On a consistent dynamic finite-strain plate theory and its linearization

DOI10.1007/s10659-016-9575-4zbMath1349.74248OpenAlexW2316033982MaRDI QIDQ346534

Zilong Song, Hui-Hui Dai

Publication date: 29 November 2016

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-016-9575-4

zbMATH Keywords

dynamicsasymptotic analysisplate theoryfinite and linearized elasticity

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Plates (74K20)

Related Items

On a consistent rod theory for a linearized anisotropic elastic material II. Verification and parametric study, A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates, A uniform framework for the dynamic behavior of linearized anisotropic elastic rods, A novel reduced model for a linearized anisotropic rod with doubly symmetric a cross-section: I. Theory, Interfacial delamination-induced unidirectional propagation of guided waves in multilayered media, On a consistent finite-strain plate theory of growth, A midsurface elasticity model for a thin, nonlinear, gradient elastic plate, On a consistent dynamic finite-strain shell theory and its linearization, Asymptotic Derivation of Nonlinear Plate Models from Three-Dimensional Elasticity Theory, A Discontinuous Galerkin Method with Minimal Dissipation for a Finite-Strain Plate, A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle, On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mechanics of generalized continua
• Thin-plate theory for large elastic deformations
• A refined nonlinear theory of plates with transverse shear deformation
• A classification of thin plate models by asymptotic expansion of non-linear three-dimensional equilibrium equations
• A justification of the von Kármán equations
• On Timoshenko-Reissner type theories of plates and shells
• A justification of a nonlinear model in plate theory
• On the asymptotic membrane theory of thin hyperelastic plates
• On consistent plate theories
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Koiter's shell theory from the perspective of three-dimensional nonlinear elasticity
• On generalized Cosserat-type theories of plates and shells: a short review and bibliography
• The equations of motion of a plate with residual stress
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Mechanics of materially uniform thin films
• An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
• Singular perturbation methods in the synthesis of control policies for multi-stage production-inventory systems
• On a formulation of a nonlinear theory of plates and shells with applications
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Flexure of Simply Supported Thick Homogeneous and Laminated Rectangular Plates
• An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates