Linearization stability and Signorini Series for the traction problem in elastostatics

DOI10.1017/S0308210500015870zbMath0533.73022MaRDI QIDQ3316681

Yieh-Hei Wan, Jerrold E. Marsden

Publication date: 1983

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

series expansiontraction problemcritical points of Betti formexplicit non- degeneracy conditiongeneralization of Signorini-Stoppelli schemes for power series solutionresults of Chillingworth, Marsden and Wan on symmetry and bifurcationSignorini compatibility conditions necessary and sufficient for linearization stabilitySignorini expansionthree dimensional elastostatics

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Critical points and critical submanifolds in differential topology (57R70) Elastic materials (74B99) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (6)

The Signorini perturbation scheme in an abstract setting ⋮ The Traction Problem For Incompressible Materials ⋮ On the steady motion of a coupled system solid-liquid ⋮ Symmetry and bifurcation in three-dimensional elasticity. II ⋮ Symmetry and bifurcation in three-dimensional elasticity ⋮ Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity

Cites Work

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• Symmetry and bifurcations of momentum mappings
• The structure of the space of solutions of Einstein's equations. II: Several Killing fields and the Einstein-Yang-Mills equations
• On Signorini's perturbation method in finite elasticity
• Symmetry and bifurcation in three-dimensional elasticity. I
• Linearization stability of the Einstein equations

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