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On conservation laws in elastodynamics
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DOI：10.1016/j.ijsolstr.2004.01.018.png)
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摘要
En 中文
The objective of this investigation is the establishment of governing balance and conservation laws in elastodynamics. The feature of the approach employed here consists in placing time on the same level as the space coordinates, as is done in the theory of relativity, i.e., pursuing a 4 x 4 formalism. Both the Lagrangian and the Eulerian descriptions of the postulated Lagrangian function are formulated. The Euler Lagrange equations in each of the two descriptions are discussed, as well as the results of the application of the gradient, divergence and curl. The latter two operations are made to act on the product of coordinates and the Lagrangian function, i.e., a four-vector. In this manner a variety of balance and conservation laws are derived, partly well known and partly seemingly novel. In each case the general results for elastodynamics are illustrated for the simple case of a linearly elastic bar. (C) 2004 Elsevier Ltd. All rights reserved.
Keyword:
elastodynamics
balance law
conservation law
4 x 4 formalism
Lagrangian description
Eulerian description
elastic bar
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期刊
IF:
3.8
论文数:
1.2W
被引数:
3.1W
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