Power Type Variational Principles and Work-Energy Type Quasi-Variational Principles and Their Applications

FENG Xiao-jiu; LIANG Li-fu

doi:10.3879/j.issn.1000-0887.2015.11.006

Volume 36 Issue 11

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FENG Xiao-jiu, LIANG Li-fu. Power Type Variational Principles and Work-Energy Type Quasi-Variational Principles and Their Applications[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1178-1190. doi: 10.3879/j.issn.1000-0887.2015.11.006

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Power Type Variational Principles and Work-Energy Type Quasi-Variational Principles and Their Applications

doi: 10.3879/j.issn.1000-0887.2015.11.006

FENG Xiao-jiu¹,
LIANG Li-fu²

¹School of Environmental and Safety Engineering, Changzhou University, Changzhou, Jiangsu 213164, P.R.China;²Harbin Engineering University, Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China(10272034)

Received Date: 2015-05-18
Rev Recd Date: 2015-09-09
Publish Date: 2015-11-15

Abstract

Abstract

Since the power type variational principle was established by CHIEN Wei-zang, the differences and relations between the power type variational principles and the work-energy type quasi-variational principles in theory and practice have been a hot topic in the academic circle. According to the Jourdain principle and the d’Alembert principle, the power type variational principles and the work-energy type quasi-variational principles were established for the incompressible viscous flow in liquid-filled systems with the variational integral operation method, so as to deduce their stationary condition and quasi-stationary condition, respectively. The applications of the power type variational principles and the work-energy type quasi-variational principles in the finite element method were studied. It shows that the work-energy type quasi-variational principles coincide with the d’Alembert principle and the power type variational principles do with the Jourdain principle. The power type variational principles directly work in the state space so that they not only omit some transforms in the time space during the building of the related variational principles, but also make it convenient to build numerical models for dynamic problems.

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References(22)

References

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