**43**, 1-2, pp. 83-99, 1995

### On the Stress Distrubution in Bending of Strongly Anisotropic Beams

The displacement function method for the plane problems of linearly elastic orthotropic bodies has been proposed. The method has been used for the estimation of the rate of decay of the end effects in beams and slabs subjected to bending; the results obtained turned out to be in agreement with the earlier estimates obtained by Choi and Horgan for the influence of the end effects in the case of laboratory test specimens. Some possibilities of obtaining the rigorous solutions modeling special cases of bending have been shown. A set of explicit formulae has been proposed for the approximate solutions of bending problems taking into account the end effects, normal stress nonlinear distribution at the cross-sections and the contribution of the shear deformation to the beam deflection.

**Full Text:**PDF

#### References

S. TIMOSHENKO, Course of the theory of elasticity [in Russian], vol. I, II, St. Petersburg, 1914-1916 [see also II-nd edition in one volume "Naukova Dumka", Kiev 1972].

E. REISSNER, A contribution to the theory of elasticity of non-isotropic material (with application to problems of bending and torsion), Philosophical Magazine, Ser. 7, 30, No. 202, 1940.

V.Z. VLASOV, Mechanics of thin-wall spatial systems [in Russian], Stroyizdat, Moskva - Leningrad 1949.

E. REISSNER, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech. 12, A69, 1954.

E. STERNBERG, On Saint-Venant's principle, Quart. Appl. Math., 11, 4, pp. 293-402, 1954.

R.A. TOUPIN, Saint-Venant's principle, Arch. Rat. Mech. Anal., 18, pp. 83-96, 1965.

J.K. KNOWLES, On Saint-Venant's principle in two-dimensional linear theory of elasticity, Arch. Rational Mech. Anal., 21, No. 1, pp.1-22, 1966.

J.J. ROSEMAN, A Pointwise estimate for the stress in a cylinder and its application to Saint-Venant's principle, Arch. Rational Mech. Anal., 21, 1, pp. 23-48, 1966.

J.K. KNOWLES and E. STERNBERG, On Saint-Venant's principle and the torsion of solids of revolution, Arch. Rational Mech. Anal., 22, 2, pp. 100-120, 1966.

A.J.M. SPENCER, Deformation of fibre-reinforced materials, Oxford University Press, Oxford 1972.

G.C. EVERSTINE and A.C. PIPKIN, Boundary layers in fiber-reinforced materials, J. Appl. Mech., Transactions of the ASME, pp.518-522, June 1973.

I. CHOI and C.O. HORGAN, Saint Venant principle and end effects in anisotropic elasticity, J. Appl. Mech., Transactions of the ASME, pp. 424-430, September 1977.

M. ARCISZ, Stability of fibre-reinforced prestressed elastic cylinder, Bul. Acad. Polon. Sci, Série. Sci. Tech, 26, 1, pp.1-9, 1978.

A. BLINOWSKI, Nonlinear micropolar continuum model of a composite, reinforced by elements of finite rigidity, Part II. Stability at compression, Arch. Mech., 33, 5, pp. 763-771, 1981.

O. HORGAN and J.K. KNOWLES, Recent developments concerning Saint-Venant's principle, [in:] Advances in Applied Mechanics, vol. 23, Academic Press, pp.179-269, 1983.

J. RYCHLEWSKI, On Hooke's law [in Russian], PMM, 48, 3, pp.420-4351 1984, (see English translation: Prikl. Matem. Mekhan., 48, pp. 303-314, 1984).

A. BLINOWSKI, On the application of some models of fibre-reinforced composites [in Russian], Advances Mech., 7, 3, pp. 3-35, 1984.

A. BLINOWSKI, On the stress distribution in strongly anisotropic plates, Arch. Mech., 41, 1, pp. 37-59, 1989.

A. BLINOWSKI and J. OSTROWSKA-MACIEJEWSKA, On the elastic orthotropy, [to be published].

Copyright © 2014 by Institute of Fundamental Technological Research

Polish Academy of Sciences, Warsaw, Poland