The extended Kantorovich method originally proposed by Kerr in the year 1968 for two-dimensional (2D) elasticity problems is further extended to the three-dimensional (3D) elasticity problem of a transversely loaded laminated angle-ply flat panel in cylindrical bending. The significant extensions made to the method in this study are (1) the application to the 3D elasticity problem involving an in-plane direction and a thickness direction instead of both in-plane directions in 2D elasticity problems, (2) the treatment of the nonhomogeneous boundary conditions encountered in the thickness direction, and (3) the use of a mixed variational principle to obtain the governing differential equations in both directions in terms of displacements as well as stresses. This approach not only ensures exact satisfaction of all boundary conditions and continuity conditions at the layer interfaces, but also guarantees the same order of accuracy for all displacement and stress components. The method eventually leads to a set of eight algebraic-ordinary differential equations in the in-plane direction and a similar set of equations in the thickness direction for each layer of the laminate. Exact closed form solutions are obtained for each system of equations. It is demonstrated that the iterative procedure converges very fast irrespective of whether or not the initial guess functions satisfy the boundary conditions. Comparisons of the present predictions with the available 3D exact solutions and 3D finite element solutions for laminated cross-ply and angle-ply composite panels under different boundary conditions show a close agreement between them.
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November 2011
Research Papers
Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Composite Structures in Cylindrical Bending
Poonam Kumari
Poonam Kumari
Research Scholar
Department of Applied Mechanics,
e-mail: kpmech.iitd@gmail.com
Indian Institute of Technology Delhi
, New Delhi 110016, India
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Santosh Kapuria
Professor
Poonam Kumari
Research Scholar
Department of Applied Mechanics,
Indian Institute of Technology Delhi
, New Delhi 110016, India
e-mail: kpmech.iitd@gmail.com
J. Appl. Mech. Nov 2011, 78(6): 061004 (8 pages)
Published Online: August 22, 2011
Article history
Received:
September 20, 2010
Revised:
March 7, 2011
Online:
August 22, 2011
Published:
August 22, 2011
Citation
Kapuria, S., and Kumari, P. (August 22, 2011). "Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Composite Structures in Cylindrical Bending." ASME. J. Appl. Mech. November 2011; 78(6): 061004. https://doi.org/10.1115/1.4003779
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