**4. References**

	- [4] Doyle J.F. (2001). *Nonlinear analysis of thin-walled structures.* Springer-Verlag, Berlin, Germany

**Chapter 9** 

© 2012 Kubiak, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

The buckling and postbuckling of thin-walled structures subjected to static load have been investigated by many authors for more than one hundred years. To the group of precursors of the investigation on the stability of thin-walled structures problem should be included

**Nonlinear Plate Theory** 

Additional information is available at the end of the chapter

Tomasz Kubiak

**1. Introduction** 

http://dx.doi.org/10.5772/48961

subjected to static and dynamic load.

following scientists: Euler [1], Timoshenko [2] and Volmir [3].

**1.1. Static buckling** 

**for Postbuckling Behaviour of Thin-Walled** 

**Structures Under Static and Dynamic Load** 

A thin plate or thin-walled constructions are used in the sports industry, automotive, aerospace and civil engineering. As an example of such structural elements snowboard, skis, poles may be mentioned, as well as all kinds of crane girders, structural components of automobiles (car body sheathing or all longitudinal members), aircraft fuselages and wings, supporting structures of the walls and roofs of large halls and warehouses. All the above structures, as well as many others which can be regarded as a thin, exhaust carrying capacity not by exceeding the allowable stresses but by the stability loss. Therefore, not only critical load but also the postbuckling behaviour of thin-walled structures subjected to static and dynamic load is essential knowledge for designers. The use of more accurate mathematical models allows to explore the phenomena occurring after the loss of stability and to describe more precisely their behaviour. Engineers and designers need guidelines to construct as well as quick and easy software to use for analyse the behaviour of thin-walled structures. Therefore, the author of this chapter decided to explore this issue, propose a mathematical model and the method of analysis of orthotropic thin-walled structures


Tomasz Kubiak

218 Nonlinearity, Bifurcation and Chaos – Theory and Applications

*structures.* Springer, Berlin, Germany

*systems.* Springer, Berlin, Germany

(5), 2008, 1515-1529.

Germany

1515.

Poland

[4] Doyle J.F. (2001). *Nonlinear analysis of thin-walled structures.* Springer-Verlag, Berlin,

[5] Andrianov J., Awrejcewicz J., Manewitch L.I. (2004) *Asymptotical Mechanics of thin-walled* 

[6] Awrejcewicz J., Krysko V.A., Vakakis A.F. (2004) N*onlinear dynamics of continuous elastic* 

[7] A.V. Krysko, J. Awrejcewicz, E.S. Kuznetsova, V.A. Krysko, *Chaotic vibrations of closed cylindrical shells in a temperature field*, International Journal of Bifurcation and Chaos, 18

[8] A.V. Krysko, J. Awrejcewicz, E.S. Kuznetsova, V.A. Krysko, *Chaotic vibrations of closed cylindrical shells in a temperature field*, Shock and Vibration, 15 (3-4), 2008, 335-343. [9] I.V. Andrianov, V.M. Verbonol, J. Awrejcewicz, *Buckling analysis of discretely stringerstiffened cylindrical shells*, International Journal of Mechanical Sciences, 48, 2006, 1505-

[10] Arborcz J. (1985). *Post-buckling behavior of structures. Numerical techniques for more* 

[11] Kopecki T. (2010). *Advanced deformation states in thin-walled load-bearing structure design work.* Publishing House of Rzeszów University of Technology, Rzeszów, Poland [12] Niu M. C. (1988). *Airframe structural design.* Conmilit Press Ltd., Hong Kong10] Lynch C., Murphy A., Price M., Gibson A. (2004). *The computational post buckling analysis of fuselage stiffened panels loaded in compression.* Thin-Walled Structures, 42:1445-1464, USA [13] Mohri F., Azrar L., Potier-Ferry M. (2002). *Lateral post buckling analysis of thin-walled open* 

[14] Rakowski G., Kacprzyk Z. (2005). *Finite elements method in structure mechanics.*

[15] Ramm E. (1987). *The Riks/Wempner Approach – An extension of the displacement control method in nonlinear analysis*. Pineridge Press, Swensea, UK Aben H. (1979). *Integrated* 

[16] Brzoska Z. (1965). *Statics and stability of bar and thin-walled structures.* PWN, Warszawa,

Publishing House of Technical University of Warszawa, Warszawa, Poland

*complicated structures.* Lecture Notes In Physics, 228, USA

*section beams*. Thin-Walled Structures, 40:1013-1036, USA

*photoelasticity.* Mc Graw-Hill Book Co., London, UK

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48961
