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On the Almansi-Michell Problems for an Inhomogeneous, Anisotropic Cylinder

Published online by Cambridge University Press:  05 May 2011

H.-C. Lin  and
S.B. Dong
H.-C. Lin*
Affiliation:
Department of Computer Science and Engineering, Ming Dao University, Peetow, Changhua, Taiwan 52345, R. O. C.
S.B. Dong*
Affiliation:
Civil and Environmental Engineering Department, University of California, Los Angeles, California, 90095–1593, U.S.A.
*
*Assistant Professor
**Professor Emeritus
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Abstract

A semi-analytical finite element (SAFE) method is presented for constructing solutions for an arbitrarily loaded cylinder, whose cross-section is general in terms of its shape and the number of distinct, perfectly bonded elastic, rectilinear anisotropic materials. The surface traction and body force loads need to be expressed in a power series of the axial coordinate. Linear three-dimensional theory is used. For a homogeneous isotropic cylinder, it is known as the Almansi-Michell problem, and the SAFE analysis herein is an extension to inhomogeneous, anisotropic bodies. By SAFE, the cross-section is discretized. The displacement field is expressed by interpolation functions over the cross-section and by analytical functions axially. The method herein is an extension of the authors' previous method cylinder with a general cross-section. Herein, the SAFE solution procedure is given and numerical examples will be presented.

Keywords

Semi-analytical finite element methodAlmansi-Michell problemsSaint-Venant's solutionsCross-sectional stiffness matrix.
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 1 , March 2006 , pp. 51 - 57
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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References

REFERENCES

1.Almansi, E., “Sopra la Deformazione dei Cilindri Solecitati Lateralmente,” Atti Reale Accad. naz. Lincei Rend. Cl. sci. fis., mat. e natur. Ser. 5, 10, 1: pp. 333–338 and II: pp. 400–408 (1901).Google Scholar
2.Micheli, J. H., “The Theory of Uniformly Loaded Beams,” Quart. J. Math., 32, pp. 28–42 (1901).Google Scholar
3.Dong, S. B., Kosmatka, J. B. and Lin, H. C., “On Saint-Venant's Problem for an Inhomogeneous, Anisotropic Cylinder, Part I: Saint-Venant Solutions,” Journal of Applied Mechanics, 68(3), pp. 376–381, (2001)Google Scholar
4.Kostmatka, J. B., Lm, H. C. and Dong, S. B., “On Saint-Venant's Problem for an Inhomogeneous, Anisotropic Cylinder, Part II: Cross-Sectional Properties,” Journal of Applied Mechanics, 68(3), pp. 382–391 (2001).CrossRefGoogle Scholar
5.Lin, H. C., Dong, S. B. and Kosmatka, J. B., “On Saint-Venant's Problem for an Inhomogeneous, Anisotropic Cylinder, Part III: End Effects,” Journal of Applied Mechanics, 68(3), pp. 392–398 (2001).CrossRefGoogle Scholar
6.Ieşan, D., “On Saint-Venant's Problem, Arch Rational Mechanics and Analysis,” 91, pp. 363–373 (1986).CrossRefGoogle Scholar
7.Ieşan, D., Saint-Venants Problem, Lectures Notes in Mathematics, Springer-Verlag, Heidelberg (1987).Google Scholar
8.Bors, C. L., Theory of Elasticity for Anisotropic Bodies, Editura Academiei, Bucuresti (in Romanian) (1970).Google Scholar
9.Hatiashivili, G. M., Almansi-Michell Problems for Homogeneous and Composite Bodies, Izd. Metzniereba, Tbilisi (in Russian) (1983).Google Scholar
10.Huang, C. H. and Dong, S. B., “Analysis of Laminated Circular Cylinders of Materials with the Most General Form of Cylindrical Anisotropy, Part 1—Axially Symmetric Deformations,” International Journal of Solids and Structures, 38, pp. 6163–6182 (2001).CrossRefGoogle Scholar
11.Huang, C. H. and Dong, S. B., “Analysis of Laminated Circular Cylinders of Materials with the Most General Form of Cylindrical Anisotropy, Part 2—Flexural Deformations,” International Journal of Solids and Structures, 38, pp. 6183–6205 (2001).CrossRefGoogle Scholar
12.Taweel, H., Dong, S. B. and Kazic, M., “Wave Reflection from the Free End of a Cylinder with an Arbitrary Cross-Section,” International Journal of Solids and Structures, 37, pp. 1701–1726 (2000).Google Scholar
13.Lehknitskii, S. G., Theory of Elasticity of an Anisotropic Body, 2nd ed., Mir Publisher, Moscow, p. 82 (1977).Google Scholar