Generalized Bending of Shear-Deformable Plate with Elastic Inclusion
Publication: Journal of Engineering Mechanics
Volume 127, Issue 9
Abstract
The generalized bending of a large plate with a circular elastic inclusion is discussed here. The solution for a hole or a rigid inclusion, which is the limiting case of an elastic inclusion, has been discussed frequently, but there is little work on an inclusion with arbitrary rigidity. Early investigators solved the problem of a large thin plate with a circular elastic inclusion, subjected to uniaxial bending, balanced biaxial bending, pure twisting, and transverse shear. This work was recently generalized to arbitrary bending loading, and explicit formulas were presented for dimensionless maximum circumferential bending moments in the plate and in the inclusion. This paper solves the analogous problem with Reissner's shear-deformable plate theory. Arbitrary bending loading is considered. A general solution is derived for the governing differential equations. Explicit formulas are developed for the maximum circumferential and radial moments in the plate and the inclusion. The results for four typical loadings are illustrated graphically, and two limiting forms of the solution are obtained.
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References
1.
Alblas, J. B. ( 1957). “Theorie van de Driedimensionale Spanningstoestad in een Doorboorde Plaat.” Doctoral dissertation, Tech. Univ., Delft, The Netherlands (in Dutch).
2.
Bert, C. W. ( 1988). “Generalized bending of a large plate containing a circular hole.” Mech. Res. Communications, 15(1), 55–60.
3.
Bert, C. W. ( 2001). “Generalized bending of a plate with a circular inclusion of arbitrary rigidity.” J. Strain Anal., in press.
4.
Bert, C. W., and Zeng, H. ( 2001). “Generalized bending of a large, shear deformable, isotropic plate containing a circular hole or rigid inclusion.” J. Appl. Mech., 68(1), 230–233.
5.
Bickley, W. G. ( 1924). “The effect of a hole in a bent plate.” Philosophical Mag., 6th Ser., 48, 1014–1024.
6.
Goland, M. ( 1943). “The influence of the shape and rigidity of an elastic inclusion on the transverse flexure of thin plates.” J. Appl. Mech., 10(2), A69–A75.
7.
Goldenveizer, A. L. ( 1960). “On Reissner's theory of the bending of plates.” NASA Tech. Translation F-27, Washington, D.C.
8.
Goodier, J. N. ( 1936). “The influence of circular and elliptical holes on the transverse flexure of elastic plates.” Philosophical Mag., 7th Ser., 22, 69–80.
9.
Hirsch, R. A. ( 1952). “Effect of rigid circular inclusion on bending of thick elastic plate.” J. Appl. Mech., 19(1), 28–32.
10.
Lekhnitskii, S. G. ( 1961). Stress concentration around holes, G. Savin, Pergamon, New York.
11.
Reissner, E. ( 1945). “The effect of transverse shear deformation on the bending of elastic plates.” J. Appl. Mech., 12, A69–A77.
12.
Reissner, E. ( 1980). “On the analysis of first and second-order shear deformation effects for isotropic elastic plates.” J. Appl. Mech., 47, 959–961.
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Received: Sep 18, 2000
Published online: Sep 1, 2001
Published in print: Sep 2001
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