New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics(Ⅲ)——Re-Discuss the Linear Theory of Nonlocal Elasticity

Huang Zaixing

Volume 20 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(11): 1193-1197

Huang Zaixing. New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics(Ⅲ)——Re-Discuss the Linear Theory of Nonlocal Elasticity[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1193-1197.

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New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics(Ⅲ)——Re-Discuss the Linear Theory of Nonlocal Elasticity

Huang Zaixing

Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P R China

Received Date: 1998-03-19
Rev Recd Date: 1999-04-28
Publish Date: 1999-11-15

Abstract

Abstract

In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal constitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given.
- first integral,
- antisymmetric stress,
- constitutive equation,
- linear theory of nonlocal elasticity

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References(3)

References

[1]	Eringen C.Vistas of nonlocal continuum physics[J].Int J Engrg Sci,1992,30(14):1551.
[2]	黄再兴.关于非局部场论的几个新观点及其在断裂力学中的应用(Ⅱ)——重论非线性非局部热弹性本构方程[J].应用数学和力学,1999,20(7):713～720.
[3]	Friedman,Katz M.A representation theorem for additive functionals[J].Arch Rational Mech Anal,1966,21(1):49.

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