Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-14T13:35:08.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of Cosserats' couple-stresses on the stress distribution in a semi-infinite medium with varying modulus of elasticity

Published online by Cambridge University Press:  09 April 2009

Gunadhar Paria
Gunadhar Paria
Affiliation:
Department of Applied Mathematics Shri Govindram Seksaria Technological Institute, Indore (M.P.), India
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The theory of Cosserats' couple-stresses is briefly described in a cartesian system of coordinates, and is applied to the problem of stress distribution in a semi-infinite medium which possesses a non-homogeneous elastic property of an exponential type. Effects of couple-stresses on the stress concentration factors are determined both in homogeneous and non-homogeneous materials.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 2 , May 1966 , pp. 157 - 171
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Paria, G., “Love waves in granular medium”, Bull. Calcutta Math. Soc. 52 (1960), 195–203.Google Scholar
[2]Cosserat, E. and Cosserat, F., “Théorie des Corps déformables” (A. Herman et Fils, Paris, 1909).Google Scholar
[3]Truesdell, C. and Toupin, R., “The classical field theories”, in Handbuch der Physik, Vol. III/I, edited by Flügge, S. (Springer-Verlag, 1960).Google Scholar
[4]Toupin, R., “Elastic materials with couple-stresses”, Arch. Rat. Mech. Anal. 11 (1962), 385–414.CrossRefGoogle Scholar
[5]Mindlin, R. D. and Tiersten, H. F., “Effects of couple-stresses in linear elasticity”, Arch. Rat. Mech. Anal. 11 (1962), 415–448.CrossRefGoogle Scholar
[6]Kaliski, S., Plochocki, Z. and Rogula, D., “The asymmetry of the stress tensor and the angular momentum conservation for a combined mechanical and electromagnetic field in a continuous medium”, Bull. Acad. Polo. Sci. ser. Sci. Tech. 10 (1962), 135–141.Google Scholar
[7]Gunther, W., Miscellaneous topics in applied mechanics, editor Tollmien, W. (AkadVerlag, 1962).Google Scholar
[8]Mindlin, R. D., “Influence of couple-stresses on stress concentrations”, Exper. Mech. 3 (1963), 1–7.CrossRefGoogle Scholar
[9]Kaliski, S., “On a model of the continuum with an essentially non-symmetric tensor of mechanical stress”, Arch. Mech. Stos. 15 (1963), 33–45.Google Scholar
[10]Kuvshinskii, R. V. and Aéro, E. L., “Continuum theory of asymmetric elasticity”, Fiz. Tverd. Tela. 5 (1963), 2591–2598 (in Russian). English translation: Soviet Physics, Solid State, 5 (1964), 1892–1897.Google Scholar
[11]Misicu, M., “Theory of viscoelasticity with couple-stresses and some reductions to two dimensional problems I”, Rev. Mec. Appl. 8 (1963), 921–952.Google Scholar
[12]Mindlin, R. D., “Micro-structure in linear elasticity”, Arch. Rat. Mech. Anal. 16 (1964), 51–78.CrossRefGoogle Scholar
[13]Hayart, R., “Une application simple des formules de Murnaghan généralisées”, C. R. Acad. Sci. Paris. 258 (1964), 1712–1715.Google Scholar
[14]Koiter, W. T., “Couple-stresses in the theory of elasticity, I and II”, Nederl. Akad. Wetensch. Proc. ser. B67 (1964), 17–29 and 30–44.Google Scholar
[15]Paria, G., “Radial vibration of a sphere of varying modulus of elasticity”, J. Sci. Eng. Res. 7 (1963), 1–4.Google Scholar
[16]Olszak, W., “Non-homogeneity in elasticity and plasticity”, IUTAM Symposium (Pergamon Press, 1958).Google Scholar