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A mixed variational equation for a twelfth-order theory of bending of nonhomogeneous transversely isotropic plates

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Abstract

Departing from a linear-theory statement of the three-dimensional problem of a surface and edge loaded transversely isotropic layer, with material properties which are even functions of the thickness coordinate, we use a variational statement of this problem, with independent displacement and transverse stress variations, for a direct-methods derivation of a corresponding twelfth-order two-dimensional statement, which is believed to be computationally beneficial relative to corresponding statements involving independent displacement variations only.

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References

  • Chen, P. S.; Archer, R. R. (1989): Solutions of a twelfth order thick plate theory. Acta Mechanica. 79, 97–112

    Google Scholar 

  • Hildebrand, F. B.; Reissner, E.; Thomas, G. B. (1949): Notes on the foundations of the theory of small displacements of orthotropic shells. NACA TN 1833

  • Lo, K. H.; Christensen, R. M.; Wu, E. M. (1977): A high-order theory of plate deformations. J. Appl. Mech. 44, 663–676

    Google Scholar 

  • Murakami, H. (1986): Laminated composite plate theory with improved in-plane responses. J. Appl. Mech. 53, 661–666

    Google Scholar 

  • Preusser, G. (1984): Systematische Herleitung verbesserter Plattengleichungen. Ingen. Arch. 54, 51–61

    Google Scholar 

  • Reissner, E. (1983): A twelfth-order theory of transverse bending of transversely isotropic plates. Z. Angew. Math. Mech. 63, 285–289

    Google Scholar 

  • Reissner, E. (1985): Reflections on the theory of elastic plates. Appl. Mech. Rev. 38, 1453–1464

    Google Scholar 

  • Reissner, E. (1987a): On a generalization and on the meaning of some exact formulas of the theory of “moderataly thick” elastic plates. Int. J. Solids Structures. 23, 711–717

    Google Scholar 

  • Reissner, E. (1987b): On a certain mixed variational theorem and on laminated elastic shell theory, in “Refined dynamical theories of beams, plates and shells” (Edited by I.Elishakoff and H.Irretier); Berlin, Heidelberg, New York: Springer

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mechanics & Engineering Sciences, University of California, 92093, San Diego, La Jolla, CA, USA

    E. Reissner

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  1. E. Reissner
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Communicated by S. N. Atluri, June 8, 1990

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Reissner, E. A mixed variational equation for a twelfth-order theory of bending of nonhomogeneous transversely isotropic plates. Computational Mechanics 7, 355–360 (1991). https://doi.org/10.1007/BF00350164

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  • DOI: https://doi.org/10.1007/BF00350164

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