Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements (Q2674089)

scientific article; zbMATH DE number 7589829

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English	Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements	scientific article; zbMATH DE number 7589829

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instance of

scholarly article

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title

Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

22 September 2022

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full work available at URL

https://arxiv.org/abs/2209.01747

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zbMATH Keywords

isogeometric analysis

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thin-walled structures

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membrane locking

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assumed natural strain

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Kirchhoff rods

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convergence studies

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describes a project that uses

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Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

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Isogeometric Analysis

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Seamless integration of design and Kirchhoff-Love shell analysis using analysis-suitable unstructured T-splines

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Analysis-suitable unstructured T-splines: multiple extraordinary points per face

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Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: geometric design and isogeometric analysis considerations

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On the numerical integration of trimmed isogeometric elements

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Explicit dynamic isogeometric B-rep analysis of penalty-coupled trimmed NURBS shells

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B-spline interpolation of Kirchhoff-Love space rods

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An implicit \(G^1\) multi patch B-spline interpolation for Kirchhoff-Love space rod

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An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods

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Isogeometric shell analysis with Kirchhoff-Love elements

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Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials

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An efficient blended mixed B-spline formulation for removing membrane locking in plane curved Kirchhoff rods

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Invariant Hermitian finite elements for thin Kirchhoff rods. I: The linear plane case

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A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods

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Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam

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A reconstructed local \(\bar{B}\) formulation for isogeometric Kirchhoff-Love shells

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Shear and membrane locking in curved \(C^ 0\) elements

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Locking free isogeometric formulations of curved thick beams

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

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A shear deformable, rotation-free isogeometric shell formulation

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Galerkin formulations of isogeometric shell analysis: alleviating locking with Greville quadratures and higher-order elements

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Efficient and robust quadratures for isogeometric analysis: reduced Gauss and Gauss-Greville rules

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Reduced integration technique in general analysis of plates and shells

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A uniform strain hexahedron and quadrilateral with orthogonal hourglass control

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Hourglass control in linear and nonlinear problems

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Explicit algorithms for the nonlinear dynamics of shells

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A simple and efficient finite element for plate bending

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Nonlinear finite element analysis of shells. II. Two-dimensional shells

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A simple quadrilateral shell element

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Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element

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Mixed finite element methods - reduced and selective integration techniques: a unification of concepts

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On the Variational Foundations of Assumed Strain Methods

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Efficient isogeometric NURBS-based solid-shell elements: mixed formulation and \(\overline B\)-method

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Efficient quadrature for NURBS-based isogeometric analysis

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Selective and reduced numerical integrations for NURBS-based isogeometric analysis

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Improved numerical integration for locking treatment in isogeometric structural elements. I: Beams

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Improved numerical integration for locking treatment in isogeometric structural elements. II: Plates and shells

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

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A simplified Kirchhoff-Love large deformation model for elastic shells and its effective isogeometric formulation

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\(\overline {\text B}\) and \(\overline {\text F}\) projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order NURBS elements

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The discrete strain gap method and membrane locking

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Numerical efficiency, locking and unlocking of NURBS finite elements

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A hierarchic family of isogeometric shell finite elements

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Bézier \(\bar{B}\) projection

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Convergence of an efficient local least-squares fitting method for bases with compact support

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Blending moving least squares techniques with NURBS basis functions for nonlinear isogeometric analysis

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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

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An isogeometric Reissner-Mindlin shell element based on Bézier dual basis functions: overcoming locking and improved coarse mesh accuracy

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Isogeometric Bézier dual mortaring: refineable higher-order spline dual bases and weakly continuous geometry

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Isogeometric Bézier dual mortaring: the enriched Bézier dual basis with application to second- and fourth-order problems

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Order reduction method for locking free isogeometric analysis of Timoshenko beams

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A simple and effective method based on strain projections to alleviate locking in isogeometric solid shells

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On the assumed natural strain method to alleviate locking in solid-shell NURBS-based finite elements

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Assumed natural strain NURBS-based solid-shell element for the analysis of large deformation elasto-plastic thin-shell structures

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PetIGA: a framework for high-performance isogeometric analysis

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Isogeometric analysis of plane-curved beams

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CMA.2022.115354

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Sitelinks

Mathematics(1 entry)

mardi Publication:2674089