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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A closed form solution for the ordinary differential equation of Hill’s type, \[ (1-\varepsilon \cos x)y^{”}(x)+a\varepsilon \sin xy’(x)+[a(a-1)/2-\{(a^2-1)/4\} (1-\varepsilon \cos x)]y(x)=0,\] is found and is applied to the stress analysis for an anisotropic medium whose axis of anisotropy is varying periodically with depth.
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.
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.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
34A05,
35J05
Retrieve articles in all journals
with MSC (2000):
34A05,
35J05
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
Received by editor(s):
April 12, 2004
Published electronically:
February 18, 2005
Article copyright:
© Copyright 2005
Brown University
