Classical plate buckling theory as the small‐thickness limit of three‐dimensional incremental elasticity

DOI10.1002/ZAMM.201200160zbMath1432.74073OpenAlexW1501575828MaRDI QIDQ5404732

Ray W. Ogden, David J. Steigmann

Publication date: 28 March 2014

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201200160

zbMATH Keywords

elastic stabilityincremental elasticityplate buckling

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Plates (74K20) Bifurcation and buckling (74G60)

Related Items (8)

A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates ⋮ Asymptotically correct boundary conditions for the higher-order theory of plate bending ⋮ Bifurcation of elastic solids with sliding interfaces ⋮ Design of pre-stressed plate-strips to cover non-developable shells ⋮ Mechanics of materially uniform thin films ⋮ Buckling of thin-walled cylinders from three dimensional nonlinear elasticity ⋮ Shell design from planar pre-stressed structures ⋮ A well-posed finite-strain model for thin elastic sheets with bending stiffness

Cites Work

• Two-dimensional models for the combined bending and stretching of plates and shells based on three-dimensional linear elasticity
• Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina
• On uniqueness and stability in the theory of finite elastic strain
• The Graves condition for variational problems of arbitrary order
• The Rotation Associated with Large Strains
• Theory of Linearly Elastic Residually Stressed Plates

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