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 consitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given.
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References
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Communicated by Fan Weixum
Foundation item: the Natural Science Foundation of Jiangsu Province, China (BK97063)
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Zaixing, H. 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. Appl Math Mech 20, 1286–1290 (1999). https://doi.org/10.1007/BF02463798
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DOI: https://doi.org/10.1007/BF02463798