Bending instabilities of elastic tubes

The present paper examines instabilities of long thin elastic tubes. Both initially straight and initially bent tubes are analyzed under in-plane bending. Tube response, a combination of ovalization instability and bifurcation instability (buckling), is investigated using a nonlinear finite element (FE) technique, which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross-sectional deformation. It is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature. The ovalization of initially bent tubes is examined in detail and, in particular, the case of opening moments. Furthermore, the paper emphasizes on bifurcation instability. It is shown that buckling may occur prior to or beyond the ovalization limit point, depending on the value of the initial curvature. Using the nonlinear FE formulation, the location of bifurcation on the primary path is detected, post-buckling equilibrium paths are traced, and the corresponding wavelengths of the buckled configurations are calculated. Moreover, results over a wide range of initial curvature values are presented, extending the findings of previous works. Finally, several analytical approaches, introduced in previous research works, are also employed to estimate the moments causing ovalization and bifurcation instability. These approaches are based on nonlinear flexible shell theory or simplified ring analysis. The efficiency and accuracy of those analytical methods with respect to the nonlinear FE formulation are examined.

[1]  G. A. Thurston.  Critical Bending Moment of Circular Cylindrical Tubes , 1977 .

[2]  Spyros A. Karamanos,et al.  TUBULAR MEMBERS. II: LOCAL BUCKLING AND EXPERIMENTAL VERIFICATION , 1996 .

[3]  E. Reissner.  FINITE PURE BENDING OF CIRCULAR CYLINDRICAL TUBES , 1963 .

[4]  Stelios Kyriakides,et al.  Response and stability of elastoplastic circular pipes under combined bending and external pressure , 1982 .

[5]  F. Emmerling.  Nichtlineare Biegung und Beulen von Zylindern und krummen Rohren bei Normaldruck , 1982 .

[6]  O. Fabian.  Collapse of cylindrical, elastic tubes under combined bending, pressure and axial loads , 1977 .

[7]  S. Gellin.  The plastic buckling of long cylindrical shells under pure bending , 1980 .

[8]  John W. Hutchinson,et al.  Buckling and Initial Postbuckling Behavior of Oval Cylindrical Shells Under Axial Compression , 1968 .

[9]  E. L. Axelrad,et al.  Theory of flexible shells , 1987 .

[10]  Spyros A. Karamanos,et al.  Stability of Inelastic Tubes under External Pressure and Bending , 1991 .

[11]  L. Brazier.  ON THE FLEXURE OF THIN CYLINDRICAL SHELLS AND OTHER SECTION , 1927 .

[12]  Stelios Kyriakides,et al.  Inelastic analysis of thin-walled tubes under cyclic bending , 1985 .

[13]  J. Hutchinson,et al.  Buckling of Bars, Plates and Shells , 1975 .

[14]  C. R. Calladine,et al.  Theory of Shell Structures , 1983 .

[15]  M. Crisfield.  An arc‐length method including line searches and accelerations , 1983 .

[16]  L. H. Sobel.  In-plane bending of elbows☆ , 1977 .

[17]  Nicol Gross,et al.  Experiments on Short-radius Pipe-bends , 1953 .

[18]  Hugh Ford,et al.  The Flexibility of Short-radius Pipe-bends , 1953 .

[19]  Klaus-Jürgen Bathe,et al.  A Simple and Effective Pipe Elbow Element—Linear Analysis , 1980 .

[20]  J. T. Boyle.  The finite bending of curved pipes , 1981 .

[21]  Y. N. Chen,et al.  Buckling of oval cylindrical shells under compression and asymmetricbending , 1976 .

[22]  Stelios Kyriakides,et al.  On the collapse of inelastic tubes under combined bending and pressure , 1988 .

[23]  James H. Starnes,et al.  Collapse of Long Cylindrical Shells under Combined Bending and Pressure Loads , 1974 .

[24]  S. Kyriakides,et al.  Bifurcation and localization instabilities in cylindrical shells under bending-II. Predictions , 1992 .

[25]  D. H. Cheng,et al.  On Bending of Curved Circular Tubes , 1970 .

[26]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[27]  F. Emmerling,et al.  Große Verformungen und Traglasten elastischer Rohre unter Biegung und Außendruck , 1983 .

[28]  E. Reissner,et al.  Bending of Curved Tubes , 1951 .

[29]  P. Seide,et al.  On the Buckling of Circular Cylindrical Shells Under Pure Bending , 1961 .

[30]  Spyros A. Karamanos,et al.  Tubular Members. I: Stability Analysis and Preliminary Results , 1996 .