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Research Papers

The Refined Theory of Plane Problems for One-Dimensional Quasicrystalline Bodies

[+] Author and Article Information
Yang Gao1

University of Kassel,  Institute of Mechanics, Kassel D-34125, Germanygaoyangg@gmail.com

Andreas Ricoeur

University of Kassel,  Institute of Mechanics, Kassel D-34125, Germanyricoeur@uni-kassel.de

1

Corresponding author.

J. Appl. Mech 79(1), 011004 (Nov 14, 2011) (7 pages) doi:10.1115/1.4004593 History: Received February 24, 2011; Revised July 08, 2011; Posted July 13, 2011; Published November 14, 2011; Online November 14, 2011

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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References

Figures

Grahic Jump Location
Figure 1

Stress-free hole in an infinite plate under remote shear loading τ

Grahic Jump Location
Figure 2

Stress-free hole in an infinite medium under remote tension loading T

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