Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models
From MaRDI portal
Publication:5243043
DOI10.1177/1081286517739669zbMath1425.74264OpenAlexW2768661852MaRDI QIDQ5243043
Sb Hosseini, Josef Kiendl, Viacheslav Balobanov, Jarkko Niiranen
Publication date: 13 November 2019
Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1177/1081286517739669
convergence analysissize effectsEuler-Bernoulli beamscouple stress theorystrain gradient elasticityauxeticsGalerkin formulations
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Micromechanics of solids (74M25) Energy minimization in equilibrium problems in solid mechanics (74G65)
Related Items
Isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects, Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory, Strain gradient elasticity theory of polymer networks, Generalized beam model for the analysis of wave propagation with a symmetric pattern of deformation in planar pantographic sheets, Anisotropic strain gradient thermoelasticity for cellular structures: plate models, homogenization and isogeometric analysis, The models of gradient mechanics and singularly perturbed boundary value problems, Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations, Nonclassical linear theories of continuum mechanics, An efficient numerical method for the quasi-static behaviour of micropolar viscoelastic Timoshenko beams for couple stress problems, On weak solutions of boundary value problems within the surface elasticity of Nth order, A weak form quadrature element formulation of geometrically exact beams with strain gradient elasticity, Variational asymptotic homogenization of beam-like square lattice structures, A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory, A discrete formulation of Kirchhoff rods in large-motion dynamics, Surface energy-enriched gradient elastic Kirchhoff plate model and a novel weak-form solution scheme, Nonlocal layerwise formulation for bending of multilayered/functionally graded nanobeams featuring weak bonding, Constitutively optimal governing equations for higher-grade elastic beams, Material characterization and computations of a polymeric metamaterial with a pantographic substructure, A geometrically nonlinear Euler-Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications, Nonlinear finite element analysis within strain gradient elasticity: Reissner-Mindlin plate theory versus three-dimensional theory, Three-point bending test of pantographic blocks: numerical and experimental investigation, Finite element method for stress-driven nonlocal beams, Strain gradient elasto-plasticity model: 3D isogeometric implementation and applications to cellular structures, 3D strain gradient elasticity: variational formulations, isogeometric analysis and model peculiarities, Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?, On boundary layers observed in some 1D second-gradient theories
Cites Work
- Unnamed Item
- Unnamed Item
- Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory
- B-spline interpolation of Kirchhoff-Love space rods
- Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
- Static and dynamic analysis of micro beams based on strain gradient elasticity theory
- A microstructure-dependent Timoshenko beam model based on a modified couple stress theory
- A review on the application of modified continuum models in modeling and simulation of nanostructures
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials
- Isogeometric analysis of structural vibrations
- Wave dispersion in gradient elastic solids and structures: a unified treatment
- Surface stress in solids
- Gradient elasticity with surface energy: Mode-III crack problem
- Experiments and theory in strain gradient elasticity.
- Bending of Euler-Bernoulli beams using Eringen's integral formulation: a paradox resolved
- Exact solution of Eringen's nonlocal integral model for bending of Euler-Bernoulli and Timoshenko beams
- Variational formulations and general boundary conditions for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
- On the gradient strain elasticity theory of plates
- Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams
- Single-variable formulations and isogeometric discretizations for shear deformable beams
- Couple stress based strain gradient theory for elasticity
- Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem
- A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams
- Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems
- Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
- Finite element static and stability analysis of gradient elastic beam structures
- A new Bernoulli-Euler beam model incorporating microstructure and surface energy effects
- Micro-structure in linear elasticity
- Strain and velocity gradient theory for higher-order shear deformable beams
- Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
- A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS