Variational formulations and general boundary conditions for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
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Publication:1658575
DOI10.1016/j.euromechsol.2016.09.001zbMath1406.74446OpenAlexW2518763258MaRDI QIDQ1658575
Antti H. Niemi, Jarkko Niiranen
Publication date: 15 August 2018
Published in: European Journal of Mechanics. A. Solids (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.euromechsol.2016.09.001
existenceboundary conditionsuniquenessvariational formulationstrain gradient elasticityKirchhoff plates
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Cites Work
- Unnamed Item
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- Torsional vibrations of a column of fine-grained material: a gradient elastic approach
- A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory
- A classification of higher-order strain-gradient models --- linear analysis
- 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 new Kirchhoff plate model based on a modified couple stress theory
- 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 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
- Elastic materials with couple-stresses
- 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
- On the range of applicability of the Reissner--Mindlin and Kirchhoff--Love plate bending models
- Experiments and theory in strain gradient elasticity.
- Bending of Euler-Bernoulli beams using Eringen's integral formulation: a paradox resolved
- A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory
- On the gradient strain elasticity theory of plates
- Couple stress based strain gradient theory for elasticity
- 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
- Variational analysis of gradient elastic flexural plates under static loading
- On generalized Cosserat-type theories of plates and shells: a short review and bibliography
- 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
- Theoretical analysis of a class of mixed, \(C^{0}\) continuity formulations for general dipolar gradient elasticity boundary value problems
- Micro-structure in linear elasticity
- Analysis of plate in second strain gradient elasticity
- Plane strain gradient elastic rectangle in tension
- Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids
- On the accuracy of Reissner–Mindlin plate model for stress boundary conditions
- Generalized Continuum Mechanics: What Do We Mean by That?
- Asymptotic Analysis of the Boundary Layer for the Reissner–Mindlin Plate Model
- Mixed Finite Element Methods and Applications
- Existence of weak solutions in elasticity
- A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS
- The Mathematical Theory of Finite Element Methods
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