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A Homogenization-Based Laminated Plate Theory

[+] Author Affiliations
Irene Guiamatsia, Jorn S. Hansen

University of Toronto

Paper No. IMECE2004-61763, pp. 421-436; 16 pages
doi:10.1115/IMECE2004-61763
From:
  • ASME 2004 International Mechanical Engineering Congress and Exposition
  • Aerospace
  • Anaheim, California, USA, November 13 – 19, 2004
  • Conference Sponsors: Aerospace Division
  • ISBN: 0-7918-4700-4 | eISBN: 0-7918-4178-2, 0-7918-4179-0, 0-7918-4180-4
  • Copyright © 2004 by ASME

abstract

A new approach to plate theory is presented which yields a straight-forward yet extremely accurate plate model. The approach yields precise and complete three-dimensional stress and strain states with minimal computational effort. This development is based on the assumption that the plate response characteristics can be represented in terms of far-field stress and strain solutions corresponding to constant, linear, quadratic, , nth degree bending states; such solutions, referred to as Fundamental State Solutions (FS), can be determined uniquely and are independent of boundary conditions. Defining the problem variables as through-thickness moments eliminates difficulties in classical plate theories associated with discontinuous or non-differentiable solution fields and is therefore an enormous advantage. Also, post-processing is based on the FS and yields a completely internally consistent approximation. In order to illustrate the capabilities of this approach, comparisons are made to three-dimensional finite element analyses performed with the commercial code ASAS. The results show an excellent agreement between the new plate theory and the finite element calculations for all stress and strain components. In particular, the transverse shear stresses and strains, and the transverse normal stress and strain are obtained extremely accurately. A few millimeters in from the plate edge, the results of the theory and 3D model coalesce. Complete results show that the through-thickness distribution of all stress and strain components is accurately captured with the new theory; the expected parabolic distribution for transverse shear components in the isotropic case, and the discontinuous strains/continuous stresses for the sandwich plate.

Copyright © 2004 by ASME

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