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Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing forces

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Abstract

The stability of clamped stepped and stiffened rectangular plate subjected to in-plane forces is examined. The plate is divided into 900 rectangular meshes and the partial derivatives are approximated using central difference formula. Altogether 841 equations of equilibrium and 248 equations representing boundary conditions are formed, finally leading to the solution of eigenvalue problem. The buckling coefficients are calculated for various types of stepped plates and the results are presented in tables for ready use by designers. The results are compared with the published results and they are in close agreement.

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Abbreviations

a :

length of the plate

a 1 :

step length

b :

width of the plate

a/b :

panel aspect ratio

D :

flexural rigidity of the plate

E :

Young’s modulus

K :

flexural stiffness

\({\overline{K}_{G}}\) :

geometric stiffness

k,k e :

buckling coefficients

l :

mesh length

m :

mesh breadth

M :

number of divisions in y direction

M :

mass matrix

N :

number of divisions in x direction

nj :

number of joints

N x ,N y ,N xy :

in-plane forces

Pcr :

critical load

t :

thickness of the plate

t i :

step thickness

w :

lateral deflection

x,y :

Cartesian coordinates

α :

ratio between the breadth and length of a mesh

β,γ,δ :

tracers corresponding to N x ,N y ,N xy

λ :

eigenvalue

ν :

Poison’s ratio

τ :

shear stress

σ x ,σ y ,σ :

compressive stresses

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Acknowledgements

The first author wishes to express his thanks to Dr. T. Venkatachlam department of physics of Coimbatore Institute of Technology for his help in preparing the diagrams and charts. The second author thanks the management and Principal of P.S.G College of Technology for giving necessary facilities to carry out the research work reported in this paper. The authors would like to express their gratitude to the anonymous reviewers for their constructive comments and thoughtful suggestions towards enhancing the quality of the paper.

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Authors and Affiliations

  1. Dept. of Mathematics, Coimbatore Institute of Technology, Coimbatore, 641014, India

    A. John Wilson

  2. Dept. of Civil Engineering, P.S.G. College of Technology, Coimbatore, 641004, India

    S. Rajasekaran

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  1. A. John Wilson
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  2. S. Rajasekaran
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Correspondence to A. John Wilson.

Additional information

A. John Wilson was retired from Dept. of Mathematics, Coimbatore Institute of Technology.

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John Wilson, A., Rajasekaran, S. Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing forces. Meccanica 48, 2325–2337 (2013). https://doi.org/10.1007/s11012-013-9751-6

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