On bifurcation in finite elasticity: Buckling of a rectangular rod
From MaRDI portal
Publication:1024800
DOI10.1007/s10659-008-9162-4zbMath1163.74017OpenAlexW1997294733MaRDI QIDQ1024800
Henry C. Simpson, Spector, Scott J.
Publication date: 17 June 2009
Published in: Journal of Elasticity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10659-008-9162-4
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Bifurcation and buckling (74G60)
Related Items (18)
On the positivity of the second variation in finite elasticity ⋮ Marginal material stability ⋮ Fourier decomposition of properly elliptic boundary value problems in a half-plane ⋮ ANALYTICAL SOLUTIONS FOR THE POST-BUCKLING STATES OF AN INCOMPRESSIBLE HYPERELASTIC LAYER ⋮ The exponentiated Hencky-logarithmic strain energy. I: Constitutive issues and rank-one convexity ⋮ Violation of the complementing condition and local bifurcation in nonlinear elasticity ⋮ On the uniqueness of energy minimizers in finite elasticity ⋮ The complementing and Agmon's conditions in finite elasticity, three dimensions ⋮ Buckling and barrelling instabilities in finite elasticity ⋮ A continuously perturbed Dirichlet energy with area-preserving stationary points that `buckle' and occur in equal-energy pairs ⋮ Buckling of residually stressed plates: An asymptotic approach ⋮ Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition ⋮ Shear-driven planar Couette and Taylor-like instabilities for a class of compressible isotropic elastic solids ⋮ BMO and elasticity: Korn's inequality; local uniqueness in tension ⋮ The flip side of buckling ⋮ The complementing and Agmon's conditions in finite elasticity ⋮ On bifurcation in finite elasticity: Buckling of a rectangular rod ⋮ On failure of the complementing condition and nonuniqueness in linear elastostatics
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On copositive matrices and strong ellipticity for isotropic elastic materials
- On barrelling instabilities in finite elasticity
- Quasiconvexity at the boundary, positivity of the second variation and elastic stability
- Energy minimizers in nonlinear elastostatics and the implicit function theorem
- Buckling and barrelling instabilities in finite elasticity
- Weak local minimizers in finite elasticity
- The flip side of buckling
- On bifurcation in finite elasticity: Buckling of a rectangular rod
- On failure of the complementing condition and nonuniqueness in linear elastostatics
- Singularities and groups in bifurcation theory. Volume I
- On the differentiability of O(n) invariant functions of symmetric matrices
- On the positivity of the second variation in finite elasticity
- Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
- Buckling instabilities in a thick elastic three-ply composite plate under thrust
- Bifurcation phenomena in the plane compression test
- On the failure of ellipticity of the equations for finite elastostatic plane strain
- Ordinary differential equations of non-linear elasticity. II: Existence and regularity theory for conservative boundary value problems
- Convexity conditions and existence theorems in nonlinear elasticity
- Some properties of the set of fourth-order tensors, with application to elasticity
- Global continuation in nonlinear elasticity
- Quasiconvexity at the boundary and a simple variational formulation of Agmon's condition
- Global bifurcation in nonlinear elasticity with an application to barrelling states of cylindrical columns
- Differentiability properties of isotropic functions
- Necessary conditions at the boundary for minimizers in finite elasticity
- An introduction to continuum mechanics
- Post-bifurcation equilibria in the plane-strain test of a hyperelastic rectangular block
- Localized thickening of a compressed elastic band
- Some existence theorems of the traction boundary value problem of linearized elastostatics
- Stability of a compressed neo-Hookean rectangular parallelepiped
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- The instability of slightly compressible rectangular rubberlike solids under biaxial loadings
- On the definition of elastic moduli
- A theorem of tensor calculus and its application to isotropic elasticity
- The coerciveness problem for integro-differential forms
- Another approach to elliptic boundary problems
- On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
- On Korn's second inequality
- Buckling and barrelling instabilities on non-linearly elastic columns
- Leonhard Euler's Elastic Curves
- Buckling, barrelling, and surface instabilities of a finite, transversely isotropic circular cylinder
- The coerciveness problem for forms over vector valued functions
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
- General boundary value problems for elliptic partial differential equations
This page was built for publication: On bifurcation in finite elasticity: Buckling of a rectangular rod
