scholarly journals On finite anti-plane shear for imcompressible elastic materials

1976 ◽  
Vol 19 (4) ◽  
pp. 400-415 ◽  
Author(s):  
James K. Knowles
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Antiplane Shear ◽  
Principal Result ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Elastic Materials ◽  
Plane Shear ◽  
Necessary And Sufficient

AbstractThis paper is concerned with deformations corresponding to antiplane shear in finite elastostatics. The principal result is a necessary and sufficient condition for a homogeneous, isotropic, incompressible material to admit nontrivial states of anti-plane shear. The condition is given in terms of the strain energy density characteristic of the material and is illustrated by means of special examples.

scholarly journals A note on anti-plane shear for compressible materials in finite elastostatics

1977 ◽  
Vol 20 (1) ◽  
pp. 1-7 ◽  
Author(s):  
James K. Knowles
Keyword(s):  
Elastic Material ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plane Shear ◽  
Isotropic Elastic Material ◽  
Necessary And Sufficient ◽  
Compressible Materials

AbstractThis note gives a necessary and sufficient condition that a compressible, isotropic elastic material should admit non-trivial states of finite anti-plane shear.

A Closure Criterion for Orthogonal Functions

1952 ◽  
Vol 4 ◽  
pp. 198-203 ◽  
Author(s):  
Ross E. Graves
Keyword(s):  
Infinite Series ◽  
Principal Result ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Orthogonal Functions ◽  
Necessary And Sufficient

In this paper we give a simple, necessary, and sufficient condition for a sequence of orthogonal functions to be closed in L2. In theory the question of closure is reduced to the evaluation of certain integrals and the summation of an infinite series whose terms depend only upon the index n. Our principal result isLet p(t) be a function whose zeros and discontinuities have Jordan content zero, such that for each x ∊ (a, b), p(t) ∊ L2 on min (c, x) < t < max (c, x), where a ≤ c ≤ b. (a, b, and c may be infinite.)

Strain energy density bounds for linear anisotropic elastic materials

1993 ◽  
Vol 30 (2) ◽  
pp. 191-196 ◽  
Author(s):  
M. M. Mehrabadi ◽  
S. C. Cowin ◽  
C. O. Horgan
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Materials ◽  
Anisotropic Elastic
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