Without employing ad hoc assumptions, various equations and solutions for plane problems of one-dimensional quasicrystals are deduced systematically. A method for the exact solution of three-dimensional equations is presented under homogeneous and nonhomogeneous boundary conditions. The equations and solutions are used to construct the refined theory of thick plates for both an in-plane extensional deformation regime and a normal or shear surface loading. With this method, the refined theory can now be explicitly established from the general solution of quasicrystals and the Lur’e method. In two illustrative examples of infinite plates with a circular hole, it is shown that explicit expressions of analytical solutions can be obtained by using the refined theory.
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January 2012
Research Papers
The Refined Theory of Plane Problems for One-Dimensional Quasicrystalline Bodies
Andreas Ricoeur
Andreas Ricoeur
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Yang Gao
Andreas Ricoeur
J. Appl. Mech. Jan 2012, 79(1): 011004 (7 pages)
Published Online: November 14, 2011
Article history
Received:
February 24, 2011
Revised:
July 8, 2011
Posted:
July 13, 2011
Published:
November 14, 2011
Online:
November 14, 2011
Citation
Gao, Y., and Ricoeur, A. (November 14, 2011). "The Refined Theory of Plane Problems for One-Dimensional Quasicrystalline Bodies." ASME. J. Appl. Mech. January 2012; 79(1): 011004. https://doi.org/10.1115/1.4004593
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