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Comparison of nonlinear Von Karman and Cosserat theories in very large deformation of skew plates

Authors
  • Ghassemi, Aazam1
  • Hassani, Mohsen1
  • Oveissi, Soheil1
  • 1 Islamic Azad University, Department of Mechanical Engineering, Najafabad Branch, Najafabad, Iran , Najafabad (Iran)
Type
Published Article
Journal
International Journal of Advanced Structural Engineering
Publisher
Springer Berlin Heidelberg
Publication Date
Feb 10, 2018
Volume
10
Issue
1
Pages
73–84
Identifiers
DOI: 10.1007/s40091-018-0184-2
Source
Springer Nature
Keywords
License
Green

Abstract

Prediction of plate behavior in large deformation is one of the important problems in plate theories. Cosserat theory is an advanced theory for simulation of plates in very large deformation, but it is complex from mathematical viewpoint. Another theory that has been used extensively for large deformation problems is nonlinear Von Karman theory which is easy for formulation and computation. In this paper, these theories were compared for rectangular and skew plates in simply supported and clamped boundary conditions to propose the acceptable range of using nonlinear Von Karman in very large deformation as a simpler theory. Higher order shear deformation plate theory was used with Von Karman nonlinearity. Whole domain method was employed for numerical solution. Each theory was validated with the literature for verification of the numerical method. Deflection and stress distribution were compared from small to very large deformations. The obtained results show that two theories were matched up to the maximum nondimensional deflection of 5 and 3 for simply supported and clamped boundary conditions, respectively. Moreover, by increasing the skew angle, the consistency of two theories would decrease even in deflections smaller than the thickness of the plate.

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