Sage Journals: Discover world-class research

Abstract

Classical beam models do not account for partial restraint of anticlastic bending and are therefore inherently inaccurate. This article proposes a modification of the exact Bernoulli–Euler equation which allows for an exact prediction of the beam's deflection without the need of two-dimensional finite element calculations. This approach offers a substantial reduction in the computational effort, especially when coupled with a fast-solving schema like the circle-arc method.

Besides the description of the new method and its validation, this article offers an insight into the somewhat disregarded topic of anticlastic bending by a short review of the published theories and a selection of representative numerical results.

Keywords

circle-arc method elastica anticlastic bending non-linear beam bending

Get full access to this article

View all access options for this article.

References

Gorski

A review of literature and a bibliography on finite elastic deflection of bars. Civil Eng. Trans., 1976, 18(2), 74–85.

Bisshopp

K. E.

Drucker

D. C.

Large deflections of cantilever beams. Q. Appl. Math., 1945, 3(3), 272–275.

Thorp

A. G.

Flexure pivots-design. Prod. Eng., 1953, 24, 192–200.

Hopkins

R. B.

Design analysis of shafts and beams, 1970 (McGraw-Hill, New York)76–76.

Hearn

E. J.

Mechanics of materials, 1977, Vol. 1 (Butterworth-Heinemann, London)79–79.

DeVoe

D. L.

Pisano

A. P.

Modeling and optimal design of piezoelectric cantilever microactuators. J. Microelectromech. Syst., 1997, 6(3), 266–270.

Ragab

A.-R.

Bayoumi

S. E.

Engineering solid mechanics: fundamentals and applications, 1998 (CRC Press, Boca Raton)820–820.

Ugural

A. C.

Stresses in beams, plates and shells, 1999 (CRC Press, Boca Raton)58–58.

Timoshenko

Strength of materials. Part II, 1980 (Van Nostrand Reinhold, NewYork)119–120.

10.

Szabó

Einführung in die Technische Mechanik (in German), 1963 (Springer, Berlin)128–129.

11.

Campanile

L. F.

Hasse

A simple and effective solution of the elastica problem. J. Mech. Eng. Sci., 2008, 222(c12), 2513–2516.

12.

Lamb

On the flexure of a flat elastic spring. Philos. Mag., 1891, 5(31), 182–188.

13.

Ashwell

D. G.

The anticlastic curvature of rectangular beams and plates. J. R. Aeronaut. Soc., 1950, 54, 708–715.

14.

Pomeroy

R. J.

The effect of anticlastic bending on the curvature of beams. Int. J. Solids Struct., 1970, 6, 277–285.

15.

Angeli

De Bona

Munteanu

M. G.

Flexural stiffness of leaf springs for compliant micromechanisms. J. Mech. Eng. Sci., 2008, 222(c12), 2505–2511.

16.

Ferguson

M. A.

Andrews

J. P.

An experimental study of the anticlastic bending of rectangular bars of different cross-sections. Proc. Phys. Soc., 1928, 41(1), 1–17.

17.

Conway

H. D.

Nickola

W. E.

Anticlastic action of flat sheets in bending. Exp. Mech., 1965, 5(1), 115–119.

18.

Bellow

D. G.

Ford

Kennedy

J. S.

Anticlastic behaviour of flat plates. Exp. Mech., 1965, 5(7), 227–232.

Exact analysis of the bending of wide beams by a modified elastica approach

Abstract

Keywords

Get full access to this article

References