Post Buckling Behavior of Shells Using Total Lagrangian Method

Abstract

In this study, the post-buckling behavior of shells is investigated using 9-noded isoparametric shell
elements. Total Lagrangian approach is used in the formulation and shell material is assumed to be linearly elastic.
Non-linear equilibrium equations are solved by arc-length method. Various examples were analyzed to obtain postbuckling behavior of shells

Keywords

• Shell element,post-buckling behavior

Toplam Lagrange Yöntemi ile Kabukların Burkulma Ötesi Analizi

Abstract

Bu çalışmada, 9-düğümlü izoparametrik kabuk eleman kullanılarak kabukların burkulma ötesi davranışı
incelenmektedir. Formülasyonda toplam Lagrange yaklaşımı esas alınmakta ve malzeme lineer elastik kabul
edilmektedir. Lineer olmayan denge denklemleri yay-boyu metodu (arc-length method) ile çözülmektedir. Değişik
nümerik örnekler çözülerek kabukların burkulma ötesi davranışı elde edilmiştir

Keywords

• Kabuk eleman,burkulma ötesi davranış

References

1. Bathe KJ, 1996. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, New Jersey.
2. Crisfield MA, 1991. Non-linear Finite Element Analysis of Solids and Structures. Volume I, John Wiley and Sons, New York.
3. Felippa CA, Haugen B, 2005. A unified formulation of small strain co-rotational finite elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, 194: 2285-2335.
4. Feng YT, Peric D, Owen DRJ, 1996. A New Criterion for Determination of Initial Loading Parameter in Arc-Length Methods. Computers and Structures, 58: 479-485.
5. McNeal RH, 1998. Perspective on Finite Elements for Shell Analysis. Finite Elements in Analysis and Design, 30:175–186.
6. Nuhoğlu A, 2005. Noktasal İterativ Yaklaşım ile Kablolu ve Kafes Sistemlerin Geometrik Nonlineer Analizi. Teknik Dergi, 16(76): 3425-3443.
7. Parente E, Vaz LE, 2003. On Evaluation of Shape Sensitivities of Non-Linear Critical Loads. International Journal for Numerical Methods in Engineering, 56(6): 809-846.
8. Polat C, 2006. Geometrik Bakımdan Lineer Olmayan Kabuk Yapıların Statik Ve Dinamik Davranışı. Doktora Tezi, Elazığ.

9. Polat C, Calayır Y, 2010. Nonlinear Static and Dynamic Analysis of Shells of Revolution. Mechanics Research Communications, 37(2): 205-209.
10. Polat C, Ulucan ZÇ, 2007. Geometrically Non-linear Analysis of Axisymmetric Plates and Shells. F. Ü. International Journal of Science & Technology, 2 (1): 33-40.
11. Polat C, Calayır Y, 2007. Dikdörtgen Plakların Geometrik Bakımdan Lineer Olmayan Statik Analizi. F. Ü. Fen ve Mühendislik Bilimleri Dergisi, 19 (3): 357-362.
12. Polat C, Calayır Y, 2007. Lineer Olmayan Yapı Sistemlerinin Analizi İçin Yay-Boyu Metodu. F. Ü. Fen ve Mühendislik Bilimleri Dergisi, 19 (4): 525-530.
13. Reddy JN, 1997. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. 2nd edition, CRC Press, New York.
14. Souza NEA, Feng YT, 1999. On the Determination of the Path Direction for Arc-Length Methods in the Presence of Bifurcations and `Snap-Backs'. Computer Methods in Applied Mechanics and Engineering, 179: 81-89.
15. Zienkiewicz OC, Taylor RL, 2000. The finite element method: solid mechanics. Vol. 2, Butterworth-heinemann.