Postbuckling analysis of elastic shells of revolution considering mode switching and interaction

The postbuckling response of shells is known to exhibit complex phenomena including mode switching and interaction, particularly in the advanced postbuckling range. The existing literature contains many initial postbuckling analyses as well as advanced postbuckling analyses for a single buckling mode, but little work is available on the advanced postbuckling analysis of shells of revolution considering mode switching and interaction. In this paper, a numerical method for the advanced postbuckling analysis of thin shells of revolution subject to torsionless axisymmetric loads is presented, in which such mode switching and interaction are properly captured. Numerical results obtained using the present method for several typical problems not only demonstrate the capability of the method, but also lead to significant observations concerning the postbuckling behavior of thin shells of revolution. In particular, the results show that strong interaction between different harmonic modes may exist and the transition of deformation mode from one to another is gradual. Consequently, the conventional approach of finding the postbuckling path of a shell as the lower festoon curve of postbuckling paths of individual harmonic modes is not valid and is at best a convenient approximation.

[1]  Jin-Guang Teng,et al.  POST-COLLAPSE BIFURCATION ANALYSIS OF SHELLS OF REVOLUTION BY THE ACCUMULATED ARC-LENGTH METHOD , 1997 .

[2]  J. G. Teng,et al.  Elastic-plastic large deflection analysis of axisymmetric shells , 1989 .

[3]  W. T. Koiter.  THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[4]  G. Simitses,et al.  Elastic stability of circular cylindrical shells , 1984 .

[5]  Bruno Cochelin,et al.  An asymptotic‐numerical method to compute the postbuckling behaviour of elastic plates and shells , 1993 .

[6]  F. A. Brogan,et al.  On the solution of mode jumping phenomena in thin walled shell structures , 1996 .

[7]  J. G. Teng,et al.  Nonlinear thin shell theories for numerical buckling predictions , 1998 .

[8]  Alan S. Kushner.  Bifurcation buckling eigenvector characteristics for structures exhibiting buckling mode interactions , 1997 .

[9]  A. Combescure.  Are the static postbuckling predictions conservative , 1999 .

[10]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[11]  Jin-Guang Teng,et al.  Non-linear analysis of shells of revolution under arbitrary loads , 2002 .

[12]  Walter Wunderlich,et al.  Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetric loading , 1985 .

[13]  J. Hutchinson,et al.  A survey of some buckling problems. , 1966 .

[14]  Maria Esslinger,et al.  Postbuckling Behavior of Structures , 1975 .

[15]  Walter Wunderlich,et al.  A Semi-Analytical Approach to the Nonlinear Analysis of Shells of Revolution , 1989 .

[16]  Hui-Shen Shen.  Postbuckling analysis of cylindrical shells under combined external liquid pressure and axial compression , 1996 .

[17]  Luis A. Godoy,et al.  Elastic postbuckling analysis via finite element and perturbation techniques part II: Application to shells of revolution , 1993 .

[18]  W. J. Supple.  Changes of wave-form of plates in the post-buckling range , 1970 .

[19]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[20]  Tao Hong.  Nonlinear, buckling and postbuckling analysis of shells of revolution , 2000 .

[21]  B. Binder,et al.  Postbuckling strength design of open thin-walled cylindrical tanks under wind load , 1998 .

[22]  Hui‐Shen Shen,et al.  Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression , 1991 .

[23]  Thin shell finite element by the mixed method formulation — Parts 2 and 3 , 1977 .

[24]  J. M. Rotter,et al.  Non-symmetric bifurcation of geometrically nonlinear elastic-plastic axisymmetric shells under combined loads including torsion , 1989 .

[25]  Ralf Peek,et al.  Postbuckling analysis and imperfection sensitivity of general shells by the finite element method , 1999 .

[26]  Ekkehard Ramm,et al.  Simulation of buckling process of shells by using the finite element method , 1998 .

[27]  W. Wunderlich.  Nonlinear Finite Element Analysis in Structural Mechanics , 1981 .

[28]  Luis A. Godoy,et al.  Elastic postbuckling analysis via finite element and perturbation techniques. Part 1: Formulation , 1992 .