Abstract
The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics. By combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress and virtual couple stress with cross terms of incremental rate type a new principle of power and energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.
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References
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Paper from Dai Tian-min, Member of Editorial Committee, AMM
Foundation item: the National Natural 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 power and energy rate of incremental rate type for generalized continuum field theories. Appl Math Mech 22, 1383–1389 (2001). https://doi.org/10.1007/BF02435541
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DOI: https://doi.org/10.1007/BF02435541
Key words
- generalized continua
- incremental rate type
- principles of power and energy rate
- generalized Piola's theorem