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New principles of work and energy as well as power and energy rate for continuum field theories

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Abstract

New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola’s theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

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Authors and Affiliations

  1. Center for the Application of Mathematics and Department of Mathematics, Liaoning University, 110036, Shenyang, P R China

    Dai Tian-min

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  1. Dai Tian-min
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Paper from DAI Tian-min, Member of Editorial Committee, AMM

Foundation item: the National Science Foundation of China (19672023); the International Cooperation project of NSFC (10011130235) and DFG (51520001); the Research Foundation of Liaoning Education Committee (990111001)

Biography: DAI Tian-min (1931-), Professor, Doctor

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Tian-min, D. New principles of work and energy as well as power and energy rate for continuum field theories. Appl Math Mech 22, 1231–1239 (2001). https://doi.org/10.1007/BF02437846

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  • DOI: https://doi.org/10.1007/BF02437846

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