TECHNICAL PAPERS
Apr 1, 1991

Stress and Deflection Analysis of Composite Cantilevered Shallow Shells

Publication: Journal of Engineering Mechanics
Volume 117, Issue 4

Abstract

The Ritz method, which is widely used for the free‐vibration analysis of isotropic plates and shells, is employed here to determine the displacements and stresses in cantilevered shallow shells that are statically loaded. The shallow shells are made of composite materials such as filamentary laminates or reinforced concrete. Displacements are assumed in the form of algebraic polynomials. Convergence for the membrane stress and bending moment resultants is demonstrated to be less rapid than for the displacements. Numerical results are presented for three‐layer cross‐ply and angle‐ply laminates made of graphite/epoxy materials. Displacements and stresses for shallow shells of spherical, circular cylindrical and hyperbolic paraboloidal curvature and square planform subjected to gravity loading are compared with those of flat plates.

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References

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Ambartsumyan, S. A. (1964). “Theory of anisotropic shells.” (English translation), NASA TT‐F118.
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Kielb, R. E., Leissa, A. W., and MacBain, J. C. (1985). “Vibrations of twisted cantilever plates—A comparison of theoretical results.” Int. J. Numer. Methods Engrg., 21, 1365–1380.
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Leissa, A. W. (1987). “A review of laminated composite plate buckling.” Appl. Mech. Rev., 40(5), 575–591.
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Qatu, M. S. (1989). “Free vibration and static analysis of laminated composite shallow shells,” dissertation presented to Ohio State University, at Columbus, Ohio, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
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Ritz, W. (1908). “Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik.” J.f.d. Reine und Angew. Math., 135, 1–61.
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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 117Issue 4April 1991
Pages: 893 - 906

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Published online: Apr 1, 1991
Published in print: Apr 1991

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Authors

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Arthur W. Leissa
Prof., Dept. of Engrg. Mech., Ohio State Univ., Columbus, OH 43210
Mohamad S. Qatu
Test and Analysis Engr., Dresser Industries, Columbus, OH 43201

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