Engineering Transactions, 24, 2, pp. 289-306, 1976

Saint-Venant's Problem for Heterogeneous Elastic Solids

D. Iesan
University of Iassy

This paper gives a method for solving Saint-Venant's problem in the case of inhomogeneous and isotropic elastic cylinders when the elastic coefficients are independent of the axial coordinate. The cross-section of the cylinder is assumed to be occupied by different inhomogeneous and isotropic elastic materials. The problem is then generalized to the case when the cylinder is subjected to body forces and to surface tractions on the lateral surface.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


A. J. C. B. DE SAINT-VENANT, Mémoiré sur la torsion des prismes, Mém. savants étrangers, 14, 233-560, 1855.

A. J. C. B. DL SAINT-VENANT, Mémoiée sur la flexion des prismes, J. Math., 2-me sér., 1, 89-189, 1856.

J. NOWIŃSKI and S. TURSKI, A study of states of stress in inhomogeneous bodies [in Polish], Arch. Mech. Stos., 5, 397-414, 1953.

A. RADU, Sisteme elastice antiplane neomogene, An. St. Univ. Iasi, Matematicà, 13, 145-159, 1967.

A. RADU, Echilibrul barelor elastice izotrope neomogene, An. St. Univ. Iasi, Matematica, 13, 421-442, 1967.

E. SOOS, Despre problema lui Saint-Venant in cazul unui material anizotrop si neomogen, An. Univ. Bucuresti, Matematicã, 12, 70-77, 1973.

G. FICHERA, Existence theorems in elasticity, Handbuch der Physik, Vol. VIa/2, Springer, Berlin- Heidelberg-New York, 1972.

D. LESAN, Bending of micropolar elastic beams by terminal couples, An. St. Univ. lasi, Matematica, 17, 583-490, 1971.

D. IESAN, Saint-Venant's problem for inhomogeneous bodies, J. Elasticity (to appear).

N. I. MUSHELISHVILI, Some basic problems of the mathematical theory of elasticity, Groningen, 1953.

E. ALMANSI, Sopra la deformazione dei cilindri solecitati lateralmente, Rend. Accad. Lincei, Ser. 5, 10, I: 333-338, II: 400-408, 1901.

J. H. MICHELL, The theory of uniformly loaded beams, Quart. J. Math., 32, 28-42, 1901.

D. IESAN, On Almansi's problem for elastic cylinders, Atti Accad. Sci. Ist. Bologna, Rend., Ser. 12, 9, 128-139, 1972.

D. IESAN, Almansi's problem in micropolar elasticity, Int. J. Eng. Sci., 12, 361-374, 1974.