Theory of Elastic Stability

Knops, R. J.; Wilkes, E. W.

doi:10.1007/978-3-642-69569-8_2

Cited by 104 publications

(68 citation statements)

References 206 publications

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“…The mechanical interpretation of (16) is obvious. Estimate (17) may be interpreted with the help of the theory of elastic stability [14]. Finally, estimate (18) is related to the defining property of a definite elastic heat conductor and is in accordance with the consequence (9) of the heat conduction inequality.…”

mentioning

confidence: 93%

On the asymptotic partition of energy in linear thermoelasticity

Chiriţă¹

1987

Quart. Appl. Math.

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1. Introduction. The question of partition of energy in the asymptotic form was first investigated by Lax and Phillips [1] and Brodsky [2], Further, this problem has been studied by Goldstein [3,4], In his elegant analysis of the abstract wave equation, Goldstein applies the semigroup theory in order to obtain an equipartition theorem stating that the difference of the kinetic energy and the potential energy vanishes as the time approaches infinity. By means of the Paley-Wiener theorem, Duffin [5] has shown that if a solution of the classical wave equation has compact support, then after a finite time the kinetic energy of the wave is constant and equals the potential energy.Levine [6] later treated an abstract version of Goldstein's approach by use of the Lagrange identity method. His result represents a simplified proof that asymptotic equipartition occurs between the Cesaro means of the kinetic and potential energies, a fact first demonstrated by Goldstein [4], The asymptotic equipartition between the mean kinetic and strain energies within the context of linear elastodynamics was established by

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confidence: 93%

On the asymptotic partition of energy in linear thermoelasticity

Chiriţă¹

1987

Quart. Appl. Math.

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“…are prescribed then the primary state [6] is defined to be a motion whose deformation function (1) satisfies the equation at motion (3) subject to the consitutive equation (4) and the boundary conditions (10) and (11). It should be noted that, in the conditions (10) and (11) 3Br denotes the boundary of Br, Q, is some subset of 3Br and N is the outward unit normal on 3Br.…”

mentioning

confidence: 99%

“…It should be noted that, in the conditions (10) and (11) 3Br denotes the boundary of Br, Q, is some subset of 3Br and N is the outward unit normal on 3Br. A secondary state [6] of the body SS is a motion, defined by the deformation, x* = x*(X, t).…”

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confidence: 99%

An existence and uniqueness theorem for incremental viscoelasticity

Quintanilla¹,

Williams²

1985

Quart. Appl. Math.

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“…The meaning is to be understood by context. Moreover, the stability for elastic body is equivalent to that the Rayleigh's quotient having a positive lower bound [24]. Thus, Rayleigh's quotient could be a preferred approach to investigate stability of an elastic body.…”

Section: Rayleigh's Quotientmentioning

confidence: 99%

Stability of elastic material with negative stiffness and negative Poisson's ratio

Shang

Lakes

2007

Physica Status Solidi (b)

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PACS 46. 05.+b, 62.20.Dc Stability of cuboids and cylinders of an isotropic elastic material with negative stiffness under partial constraint is analyzed using an integral method and Rayleigh quotient. It is not necessary that the material exhibit a positive definite strain energy to be stable. The elastic object under partial constraint may have a negative bulk modulus K and yet be stable. A cylinder of arbitrary cross section with the lateral surface constrained and top and bottom planar surfaces is stable provided the shear modulus G > 0 and -G/3 < K < 0 or K > 0. This corresponds to an extended range of negative Poisson's ratio, -∞ < ν < -1. A cuboid is stable provided each of its surfaces is an aggregate of regions obeying fully or partially constrained boundary conditions.

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Theory of Elastic Stability

Cited by 104 publications

References 206 publications

On the asymptotic partition of energy in linear thermoelasticity

On the asymptotic partition of energy in linear thermoelasticity

An existence and uniqueness theorem for incremental viscoelasticity

Stability of elastic material with negative stiffness and negative Poisson's ratio

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