Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
DOI10.1016/j.cma.2016.07.008zbMath1439.74037OpenAlexW2502356463MaRDI QIDQ2308974
Antti H. Niemi, Jarkko Niiranen, Josef Kiendl, Alessandro Reali
Publication date: 6 April 2020
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.2016.07.008
convergence analysiserror estimatesKirchhoff plategradient elasticityisogeometric analysisgeneralized continuum
Boundary value problems for higher-order elliptic equations (35J40) Plates (74K20) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Micromechanical theories (74A60) PDEs in connection with mechanics of deformable solids (35Q74) Variational methods for higher-order elliptic equations (35J35)
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Cites Work
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- Torsional vibrations of a column of fine-grained material: a gradient elastic approach
- Asymptotic fracture modes in strain-gradient elasticity: size effects and characteristic lengths for isotropic materials
- A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory
- Anisotropic NURBS approximation in isogeometric analysis
- THB-splines: The truncated basis for hierarchical splines
- Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems
- Isogeometric analysis of 2D gradient elasticity
- Isogeometric shell analysis with Kirchhoff-Love elements
- Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory
- Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates
- 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
- A posteriori error estimates for the Morley plate bending element
- Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials
- On bending of strain gradient elastic micro-plates
- A family of \(C^{0}\) finite elements for Kirchhoff plates. II: Numerical results
- A novel atomistic approach to determine strain-gradient elasticity constants: tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir)relevance for nanotechnologies
- Wave dispersion in gradient elastic solids and structures: a unified treatment
- On the role of gradients in the localization of deformation and fracture
- Cone conditions and properties of Sobolev spaces
- A simple approach to solve boundary-value problems in gradient elasticity
- Experiments and theory in strain gradient elasticity.
- Three-dimensional isogeometric solutions to general boundary value problems of Toupin's gradient elasticity theory at finite strains
- A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory
- On the gradient strain elasticity theory of plates
- Hierarchical T-splines: analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis
- Single-variable formulations and isogeometric discretizations for shear deformable beams
- Finite element approximation of the Dirichlet problem using the boundary penalty method
- 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
- On some techniques for approximating boundary conditions in the finite element method
- Mathematical analysis of thin plate models
- How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert
- Polynomial splines over locally refined box-partitions
- Variational analysis of gradient elastic flexural plates under static loading
- Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem
- Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems
- 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)
- Micro-structure in linear elasticity
- Analysis of plate in second strain gradient elasticity
- Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with \(k\)-method NURBS
- Isogeometric analysis of the Cahn-Hilliard phase-field model
- An isogeometric analysis approach to gradient damage models
- Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids
- A Family of ${C}^0$ Finite Elements For Kirchhoff Plates I: Error Analysis
- A posteriori error analysis for the Morley plate element with general boundary conditions
- Nitsche's method for interface problems in computa-tional mechanics
- The Finite Element Method with Penalty
- Survey of meshless and generalized finite element methods: A unified approach
- Generalized Continuum Mechanics: What Do We Mean by That?
- Asymptotic Analysis of the Boundary Layer for the Reissner–Mindlin Plate Model
- A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS
- The Mathematical Theory of Finite Element Methods
- A REFINED ERROR ANALYSIS OF MITC PLATE ELEMENTS
- ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES