0
Research Papers

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

[+] Author and Article Information
Santosh Kapuria

Poonam Kumari

 Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, Indiakpmech.iitd@gmail.com

J. Appl. Mech 79(6), 061018 (Sep 21, 2012) (9 pages) doi:10.1115/1.4006495 History: Received December 20, 2011; Revised March 21, 2012; Posted April 02, 2012; Published September 21, 2012; Online September 21, 2012

In an article recently published in this journal, the powerful single-term extended Kantorovich method (EKM) originally proposed by Kerr in 1968 for two-dimensional (2D) elasticity problems was further extended by the authors to the three-dimensional (3D) elasticity solution for laminated plates. The single-term solution, however, failed to predict accurately the stress field near the boundaries; thus limiting its applicability. In this work, the method is generalized to the multiterm solution. The solution is developed using the Reissner-type mixed variational principle that ensures the same order of accuracy for displacements and stresses. An n-term solution generates a set of 8n algebraic-ordinary differential equations in the in-plane direction and a similar set in the thickness direction for each lamina, which are solved in close form. The problem of large eigenvalues associated with higher order terms is addressed. In addition to the composite laminates considered in the previous article, results are also presented for sandwich laminates, for which the inaccuracy in the single-term solution is even more prominent. It is shown that considering just one or two additional terms in the solution (n = 2 or 3) leads to a very accurate prediction and drastic improvement over the single-term solution (n = 1) for all entities including the stress field near the boundaries. This work will facilitate development of near-exact solutions of many important unresolved problems involving 3D elasticity, such as the free edge stresses in laminated structures under bending, tension and torsion.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Geometry of the laminated plate in cylindrical bending

Grahic Jump Location
Figure 2

Convergence of stresses with number of terms and iterations for a very thick (S = 2) cantilever single-layered composite panel

Grahic Jump Location
Figure 12

Effect of boundary conditions on the boundary layer effect of σz for panel (a)

Grahic Jump Location
Figure 13

Effect of S on the through-thickness distributions of in-plane displacement and stresses for CC panel (a)

Grahic Jump Location
Figure 3

Comparison of stresses distributions at different ξ locations with 3D approximate solution of [3] for a very thick (S = 2) cantilever single-layered composite panel (line: present result, × : Vel and Batra [3])

Grahic Jump Location
Figure 4

Lay ups of laminated panels (a), (b), and (c)

Grahic Jump Location
Figure 5

Longitudinal variations of deflection and stresses for angle-ply composite and sandwich panels with CS boundary condition

Grahic Jump Location
Figure 6

Longitudinal variations of deflection and stresses for angle-ply composite and sandwich panels with CC boundary condition

Grahic Jump Location
Figure 7

Longitudinal variations of deflection and stresses for sandwich panel (c) with CF boundary condition

Grahic Jump Location
Figure 8

Longitudinal variations of deflection and stresses for cross-ply composite panel (a) with CS boundary condition

Grahic Jump Location
Figure 9

Through-thickness distributions of u¯ and σ¯x for cross-ply composite and sandwich panels with CS boundary condition

Grahic Jump Location
Figure 10

Through-thickness distributions of σ̃z and τ¯zx for cross-ply composite and sandwich panels with CS boundary condition

Grahic Jump Location
Figure 11

Effect of ξ locations on the through-thickness distributions of in-plane displacement and stresses for CS panels (a) and (c)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In