Symmetry and bifurcation in three-dimensional elasticity

DOI10.1007/BF00281519zbMath0536.73011MaRDI QIDQ792119

Jerrold E. Marsden, Yieh-Hei Wan

Publication date: 1983

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

existencenumber of solutionsmaterial symmetryequilibrium solutionsundeformed statebifurcation of the stress potentialstress is the derivative of a potentialsystem of forces

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Nonlinear elasticity (74B20) Bifurcation and buckling (74G60) Dynamical problems in solid mechanics (74H99) Bifurcations in context of PDEs (35B32) Equilibrium (steady-state) problems in solid mechanics (74G99)

Related Items (11)

Bifurcation in the traction problem for a transversely isotropic material ⋮ The Signorini perturbation scheme in an abstract setting ⋮ The Traction Problem For Incompressible Materials ⋮ On the hydrodynamics of biaxial nematic liquid crystals. I: General theory ⋮ Minimization in nonlinear elasticity theory for bodies reinforced with inextensible cords ⋮ Heteroclinic cycles in dynamical systems with broken spherical symmetry ⋮ Elastostatics in the presence of a temperature distribution or inhomogeneity ⋮ On the traction problem of dead loading in linear elasticity with initial stress ⋮ Abstract forced symmetry breaking and forced frequency locking of modulated waves ⋮ On the steady motion of a coupled system solid-liquid ⋮ Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity

Cites Work

• Group theoretic methods in bifurcation theory. With an appendix by P. Olver
• Sull'esistenza di soluzioni delle equazioni dell'elastostatica isoterma nel caso di sollecitazioni dotate di assi di equilibrio. I-III
• Symmetry and bifurcation in three-dimensional elasticity. II
• The role of Fredholm conditions in Signorini's perturbation method
• Imperfect bifurcation in the presence of symmetry
• Signorini's perturbation scheme for a general reference configuration in finite elastostatics
• Symmetry and bifurcation in three-dimensional elasticity. I
• Morse theory of certain symmetric spaces
• Groups of diffeomorphisms and the motion of an incompressible fluid
• The Morse Lemma in Infinite Dimensions via Singularity Theory
• Linearization stability and Signorini Series for the traction problem in elastostatics
• Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions
• Almost-Riemannian Structures on Banach Manifolds: The Morse Lemma and the Darboux Theorem
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