Nonlinear Theory of Elastic Stability

Uniform stability of damped nonlinear vibrations of an elastic string

Abstract. Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the ...

The Nonlinear Theory of Elastic Shells with Phase Transitions

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Elastic stability of DNA configurations. I. General theory.

Results are presented in the theory of the elastic rod model for DNA, among which are criteria enabling one to determine whether a calculated equilibrium configuration of a DNA segment is stable in the sense that it gives a local minimum to the sum of the segment's elastic energy and the potential of forces acting on it. The derived stability criteria are applicable to plasmids and to linear se...

Non-Classical Problems in the Theory of Elastic Stability

When a structure is put under an increasing compressive load, it may become unstable and buckle. Buckling is a particularly significant concern in designing shell structures such as aircraft, automobiles, ships, or bridges. This book discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that inherently exist in real systems. The techniques ...

Nonlinear Elastic