A hierarchic family of isogeometric shell finite elements
From MaRDI portal
Publication:465734
DOI10.1016/j.cma.2012.10.018zbMath1297.74071OpenAlexW2009042773MaRDI QIDQ465734
Manfred Bischoff, Bastian Oesterle, Ralph Echter
Publication date: 24 October 2014
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.2012.10.018
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)
Related Items
Strategy for Preventing Membrane Locking Through Reparametrization ⋮ Frontiers in Mortar Methods for Isogeometric Analysis ⋮ Innovative and efficient stent flexibility simulations based on isogeometric analysis ⋮ Development of a mixed displacement-stress formulation for the analysis of elastoplastic structures under small strains: application to a locking-free, NURBS-based solid-shell element ⋮ A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids ⋮ Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements ⋮ An optimally convergent smooth blended B-spline construction for semi-structured quadrilateral and hexahedral meshes ⋮ An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis ⋮ Propagation of delamination in composite materials with isogeometric continuum shell elements ⋮ A unified approach for embedded boundary conditions for fourth-order elliptic problems ⋮ Extending CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane Timoshenko rods ⋮ Investigation and elimination of nonlinear Poisson stiffening in 3d and solid shell finite elements ⋮ High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation ⋮ An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split ⋮ Isogeometric analysis for multi-patch structured Kirchhoff-Love shells ⋮ Full-field order-reduced Gaussian process emulators for nonlinear probabilistic mechanics ⋮ Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics ⋮ Embedded boundary conditions for shear-deformable plate bending ⋮ Overcoming membrane locking in quadratic NURBS-based discretizations of linear Kirchhoff-Love shells: CAS elements ⋮ Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis ⋮ Large elastic deformation of micromorphic shells. Part I: Variational formulation ⋮ Virtual elements for a shear-deflection formulation of Reissner–Mindlin plates ⋮ A Reduced Integration for Reissner-Mindlin Non-linear Shell Analysis Using T-Splines ⋮ A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS ⋮ Meshfree truncated hierarchical refinement for isogeometric analysis ⋮ \(l_1\)-norm based dynamic analysis of flexible multibody system modeled with trimmed isogeometry ⋮ Hellinger-Reissner principle based stress-displacement formulation for three-dimensional isogeometric analysis in linear elasticity ⋮ Consistent tangent operator for an exact Kirchhoff rod model ⋮ A scaled boundary finite element method for static and dynamic analyses of cylindrical shells ⋮ The effect of parameterization on isogeometric analysis of free-form curved beams ⋮ A study on the approximation power of NURBS and the significance of exact geometry in isogeometric pre-buckling analyses of shells ⋮ Isogeometric rotation-free analysis of planar extensible-elastica for static and dynamic applications ⋮ Discontinuous Galerkin isogeometric analysis with peridynamic model for crack simulation of shell structure ⋮ Developments of the mixed grid isogeometric Reissner-Mindlin shell: serendipity basis and modified reduced quadrature ⋮ Efficient isogeometric formulation for vibration analysis of complex spatial beam structures ⋮ Treatment of Reissner-Mindlin shells with Kinks without the need for drilling rotation stabilization in an isogeometric framework ⋮ Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis ⋮ A seven-parameter spectral/\(hp\) finite element formulation for isotropic, laminated composite and functionally graded shell structures ⋮ A scaled boundary shell element formulation using Neumann expansion ⋮ Explicit dynamic isogeometric B-rep analysis of penalty-coupled trimmed NURBS shells ⋮ Two new triangular \(\operatorname{G}^1\)-conforming finite elements with cubic edge rotation for the analysis of Kirchhoff plates ⋮ Multi-patch isogeometric analysis for Kirchhoff-Love shell elements ⋮ One-step inverse isogeometric analysis for the simulation of sheet metal forming ⋮ The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures ⋮ Seamless integration of design and Kirchhoff-Love shell analysis using analysis-suitable unstructured T-splines ⋮ Crosspoint modification for multi-patch isogeometric analysis ⋮ Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method ⋮ A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff-Love shells ⋮ An efficient and robust rotational formulation for isogeometric Reissner-Mindlin shell elements ⋮ Nonlinear isogeometric spatial Bernoulli beam ⋮ Integrated design and analysis of structural membranes using the isogeometric B-rep analysis ⋮ A parameter-free variational coupling approach for trimmed isogeometric thin shells ⋮ Isogeometric analysis of ice accretion on wind turbine blades ⋮ Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting ⋮ An isogeometric continuum shell element for non-linear analysis ⋮ Novel higher order mass matrices for isogeometric structural vibration analysis ⋮ Isogeometric rotation-free bending-stabilized cables: statics, dynamics, bending strips and coupling with shells ⋮ 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 ⋮ Isogeometric analysis: an overview and computer implementation aspects ⋮ Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials ⋮ Galerkin formulations of isogeometric shell analysis: alleviating locking with Greville quadratures and higher-order elements ⋮ Isogeometric multi-patch analyses for mixed thin shells in the framework of non-linear elasticity ⋮ Efficient computation of nonlinear isogeometric elements using the adjoint method and algorithmic differentiation ⋮ Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format ⋮ An isogeometric formulation of the Koiter's theory for buckling and initial post-buckling analysis of composite shells ⋮ From nonlinear micromorphic to nonlinear micropolar shell theory ⋮ Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity ⋮ Isogeometric Kirchhoff-Love shell formulation for elasto-plasticity ⋮ Skew-symmetric Nitsche's formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact ⋮ An interpolation method for coupling non-conforming patches in isogeometric analysis of vibro-acoustic systems ⋮ A volume-averaged nodal projection method for the Reissner-Mindlin plate model ⋮ A new mixed approach to Kirchhoff-Love shells ⋮ Kirchhoff-Love shell formulation based on triangular isogeometric analysis ⋮ A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells ⋮ Reissner-Mindlin shell theory based on tangential differential calculus ⋮ A simplified Kirchhoff-Love large deformation model for elastic shells and its effective isogeometric formulation ⋮ Adjusted approximation spaces for the treatment of transverse shear locking in isogeometric Reissner-Mindlin shell analysis ⋮ A displacement-free formulation for the Timoshenko beam problem and a corresponding isogeometric collocation approach ⋮ High order exact geometry finite elements for seven-parameter shells with parametric and implicit reference surfaces ⋮ Weak Dirichlet boundary conditions for trimmed thin isogeometric shells ⋮ An isogeometric Reissner-Mindlin shell element based on Bézier dual basis functions: overcoming locking and improved coarse mesh accuracy ⋮ Isogeometric analysis of 3D beams for arbitrarily large rotations: locking-free and path-independent solution without displacement DOFs inside the patch ⋮ Phase-field model of brittle fracture in Reissner-Mindlin plates and shells ⋮ Avoiding membrane locking with Regge interpolation ⋮ A stochastic multiscale formulation for isogeometric composite Kirchhoff-Love shells ⋮ A robust penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches in large deformations ⋮ Nitsche's method for linear Kirchhoff-Love shells: formulation, error analysis, and verification ⋮ A priori penalty factor determination for (trimmed) NURBS-based shells with Dirichlet and coupling constraints in isogeometric analysis ⋮ Isogeometric MITC shell ⋮ A \(C^1\)-continuous trace-finite-cell-method for linear thin shell analysis on implicitly defined surfaces ⋮ Approximation of linear elastic shells by curved triangular finite elements based on elastic thick shells theory ⋮ Nitsche's method for two and three dimensional NURBS patch coupling ⋮ On the assumed natural strain method to alleviate locking in solid-shell NURBS-based finite elements ⋮ Uncertainty quantification of spatially uncorrelated loads with a reduced-order stochastic isogeometric method ⋮ Isogeometric analysis of continuum damage in rotation-free composite shells ⋮ Analysis in computer aided design: nonlinear isogeometric B-Rep analysis of shell structures ⋮ Isogeometric collocation methods for the Reissner-Mindlin plate problem ⋮ An isogeometric collocation approach for Bernoulli-Euler beams and Kirchhoff plates ⋮ Assumed natural strain NURBS-based solid-shell element for the analysis of large deformation elasto-plastic thin-shell structures ⋮ Nitsche's method for a coupling of isogeometric thin shells and blended shell structures ⋮ Single-variable formulations and isogeometric discretizations for shear deformable beams ⋮ Superconvergent isogeometric free vibration analysis of Euler-Bernoulli beams and Kirchhoff plates with new higher order mass matrices ⋮ A consistently coupled isogeometric-meshfree method ⋮ Quasi-conforming analysis method for trimmed CAD surfaces ⋮ A shear deformable, rotation-free isogeometric shell formulation ⋮ Order reduction method for locking free isogeometric analysis of Timoshenko beams ⋮ Phase-field description of brittle fracture in plates and shells ⋮ Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler-Bernoulli beam ⋮ An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS ⋮ On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems ⋮ A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries ⋮ Dual and approximate dual basis functions for B-splines and NURBS -- comparison and application for an efficient coupling of patches with the isogeometric mortar method ⋮ A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling ⋮ Quadrature rules for isogeometric shell formulations: study using a real-world application about metal forming ⋮ Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization ⋮ An efficient blended mixed B-spline formulation for removing membrane locking in plane curved Kirchhoff rods ⋮ Embedded structural entities in NURBS-based isogeometric analysis ⋮ Isogeometric collocation for the Reissner-Mindlin shell problem ⋮ An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells ⋮ A reconstructed local \(\bar{B}\) formulation for isogeometric Kirchhoff-Love shells ⋮ Bézier \(\bar{B}\) projection ⋮ A simple and effective method based on strain projections to alleviate locking in isogeometric solid shells ⋮ Two-field formulations for isogeometric Reissner-Mindlin plates and shells with global and local condensation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An isogeometric method for the Reissner-Mindlin plate bending problem
- Isogeometric Reissner-Mindlin shell analysis with exactly calculated director vectors
- Isogeometric shell analysis: the Reissner-Mindlin shell
- Efficient quadrature for NURBS-based isogeometric analysis
- Numerical efficiency, locking and unlocking of NURBS finite elements
- Isogeometric shell analysis with Kirchhoff-Love elements
- The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches
- The discrete strain gap method and membrane locking
- A fully ``locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- On the mathematical foundation of the \((1,1,2)\)-plate model
- \(\overline {\text B}\) and \(\overline {\text F}\) projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order NURBS elements
- Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis
- Shear-flexible subdivision shells
- Rational approach for assumed stress finite elements
- Alternative ways for formulation of hybrid stress elements
- Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept
- Isogeometric Analysis
- A class of mixed assumed strain methods and the method of incompatible modes
- On a Variational Theorem in Elasticity