Nitsche's method for linear Kirchhoff-Love shells: formulation, error analysis, and verification
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Publication:2021229
DOI10.1016/j.cma.2020.113544zbMath1506.74185arXiv2007.01279OpenAlexW3039431589MaRDI QIDQ2021229
Rasmus Tamstorf, Joseph Benzaken, Stephen F. McCormick, John A. Evans
Publication date: 26 April 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.01279
Shells (74K25) PDEs in connection with mechanics of deformable solids (35Q74) Isogeometric methods applied to problems in solid mechanics (74S22)
Related Items (12)
An open-source framework for coupling non-matching isogeometric shells with application to aerospace structures ⋮ A DPG method for shallow shells ⋮ Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff-Love shells ⋮ Extending CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane Timoshenko rods ⋮ Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics ⋮ Interpolation-based immersed finite element and isogeometric analysis ⋮ A comparison of smooth basis constructions for isogeometric analysis ⋮ Embedded boundary conditions for shear-deformable plate bending ⋮ Blended isogeometric Kirchhoff-Love and continuum shells ⋮ Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach ⋮ \(C^1\) triangular isogeometric analysis of the von Karman equations ⋮ A new mixed finite-element method for \(H^2\) elliptic problems
Cites Work
- Isogeometric fluid structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines
- An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
- Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
- A hierarchic family of isogeometric shell finite elements
- Isogeometric analysis using T-splines
- Isogeometric shell analysis with Kirchhoff-Love elements
- The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches
- Rotation-free isogeometric thin shell analysis using PHT-splines
- A robust Nitsche's formulation for interface problems
- Imposing essential boundary conditions in mesh-free methods
- An introduction to differential geometry with applications to elasticity
- Weak imposition of Dirichlet boundary conditions in fluid mechanics
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Stress projection for membrane and shear locking in shell finite elements
- A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
- The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition
- The continuous Galerkin method is locally conservative
- A parameter-free variational coupling approach for trimmed isogeometric thin shells
- Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials
- Analysis in computer aided design: nonlinear isogeometric B-Rep analysis of shell structures
- Nitsche's method for a coupling of isogeometric thin shells and blended shell structures
- An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves
- Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
- A discontinuous Galerkin method for the plate equation
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- On some techniques for approximating boundary conditions in the finite element method
- Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
- Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format
- Penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches with application to composite wind turbine blades
- Kirchhoff-Love shell theory based on tangential differential calculus
- Weak Dirichlet boundary conditions for trimmed thin isogeometric shells
- Multi-patch isogeometric analysis for Kirchhoff-Love shell elements
- Hierarchically refined isogeometric analysis of trimmed shells
- A \(C^0 / G^1\) multiple patches connection method in isogeometric analysis
- A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
- Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling
- Nitsche's method for two and three dimensional NURBS patch coupling
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- The finite element method with Lagrangian multipliers
- Isogeometric Kirchhoff-Love shell formulations for biological membranes
- A new discontinuous Galerkin method for Kirchhoff-Love shells
- Manifolds with Boundary and of Bounded Geometry
- Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis
- Domain Decomposition Methods and Kirchhoff-Love Shell Multipatch Coupling in Isogeometric Analysis
- Embedded kinematic boundary conditions for thin plate bending by Nitsche's approach
- Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method
- A Nitsche-type formulation and comparison of the most common domain decomposition methods in isogeometric analysis
- A unified approach for embedded boundary conditions for fourth-order elliptic problems
- Nitsche’s method for general boundary conditions
- Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements
- A discontinuous-Galerkin-based immersed boundary method
- A formulation of general shell elements—the use of mixed interpolation of tensorial components
- An Interior Penalty Finite Element Method with Discontinuous Elements
- Isogeometric Analysis
- ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE DARCY–STOKES–BRINKMAN EQUATIONS
- ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES
- Discretization error estimates for penalty formulations of a linearized Canham–Helfrich-type energy
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