Variational analysis of gradient elastic flexural plates under static loading

DOI10.1016/j.ijsolstr.2010.06.003zbMath1196.74093OpenAlexW1989459215MaRDI QIDQ1960019

Sofia Papargyri-Beskou, Dimitrios E. Beskos, Antonios E. Giannakopoulos

Publication date: 12 October 2010

Published in: International Journal of Solids and Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ijsolstr.2010.06.003

zbMATH Keywords

variational methods static analysis gradient elasticity flexural plates classical and non-classical boundary conditions

Mathematics Subject Classification ID

Plates (74K20) Energy minimization in equilibrium problems in solid mechanics (74G65)

Related Items (47)

Revisiting bending theories of elastic gradient beams ⋮ Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates ⋮ Analysis of plate in second strain gradient elasticity ⋮ Lamé's strain potential method for plane gradient elasticity problems ⋮ Analytical solutions for the thermal vibration of strain gradient beams with elastic boundary conditions ⋮ Axisymmetric bending of strain gradient elastic circular thin plates ⋮ A non-classical Kirchhoff plate model incorporating microstructure, surface energy and foundation effects ⋮ 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 ⋮ Closed-form frequency solutions for simplified strain gradient beams with higher-order inertia ⋮ Size dependency in vibration analysis of nano plates; one problem, different answers ⋮ Variational formulations and general boundary conditions for sixth-order boundary value problems of gradient-elastic Kirchhoff plates ⋮ A review of presentations and discussions of the workshop Computational mechanics of generalized continua and applications to materials with microstructure that was held in Catania 29–31 October 2015 ⋮ A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory ⋮ A unifying variational framework for stress gradient and strain gradient elasticity theories ⋮ A non-classical third-order shear deformation plate model based on a modified couple stress theory ⋮ A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory ⋮ Size-dependent generalized thermoelasticity model for Timoshenko microbeams ⋮ Stress-driven nonlocal integral elasticity for axisymmetric nano-plates ⋮ Static analysis of orthotropic nanoplates reinforced by defective graphene based on strain gradient theory using a simple boundary method ⋮ On the mapping procedure based on higher‐order Hermite polynomials for laminated thin plates with arbitrary domains in gradient elasticity ⋮ A class of shear deformable isotropic elastic plates with parametrically variable warping shapes ⋮ A micromorphic approach to stress gradient elasticity theory with an assessment of the boundary conditions and size effects ⋮ Transient dynamic analysis of a fluid-saturated porous gradient elastic column ⋮ Strong unique continuation and global regularity estimates for nanoplates ⋮ Variational formulation and differential quadrature finite element for freely vibrating strain gradient Kirchhoff plates ⋮ A non-classical model for an orthotropic Kirchhoff plate embedded in a viscoelastic medium ⋮ On simplified deformation gradient theory of modified gradient elastic Kirchhoff-Love plate ⋮ Inverse load identification in vibrating nanoplates ⋮ A non-classical model for circular Kirchhoff plates incorporating microstructure and surface energy effects ⋮ Nonlinear vibration analysis of micro-plates based on strain gradient elasticity theory ⋮ Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory ⋮ Surface energy-enriched gradient elastic Kirchhoff plate model and a novel weak-form solution scheme ⋮ Bending and vibration analysis of generalized gradient elastic plates ⋮ A non-classical Mindlin plate model based on a modified couple stress theory ⋮ A microstructure- and surface energy-dependent third-order shear deformation beam model ⋮ Analysis of anisotropic gradient elastic shear deformable plates ⋮ Analytical solution for strain gradient elastic Kirchhoff rectangular plates under transverse static loading ⋮ Mechanical analysis of higher order gradient nanobeams ⋮ An application of a size-dependent model on microplate with elastic medium based on strain gradient elasticity theory ⋮ Anisotropy in strain gradient elasticity: simplified models with different forms of internal length and moduli tensors ⋮ Size effect on the static, dynamic and buckling analysis of orthotropic Kirchhoff-type skew micro-plates based on a modified couple stress theory: comparison with the nonlocal elasticity theory ⋮ An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories ⋮ Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates ⋮ Nonlinear plastic buckling analysis of micro-scale thin plates established on higher order mechanism-based strain gradient plasticity framework ⋮ Variational approach to dynamic analysis of third-order shear deformable plates within gradient elasticity ⋮ Finite element static and stability analysis of gradient elastic beam structures

Cites Work

This page was built for publication: Variational analysis of gradient elastic flexural plates under static loading