EXACT CLOSED FORM SOLUTION FOR AN ANTI-PLANE DEFORMATION OF ANISOTROPIC MEDIA

A closed form solution for the ordinary differential equation of Hill's type, (1-ε cos x)y״ (x) + aεsin xy'(x)+[a(a -1)/2-{(a²-1)/4}(1-ε 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....

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Bibliographic Details
Published in:Quarterly of applied mathematics 2005-06, Vol.63 (2), p.301-307
Main Authors: WATANABE, KAZUMI, NAWI, ABU HANIPAH BIN
Format: Article
Language:English
Subjects:
Anisotropy
Boundary conditions
Deformation
Differential equations
Equilibrium equations
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical constants
Mathematical methods in physics
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
Sine function
Solid mechanics
Spherical coordinates
Static elasticity (thermoelasticity...)
Stress analysis
Structural and continuum mechanics
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Summary:A closed form solution for the ordinary differential equation of Hill's type, (1-ε cos x)y״ (x) + aεsin xy'(x)+[a(a -1)/2-{(a²-1)/4}(1-ε 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.
ISSN:0033-569X
1552-4485
DOI:10.1090/S0033-569X-05-00948-8