Analysis of post buckling behavior of circular plates with non-concentric hole using the Rayleigh–Ritz method

This study is conducted to determine the post buckling behavior of circular homogenous plates with non-concentric hole subjected to uniform radial loading using Rayleigh–Ritz method. In order to implement the method, a computer program has been developed and several numerical examples for different...

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Bibliographic Details
Published in:Applied mathematical modelling 2011-07, Vol.35 (7), p.3136-3153
Main Authors: Mazhari, E., Shahidi, A.R.
Format: Article
Language:English
Subjects:
Buckling
Displacement
Exact sciences and technology
Fourier series
Fundamental areas of phenomenology (including applications)
Hookean displacement field
Kirchhoff theory
Mathematical models
Non-concentric hole
Physics
Plates
Post buckling
Rayleigh-Ritz method
Shape function
Shape functions
Solid mechanics
Structural and continuum mechanics
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Summary:This study is conducted to determine the post buckling behavior of circular homogenous plates with non-concentric hole subjected to uniform radial loading using Rayleigh–Ritz method. In order to implement the method, a computer program has been developed and several numerical examples for different boundary conditions are presented to illustrate the scope and efficacy of the procedure. The integration is carried out in natural coordinates through a proper transformation. Consequently, the displacement fields respect to natural coordinates are expressed using the Hierarchical, Hermitian and Fourier series shape functions for interpolating the out-of-plane displacement field and Fourier series and Hierarchical, Lagrange shape functions for interpolating the in-plane displacement field of plate. The Kirchhoff theory is used to formulate the problem in buckling condition. Due to the asymmetry in geometry, the in-plane solution is required to find the stress distribution. Finally, the problem is formulated in post buckling condition using Von-Karman non-linear theory, and a proper Hookean displacement field is presented to analyze the post buckling behavior.
ISSN:0307-904X
DOI:10.1016/j.apm.2010.12.016