Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T03:52:12.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Buckling Equations of Orthotropic Thin Plates

Published online by Cambridge University Press:  09 August 2012

S.-R. Kuo  and
J. D. Yau
S.-R. Kuo
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
J. D. Yau*
Affiliation:
Department of Architecture, Tamkang University, New Taipei City, Taiwan 25137, R.O.C College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China
*
*Corresponding author ([email protected])
Get access

Abstract

Conventionally, only three components of stress, i.e., the membrane stresses (1σxx, 1σyy, 1σxy) in x-y plane along span directions, are considered in deriving the buckling equations of thin plates using energy approaches. Of particular interest in this study is to take all the six components of stress into account in formulating the potential energy for an orthotropic plate. By invoking the conditions of stress equilibrium for the plate and Green's theorem to relate the potential energy to external virtual works, all the instability potential terms associated with the non-conventional stresses (1σxz, 1σyz, 1σzz) can either cancel those terms conventionally referred to as higher-order terms or combine with them to yield some new but meaningful terms. For this reason, the present approach contains more physical and compact meaning than conventional ones in the process of derivation. With the present governing differential equations, bending buckling problems of orthotropic rectangular plates will be investigated in this study.

Keywords

Buckling analysisEdge-loaded plateIncremental virtual work equationOrthotropic plate
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 3 , September 2012 , pp. 555 - 567
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Guo, M. W., Harik, I. E. and Ren, W. X., “Buckling Behavior of Stiffened Laminated Plates,” International Journal of Solids and Structures, 39, pp. 3039–3055 (2002).CrossRefGoogle Scholar
2. Reddy, J. N., Mechanics of Laminated Composite Plates, CRC Press, Boca Raton, Florida (1997).Google Scholar
3. Roberts, J. C., Bao, G. and White, G. J., “Experimental, Numerical and Analytical Results for Bending and Buckling of Rectangular Orthotropic Plates,” Composite Structures, 43, pp. 289–299 (1998).CrossRefGoogle Scholar
4. Wang, C. M., Wang, C. Y. and Reddy, J. N., Exact Solutions for Buckling of Structural Members, CRC Press, Singapore (2005).Google Scholar
5. Bharat Kalyan, J. and Bhaskar, K., “An Analytical Parametric Study on Buckling of Non-uniformly Compressed Orthotropic Rectangular Plates,” Composite Structures, 82, pp. 10–18 (2008).CrossRefGoogle Scholar
6. Levy, R. and Sokolinsky, V., “Optimal Design of Plates for Shear Buckling,” Computers & Structures, 63, pp. 785–795 (1997).CrossRefGoogle Scholar
7. Lopatin, A. V. snd Korbut, Y. B., “Buckling of Clamped Orthotropic Plate in Shear,” Composite Structures, 76, pp. 94–98 (2006).CrossRefGoogle Scholar
8. Mittelstedt, C., “Closed-Form Analysis of the Buckling Loads of Symmetrically Laminated Orthotropic Plates Considering Elastic Edge Restraints,” Composite Structures, 81, pp. 550–558 (2007).CrossRefGoogle Scholar
9. Ahmadian, M. T. and Sherafati Zangeneh, M., “Vibration Analysis of Orthotropic Rectangular Plates Using Superelements,” Computer Methods in Applied Mechanics and Engineering, 191, pp. 2069–2075 (2002).CrossRefGoogle Scholar
10. Teo, T. M. and Liew, K. M., “Three-Dimensional Elasticity Solutions to Some Orthotropic Plate Problems,” International Journal of Solids and Structures, 36, pp. 5301–5326 (1999).CrossRefGoogle Scholar
11. Nordstrand, T., “On Buckling Loads for Edge-Loaded Orthotropic Plates Including Transverse Shear,” Composite Structures, 65, pp. 1–6 (2004).CrossRefGoogle Scholar
12. Shimpi, R. P. and Patel, H. G., “A Two Variable Refined Plate Theory for Orthotropic Plate Analysis,” International Journal of Solids and Structures, 43, pp. 6783–6799 (2006).CrossRefGoogle Scholar
13. Yang, Y. B. and Kuo, S. R., Theory & Analysis of Nonlinear Framed Structures, Prentice Hall, Singapore (1994).Google Scholar
14. Yang, Y. B., Lin, S. P. and Chen, C. S., “Rigid Body Concept for Geometric Nonlinear Analysis of 3D Frames, Plates and Shells Based on the Updated Lagrangian Formulation,” Computer Methods in Applied Mechanics and Engineering, 196, pp. 1178–1192 (2007).CrossRefGoogle Scholar
15. Kuo, S. R., Chi, C. C., Yeih, W. and Chang, J. R., “A Reliable Three-Node Triangular Plate Element Satisfying Rigid Body Rule and Incremental Force Equilibrium Conditions,” Journal of the Chinese Institute of Engineers, 29, pp. 619–632 (2006).CrossRefGoogle Scholar
16. Szilard, R., Theories and Applications of Plate Analysis: Classical, Numerical, and Engineering Methods, John Wiley & Sons, Inc., N.J. (2004).CrossRefGoogle Scholar
17. Varadan, T. K. and Bhaskar, K., Analysis of Plates: Theory and Problems, Narosa Publishing House, New Delhi (1999).Google Scholar
18. Iyengar, N. G. R., Structural Stability of Columns and Plates, Ellis Horwood Limited, England (1988).Google Scholar
19. Gould, P., Analysis of Plates and Shells, Prentice Hall, N.J. (1999).Google Scholar
20. Bloom, F. and Coffin, D., Handbook of Thin Plate Buckling and Postbuckling, Chapman & Hall/CRC, Boca Raton, Florida (2001).Google Scholar
21. Ugural, A. C., Stresses in Plates and Shells, 2nd Ed., McGraw-Hill Book Co., N.Y. (1999).Google Scholar
22. Jones, R. M., Morgan, H. S. and Whitney, J. M., “Buckling and Vibration of Anti-Symmetrically Laminated Angle-Ply and Rectangular Plates,” Journal of Applied Mechanics, 40, pp. 1143–1144 (1973).CrossRefGoogle Scholar
23. Chi, C. C., “Geometric Nonlinear Theory of Plate and Shell Structures Considering Rigid Body Rule and Incremental Force Equilibrium,” Ph.D. Dissertation, Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan (in Chinese) (2006).Google Scholar
24. Keryszig, E., Advanced Engineering Mathematics, 8th Ed., John Wiley & Sons, Inc., New York (1999).Google Scholar