Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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


Authors: Kazumi Watanabe and Abu Hanipah Bin Nawi
Journal: Quart. Appl. Math. 63 (2005), 301-307
MSC (2000): Primary 34A05, 35J05
DOI: https://doi.org/10.1090/S0033-569X-05-00948-8
Published electronically: February 18, 2005
MathSciNet review: 2150776
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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  • 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.

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Additional Information

Kazumi Watanabe
Affiliation: Department of Mechanical Engineering, Yamagata University, Yonezawa, Yamagata 992-8510 Japan
Email: kazy@yz.yamagata-u.ac.jp

Abu Hanipah Bin Nawi
Affiliation: Department of Mechanical Engineering, Yamagata University, Yonezawa, Yamagata 992-8510 Japan

DOI: https://doi.org/10.1090/S0033-569X-05-00948-8
Received by editor(s): April 12, 2004
Published electronically: February 18, 2005
Article copyright: © Copyright 2005 Brown University

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