Bending and stability analysis of gradient elastic beams
From MaRDI portal
Publication:1811567
DOI10.1016/S0020-7683(02)00522-XzbMath1022.74010MaRDI QIDQ1811567
K. G. Tsepoura, D. Polyzos, Dimitrios E. Beskos, Sofia Papargyri-Beskou
Publication date: 17 June 2003
Published in: International Journal of Solids and Structures (Search for Journal in Brave)
stabilitybendingboundary value problemsvariational principlesurface energycritical buckling loadnon-classical boundary conditionsmicrostructural effectsBernoulli-Euler beamslinear theory of gradient elasticity
Related Items (93)
Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory ⋮ Bending, buckling and vibration of small-scale tapered beams ⋮ Revisiting bending theories of elastic gradient beams ⋮ Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams ⋮ Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach ⋮ Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates ⋮ Some \(C^0\)-continuous mixed formulations for general dipolar linear gradient elasticity boundary value problems and the associated energy theorems ⋮ Size effects on strength, toughness and fatigue crack growth of gradient elastic solids ⋮ Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory ⋮ Strain and velocity gradient theory for higher-order shear deformable beams ⋮ Lamé's strain potential method for plane gradient elasticity problems ⋮ Plane strain gradient elastic rectangle in tension ⋮ A new model for thermal buckling of an anisotropic elastic composite beam incorporating piezoelectric, flexoelectric and semiconducting effects ⋮ Analytical solutions for the thermal vibration of strain gradient beams with elastic boundary conditions ⋮ Structural analysis using a dipolar elastic Timoshenko beam ⋮ Torsional vibrations of a column of fine-grained material: a gradient elastic approach ⋮ Wave propagation in and free vibrations of gradient elastic circular cylindrical shells ⋮ Size dependent analysis of functionally graded microbeams using strain gradient elasticity incorporated with surface energy ⋮ Revisiting finite difference and finite element methods applied to structural mechanics within enriched continua ⋮ A gradient elasticity model of Bernoulli-Euler nanobeams in non-isothermal environments ⋮ Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling ⋮ Closed-form frequency solutions for simplified strain gradient beams with higher-order inertia ⋮ A hierarchy of simplified constitutive models within isotropic strain gradient elasticity ⋮ Application of gradient elasticity to armchair carbon nanotubes: size effects and constitutive parameters assessment ⋮ A nonlinear strain gradient beam formulation ⋮ Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams ⋮ Wave propagation characteristics of a twisted micro scale beam ⋮ Analytical length scale calibration of nonlocal continuum from a microstructured buckling model ⋮ Strain gradient elasticity theory of polymer networks ⋮ Microstructure-dependent couple stress theories of functionally graded beams ⋮ Adhesive lap-joints: a micro-scale numerical investigation ⋮ Higher-order shear beam theories and enriched continuum ⋮ Nonlinear strain gradient elastic thin shallow shells ⋮ A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory ⋮ The basic differential equations of self-anchored cable-stayed suspension bridge ⋮ A nonlinear microbeam model based on strain gradient elasticity theory with surface energy ⋮ Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory ⋮ Wave propagation in 3-D poroelastic media including gradient effects ⋮ INVESTIGATION OF THE INFLUENCE OF AN INTERMEDIATE HINGE SUPPORT IN THE PROBLEM OF BENDING OF AN ELASTICALLY RESTRAINED ORTHOTROPIC BEAM ⋮ Size-dependent generalized thermoelasticity model for Timoshenko microbeams ⋮ Analysis of micro-rotating disks based on the strain gradient elasticity ⋮ Transient dynamic analysis of a fluid-saturated porous gradient elastic column ⋮ Coupled newmark beta technique and GDQ method for energy harvesting and vibration control of the piezoelectric MEMS/NEMS subjected to a blast load ⋮ The models of gradient mechanics and singularly perturbed boundary value problems ⋮ Wave propagation in flexoelectric microstructured solids ⋮ Initial post‐buckling of the micro‐scaled beams based on the strain gradient elasticity ⋮ A weak form quadrature element formulation of geometrically exact beams with strain gradient elasticity ⋮ SNAP-THROUGH AND BIFURCATION OF NANO-ARCHES ON ELASTIC FOUNDATION BY THE STRAIN GRADIENT AND NONLOCAL THEORIES ⋮ Size-dependent elastic properties of micro- and nano-honeycombs ⋮ A boundary element method for solving 2-D and 3-D static gradient elastic problems. I: Integral formulation. ⋮ Variational analysis of gradient elastic flexural plates under static loading ⋮ Closed-form solutions for gradient elastic beams with geometric discontinuities by Laplace transform ⋮ A new Bernoulli-Euler beam model incorporating microstructure and surface energy effects ⋮ Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration ⋮ Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates ⋮ Bending and vibration analysis of generalized gradient elastic plates ⋮ Differential quadrature-based solution for non-classical Euler-Bernoulli beam theory ⋮ Nonlocal layerwise formulation for bending of multilayered/functionally graded nanobeams featuring weak bonding ⋮ A microstructure- and surface energy-dependent third-order shear deformation beam model ⋮ Static, stability and dynamic analyses of second strain gradient elastic Euler-Bernoulli beams ⋮ Buckling analyses of three characteristic-lengths featured size-dependent gradient-beam with variational consistent higher order boundary conditions ⋮ Application of hetero junction CNTs as mass nanosensor using nonlocal strain gradient theory: an analytical solution ⋮ Multiscale Buckling and Post-Buckling Analysis: a Comprehensive Review ⋮ A novel weak form quadrature element for gradient elastic beam theories ⋮ Buckling and Nonlinear Vibration of Size-Dependent Nanobeam based on the Non-Local Strain Gradient Theory ⋮ FEM formulation for size-dependent theory with application to micro coated piezoelectric and piezomagnetic fiber-composites ⋮ Analytical solution for strain gradient elastic Kirchhoff rectangular plates under transverse static loading ⋮ Mechanical analysis of higher order gradient nanobeams ⋮ Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory ⋮ The size-dependent natural frequency of Bernoulli-Euler micro-beams ⋮ Stability analysis of gradient elastic circular cylindrical thin shells ⋮ Static and dynamic analysis of micro beams based on strain gradient elasticity theory ⋮ A new Timoshenko beam model incorporating microstructure and surface energy effects ⋮ An application of a size-dependent model on microplate with elastic medium based on strain gradient elasticity theory ⋮ On bending of strain gradient elastic micro-plates ⋮ A spectral finite element for axial-flexural-shear coupled wave propagation analysis in lengthwise graded beam ⋮ Reissner stationary variational principle for nonlocal strain gradient theory of elasticity ⋮ Electrostatic nonlinear bending, buckling and free vibrations of viscoelastic microbeams based on the modified couple stress theory ⋮ A size-dependent Reddy-Levinson beam model based on a strain gradient elasticity theory ⋮ A micro scale Timoshenko beam model based on strain gradient elasticity theory ⋮ Bending and buckling of thin strain gradient elastic beams ⋮ A microstructure-dependent Timoshenko beam model based on a modified couple stress theory ⋮ A well-posed Euler-Bernoulli beam model incorporating nonlocality and surface energy effect ⋮ Nonlocal integral static problems of nanobeams resting on an elastic foundation ⋮ Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams ⋮ Interior penalty discontinuous Galerkin FEMs for a gradient beam and cnts ⋮ On a strain gradient elastic Timoshenko beam model ⋮ Boundary element analysis of mode I and mixed mode (I and II) crack problems of 2D gradient elasticity ⋮ Wave dispersion in gradient elastic solids and structures: a unified treatment ⋮ A NONLOCAL CURVED BEAM MODEL BASED ON A MODIFIED COUPLE STRESS THEORY ⋮ Uncertainty quantification via \(\lambda\)-Neumann methodology of the stochastic bending problem of the Levinson-Bickford beam ⋮ A novel formulation for the weak quadrature element method for solving vibration of strain gradient graded nonlinear nanobeams ⋮ Finite element static and stability analysis of gradient elastic beam structures
This page was built for publication: Bending and stability analysis of gradient elastic beams
