Development of a semi-analytical nonlinear finite element formulation for cylindrical shells

Abstract

This article introduces a new semi-analytical nonlinear finite element formulation for thin cylinders according to a continuum-based approach. A comparison between the continuum-based approach and the classical approach for the buckling behavior of isotropic and orthotropic perfect cylinders validates the results. The classical approach is defined according to thin shell theories based on the von Karman approximation. A mathematical modeling for geometry imperfection of cylinders is derived according to a continuum-based approach whose results are compared with the results of the classical approach for imperfect cylinders. The influence of neglecting some nonlinear terms in the classical approach for perfect and imperfect cylinders on the buckling path is investigated. In the buckling analysis, two methods, i.e. the perturbation and load disturbance methods, which undertake to switch to the post-buckling path, are compared to each other.

Keywords

Semi-analytical finite element continuum-based approach classical approach post-buckling

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References

Wriggers

. Nonlinear finite element methods, Berlin Heidelberg: Springer-Verlag, 2008.

Zienkiewicz

Taylor

. The finite element method. Fifth Edition, Volume 2: Solid mechanics, Oxford: Butterworth-Heinemann, 2000.

Crisfield

. Non-linear finite element analysis of solids and structures, Volume 2: Advanced topics, Chichester: John Wiley & Sons, 1997.

Bathe

. Finite element procedures, New Jersey: Prentice-Hall, 1996.

Reddy

. An introduction to nonlinear finite element analysis, New York: Oxford University Press, 2004.

Wood

Schrefler

. Geometrically non-linear analysis a correlation of finite element notations. Int J Numer Meth Eng 1978; 12: 635–642.

De Souza Neto

Peric

Owen

DRJ

. Computational methods for plasticity theory and applications, Chichester: John Wiley & Sons, 2008.

Bonet

Wood

. Nonlinear continuum mechanics for finite element analysis, Cambridge: Cambridge University Press, 1997.

Logan

. A first course in the finite element method, 4th ed. Canada: Thomson, 2007.

10.

Hong

Teng

. Non-linear analysis of shells of revolution under arbitrary loads. Comput Struct 2002; 80: 1547–1568.

11.

Teng

Hong

. Postbuckling analysis of elastic shells of revolution considering mode switching and interaction. Int J Solids Struct 2006; 43: 551–568.

12.

Hong

Teng

. Imperfection sensitivity and postbuckling analysis of elastic shells of revolution. Thin-Walled Struct 2008; 46: 1338–1350.

13.

Ganesan

Kadoli

. Buckling and dynamic analysis of piezothermoelastic composite cylindrical shell. Compos Struct 2003; 59: 45–60.

14.

Patel

Shukla

Nath

. Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells. Compos Struct 2005; 71: 101–114.

15.

Patel

Nath

Shukla

. Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical–cylindrical shells. Int J Solids Struct 2006; 43: 4810–4829.

16.

Patel

Singh

Nath

. Postbuckling characteristics of angle-ply laminated truncated circular conical shells. Commun Nonlinear Sci Numer Simulat 2008; 13: 1411–1430.

17.

Singh

Patel

Nath

. Postbuckling of angle-ply laminated cylindrical shells with meridional curvature. Thin-Walled Struct 2009; 47: 359–364.

18.

Patel

Singh

Nath

. Stability and nonlinear dynamic behavior of cross-ply laminated heated cylindrical shells. Latin Am J Solids Struct 2006; 3: 245–261.

19.

Bagherizadeh

Kiani

Eslami

. Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation. Compos Struct 2011; 93: 3063–3071.

20.

Reddy

. Mechanics of laminated composite plates and shells theory and analysis, Boca Raton: CRC Press, 2004.

21.

Crisfield

. A fast incremental/iterative solution procedure that handles “snap-through”. Comput Struct 1981; 13: 55–62.

22.

Crisfield

. An arc-length method including line searches and accelerations. Numer Meth Eng 1983; 19: 1269–1289.

23.

Feng

Peric

Owen

DRJ

. Determination of travel directions in path-following methods. Math Comput Model 1995; 21: 43–59.

24.

Papadrakakis

. Solving large-scale nonlinear problems in solid and structural mechanics. In: Solving large-scale problems in mechanics, Chichester: John Wiley & Sons, 1993, pp. 183–223.

25.

Debongnie

. Physical interpretation and generalization of Marguerre's shallow shell theory. Int J Eng Sci 1979; 17: 387–399.

26.

Combescure

. Static and dynamic buckling of large thin shells. Nucl Eng Des 1986; 92: 339–354.

27.

Lui

Lam

SSE

. Finite strip analysis of laminated plates with general initial imperfection under end shortening. Eng Struct 2001; 23: 673–686.

28.

Wagner

Wriggers

. A simple method for the calculation of postcritical branches. Eng Comput 1988; 5: 103–109.

29.

Soric

. Stability analysis of a torispherical subjected to internal pressure. Comput Struct 1990; 36(1): 147–156.

30.

Fang

Wickert

. Post buckling of micromachined beams. J Micromech Microeng 1994; 4: 116–122.

31.

Brush

Almorth

. Buckling of bars, plates, and shells, New York: McGraw-Hill, 1975.

32.

Sheinman

Jabareen

. Postbuckling of laminated cylindrical shells in different formulation. AIAA J 2005; 43(5): 1117–1123.

33.

Wunderlich

Cramer

Obrecht

. Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetric loading. Comput Meth Appl Mech Eng 1985; 51: 259–275.