⋮ Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam ⋮ Stable and accurate numerical methods for generalized Kirchhoff-Love plates ⋮ Weighted quadrature for hierarchical B-splines ⋮ Efficient CAD-integrated isogeometric analysis of trimmed solids ⋮ Isogeometric collocation method based on residual parameterization of planar physical domain ⋮ First-order VEM for Reissner-Mindlin plates
Uses Software
Cites Work
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- Numerical integration of discontinuities on arbitrary domains based on moment fitting
- Isogeometric collocation for elastostatics and explicit dynamics
- A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis
- Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems
- A computational formulation for constrained solid and liquid membranes considering isogeometric finite elements
- A hierarchic family of isogeometric shell finite elements
- Isogeometric Reissner-Mindlin shell analysis with exactly calculated director vectors
- Blended isogeometric shells
- High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods
- Explicit Gaussian quadrature rules for \(C^1\) cubic splines with symmetrically stretched knot sequences
- Locking free isogeometric formulations of curved thick beams
- Isogeometric shell analysis: the Reissner-Mindlin shell
- Efficient quadrature for NURBS-based isogeometric analysis
- Numerical efficiency, locking and unlocking of NURBS finite elements
- A large deformation, rotation-free, isogeometric shell
- Parameterization of computational domain in isogeometric analysis: methods and comparison
- Isogeometric shell analysis with Kirchhoff-Love elements
- Numerical integration of discontinuous functions: moment fitting and smart octree
- The discrete strain gap method and membrane locking
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Gaussian quadrature for splines via homotopy continuation: rules for \(C^2\) cubic splines
- Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis
- Improved numerical integration for locking treatment in isogeometric structural elements. I: Beams
- Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials
- Higher order B-spline collocation at the Greville abscissae
- Bézier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis
- Improved numerical integration for locking treatment in isogeometric structural elements. II: Plates and shells
- Isogeometric collocation for phase-field fracture models
- A NURBS based hybrid collocation-Galerkin method for the analysis of boundary represented solids
- Selective and reduced numerical integrations for NURBS-based isogeometric analysis
- Nonstationary tight wavelet frames. I: Bounded intervals
- S-splines: a simple surface solution for IGA and CAD
- An isogeometric Reissner-Mindlin shell element based on Bézier dual basis functions: overcoming locking and improved coarse mesh accuracy
- A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
- Optimal quadrature for univariate and tensor product splines
- Fast formation of isogeometric Galerkin matrices by weighted quadrature
- Isogeometric Bézier dual mortaring: the enriched Bézier dual basis with application to second- and fourth-order problems
- Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization
- Isogeometric collocation for Kirchhoff-Love plates and shells
- A reconstructed local \(\bar{B}\) formulation for isogeometric Kirchhoff-Love shells
- Isogeometric Bézier dual mortaring: refineable higher-order spline dual bases and weakly continuous geometry
- Bézier \(\bar{B}\) projection
- An efficient and robust rotational formulation for isogeometric Reissner-Mindlin shell elements
- Efficient isogeometric NURBS-based solid-shell elements: mixed formulation and \(\overline B\)-method
- Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations
- On the assumed natural strain method to alleviate locking in solid-shell NURBS-based finite elements
- Gaussian quadrature rules for \(C^1\) quintic splines with uniform knot vectors
- ISOGEOMETRIC COLLOCATION METHODS
- Shell structures-a sensitive interrelation between physics and numerics
- A robust non-linear mixed hybrid quadrilateral shell element
- A mixed shell formulation accounting for thickness strains and finite strain 3d material models
- A formulation of general shell elements—the use of mixed interpolation of tensorial components
- A Curved C0 Shell Element Based on Assumed Natural-Coordinate Strains
- A new nine node degenerated shell element with enhanced membrane and shear interpolation
- A new efficient approach to the formulation of mixed finite element models for structural analysis
- Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element
- A simple and efficient finite element for plate bending
- Fundamental considerations for the finite element analysis of shell structures
- Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept
- On the theoretical foundations of thin solid and liquid shells
- A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS
- Reduced integration technique in general analysis of plates and shells
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