Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The anisotropic elastic semi-infinite strip


Authors: M. Z. Wang, T. C. T. Ting and Gong Pu Yan
Journal: Quart. Appl. Math. 51 (1993), 283-297
MSC: Primary 73C05; Secondary 73B40
DOI: https://doi.org/10.1090/qam/1218369
MathSciNet review: MR1218369
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Abstract: It is known that the stresses of an isotropic elastic semi-infinite strip decay exponentially at large distance $ {x_1}$ from the end $ {x_1} = 0$ if the sides $ {x_2} = \pm 1$ are traction free and the loading at $ {x_1} = 0$ is in self-equilibrium. We study the associated problem for a general anisotropic elastic strip. Eight different side conditions at $ {x_2} = \pm 1$ and eight different end conditions at $ {x_1} = 0$ are considered. With the Stroh formalism, all these different side and end conditions are encompassed in one simple formulation. It is shown that, for certain side conditions, the loading at $ {x_1} = 0$ need not be in self-equilibrium. The decay factor for the strip of monoclinic materials with the plane of symmetry at $ {x_3} = 0$ and with the sides $ {x_2} = \pm 1$ being traction free is derived, and it has a remarkably simple expression. Numerical calculations of the smallest decay factor are presented.


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DOI: https://doi.org/10.1090/qam/1218369
Article copyright: © Copyright 1993 American Mathematical Society


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