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

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (11): 1286-1290.

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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:1998-03-19 Revised:1999-04-28 Online:1999-11-18 Published:1999-11-18
Supported by:
the Natural Science Foundation of Jiangsu Province,China(BK97063)

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.

Key words: first integral, antisymmetric stress, constitutive equation, linear theory of nonlocal elasticity

2010 MSC Number:

O346.1
O343

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. Applied Mathematics and Mechanics (English Edition), 1999, 20(11): 1286-1290.

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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

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