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Variational principles for the linear dynamic theory of micropolar viscoelasticity

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Progress in Applied Mechanics

Part of the book series: Mechanics of Surface Structures ((MOSS,volume 6))

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Abstract

In the present paper, variational principles for the linear dynamic theory of micropolar viscoelasticity are derived by using J. T. Oden and J. N. Reddy’s method of the inverse problem of the calculus of variations, M. E. Gurtin’s convolution method, and Chien Wei-zang’s method of the Lagrange multipliers.

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References

  1. Oden, J. T. and Reddy, J. N., Variational Methods in Theoretical Mechanics (1976).

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  2. Gurtin, M. E., “Variational principles in the linear theory of viscoelasticity”, Arch. Rat. Mech. Anal. 13 (1963), 179–191.

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  3. Chien Wei-zang, Variational Method and Finite Elements, (I) (in Chinese), Science Press, Beijing (1980).

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  4. Eringen, A. C., “Linear theory of micropolar viscoelasticity”, Int. J. Engng. Sci. 5 (1967), 191–204.

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  5. Guo Zhong-heng, Non-linear Elastic Theory (in Chinese), Science Press, Beijing (1980).

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  6. Hu Hai-chang, Variational Principles of Elasticity and Its Applications (in Chinese), Science Press, Beijing (1981).

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  7. Hlavácěk, I. & M., “On the existence and uniqueness of solutions and some variational principles in linear theories of elasticity with couple-stresses”, Aplikace Matematiky 14 (1969), 387–426.

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  8. Gurtin, M. E., “Variational principles for linear electrodynamics”, Arch. Rat. Mech. Anal. 16 (1964), 234–250.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Liaoning University, Shenyang, Liaoning, PRC

    Tai Tien-Min

Authors
  1. Tai Tien-Min
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Editor information

Editors and Affiliations

  1. Lanzhou University, 730001, Lanzhou, Gansu, People’s Republic of China

    Yeh Kai-yuan

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© 1987 Martinus Nijhoff Publishers, Dordrecht

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Tien-Min, T. (1987). Variational principles for the linear dynamic theory of micropolar viscoelasticity. In: Kai-yuan, Y. (eds) Progress in Applied Mechanics. Mechanics of Surface Structures, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3487-0_1

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  • DOI: https://doi.org/10.1007/978-94-009-3487-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8061-3

  • Online ISBN: 978-94-009-3487-0

  • eBook Packages: Springer Book Archive

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