Quarterly of Applied Mathematics

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Exact closed form solution for an anti-plane deformation of anisotropic media

Author(s): Kazumi Watanabe; Abu Hanipah Bin Nawi
Journal: Quart. Appl. Math. 63 (2005), 301-307.
MSC (2000): Primary 34A05, 35J05
Posted: February 18, 2005
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Abstract: A closed form solution for the ordinary differential equation of Hill's type,

$\begin{displaymath}(1-\varepsilon\cos x)y^{''}(x)+a\varepsilon\sin xy'(x)+[a(a-1)/2-\{(a^2-1)/4\} (1-\varepsilon\cos x)]y(x)=0,\end{displaymath}$

is found and is applied to the stress analysis for an anisotropic medium whose axis of anisotropy is varying periodically with depth.

References:

1.: R. Selden, Effect of processing on weld line strength in five thermoplastics, Polym. Eng. Sci., 37 (1997), pp. 205-218.
2.: K. Watanabe and K. Adachi, SH wave in a transition layer of anisotropy, Int. J. Solids & Struct., 38 (2001), 4825-4838.
3.: M. L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech., Trans. ASME, Ser. E, 19 (1952), pp. 526-528.