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The exact theory of one-dimensional quasicrystal deep beams

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Abstract

Without employing ad hoc assumptions, various equations and solutions for quasicrystal beams are deduced systematically and directly from the plane problem of one-dimensional quasicrystals. These equations and solutions can be used to construct the exact theory of deep beams for extension or compression and bending deformation forms. A method for the solution of two-dimensional equations is presented, and with the method the exact theory can now be explicitly established from the general solution of quasicrystals and the Lur’e method. The exact governing equations for beams under transverse loadings are derived directly from the exact beam theory. In three illustrative examples of quasicrystal beams it is shown that the exact or accurate solutions can be obtained by use of the exact theory.

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Authors and Affiliations

  1. College of Science, China Agricultural University, East Campus, P.O. Box 74, 100083, Beijing, China

    Yang Gao

  2. Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Yang Gao

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  1. Yang Gao
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Correspondence to Yang Gao.

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Gao, Y. The exact theory of one-dimensional quasicrystal deep beams. Acta Mech 212, 283–292 (2010). https://doi.org/10.1007/s00707-009-0257-1

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  • DOI: https://doi.org/10.1007/s00707-009-0257-1

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