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Abstract

An improved finite element model for the bending and free vibration analysis of doubly curved, laminated composite shells having spherical and ellipsoidal shapes is presented. The present formulation is based on the stress resultant-type Koiter’s shell theory and no restriction is imposed on the magnitude of curvature components to capture the deep and shallow shell cases. The twist curvature component is incorporated along with the normal curvatures to keep the strain equations complete. Transverse shear deformation is also considered according to Mindlin’s hypotheses. Both the Lagrangian and Serendipity families of isoparametric elements are incorporated in the analysis code to study their performance in different problems. The present five-DOF shell formulation is kept sufficiently general to capture both the bending- and membrane-dominated problems. The accuracy and efficiency of the proposed finite element are illustrated by examples and are compared with those existing in the open literature. The comparison shows that the present analysis yields accurate results with a relatively small number of elements.

Keywords

composites doubly curved shells finite element analysis

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References

Bathe, K. J. (1990). The Finite Element Procedures in Engineering Analysis, Prentice Hall of India, New Delhi .

Bert, C. W. and Reddy, V. S. (1982). Cylindrical Shells of Bimodulus Materials , Journal of Engineering Mechanics Division, ASCE, Vol-8, No-EM5, pp. 675–688 .

Donnell, L. H. (1938). A Discussion of the Thin Shell Theory , In: Proceedings of the 5th International Congress of Applied Mechanics, pp. 66–70 , John Wiley, New York.

Jones, R. (1998). Mechanics of Composite Materials, McGraw-Hill, Kogakusha Ltd.

Koiter, W. T. (1960). A Consistent First Approximation of the General Theory of Thin Elastic Shell , In: Proceedings of 1st IUTAM Symposium, pp. 12–33 , North Holland, Amsterdam.

Kraus, H. (1967). Thin Elastic Shells, John Wiley & Sons, New York .

Love, A. E. H. (1988). On the Small Free Vibrations and Deformations of the Elastic Shells , Philosophical Transaction of the Royal Society, 17: 491–546 .

Novozhilov, V. V. (1959). The Theory of Thin Shells, P. Noordhoff Ltd., Leiden .

Reddy, J. N. (1979). Free Vibration of Antisymmetric, Angle–Ply Laminated Plates Including Transverse Shear Deformation By The Finite Element Method , Journal of Sound and Vibration, 66(4): 565–576 .

10.

Reddy, J. N. (1984). Exact Solutions of Moderately Thick Laminated Shells , Journal of Engineering Mechanics, ASCE, 110(5): 794–809 .

11.

Reddy, J. N. and Liu, C. F. (1985). A Higher-order Shear Deformation Theory of Lam ted Elastic Shells , International Journal of Engg. Science, 23(3): 319–330 .

12.

Sanders, J. L. (1955) An Improved First Approximation Theory for Thin Shells, NASA Tech Report, R-24.

13.

Vlasov, V. Z. (1964). General Theory of Shells and Its Applications in Engineering, NASA TT F-99, National Aeronautics and Space Administration, Washington .

14.

Zienkiewicz, O. C. (1979). The Finite Element Method, 3rd edn, Tata McGraw-Hill Publishing Company Limited, New Delhi .

Improved Finite Element Analysis of Multilayered,Doubly Curved Composite Shells

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