Modelling and behaviour of cylindrical shell structures with helical features

Spiral welding or bonding is a particularly efficient and cost-effective method of constructing continuous tubes. However the understanding of the mechanics of such structures is not yet well developed. This is in no small part due to the difficulties involved in their computational analysis. Cylindrical shells are traditionally modelled using rectangular finite elements oriented parallel to the meridional and circumferential axes. However, spiral features are particularly challenging to model because such features are not orthogonal to the axes of the cylinder. Commercial finite element pre-processors often struggle to mesh these with anything other than a free triangulation. A superior mesh would consist of well-conditioned rectangular elements oriented orthogonally with respect to the axes of the helix, termed a 'helical mesh', but this requires significant programming effort. A helical mesh is particularly important if features of the shell such as geometric imperfections, residual stresses, weld material and heat affected zones, and bonding in systems using adhesives are required to follow the helical form. Helically wound structural forms are widely used in different applications that demand continuous cylindrical forms. The most common uses in structural engineering are in spiral wound tubes, piles, chimneys and pipelines. This paper describes a powerful computational procedure developed by the authors to generate high quality helical meshes. Special emphasis is placed on the modelling of geometric deviations defined relative to the helix, appropriate for the analysis of spiral welded and stiffened tubes. The effect of helical meshing is illustrated using benchmark examples of perfect and imperfect cylinders under axial compression.

[1]  Adam J. Sadowski,et al.  On the relationship between mesh and stress field orientations in linear stability analyses of thin plates and shells , 2013 .

[2]  Johann Arbocz,et al.  Buckling of imperfect stiffened cylindrical shells under axial compression , 1971 .

[3]  Nobuo Nishimura,et al.  Numerical simulation on damage to pipe piers in Hyogoken-Nanbu earthquake , 1998 .

[4]  J. M. Rotter,et al.  Steel silos with different aspect ratios: II – behaviour under eccentric discharge , 2014 .

[5]  Thomas Ummenhofer,et al.  On the modelling of different types of imperfections in silo shells , 1995 .

[6]  Jin-Guang Teng,et al.  Analysis of geometric imperfections in full-scale welded steel silos , 2005 .

[7]  Anders Eriksson,et al.  Element behavior in post-critical plane frame analysis , 1995 .

[8]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

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

[10]  Fumio Fujii,et al.  Static path jumping to attain postbuckling equilibria of a compressed circular cylinder , 2000 .

[11]  J. Michael Rotter,et al.  Buckling of Pressurized Axisymmetrically Imperfect Cylinders under Axial Loads , 1992 .

[12]  J. Kepner.  Parallel Programming with MatlabMPI , 2001, astro-ph/0107406.

[13]  Aviv Rosen,et al.  Effect of Axisymmetric Imperfections on the Vibrations of Cylindrical Shells under Axial Compression , 1974 .

[14]  Mohammad Reza Forouzan,et al.  Residual stress prediction in submerged arc welded spiral pipes , 2012 .

[15]  Mitsuhiro Hanada,et al.  Development of High Speed Submerged Arc Welding in Spiral Pipe Mill , 1986 .

[16]  B. N. Leis,et al.  Computational Simulation of Line-Pipe Fabrication Processes , 2006 .

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

[18]  Xiaoli Ding,et al.  Technique for precise measurement of large-scale silos and tanks , 1996 .

[19]  Johann Arbocz,et al.  The effect of general imperfections on the buckling of cylindrical shells , 1968 .

[20]  O. C. Zienkiewicz,et al.  The Finite Element Method for Solid and Structural Mechanics , 2013 .

[21]  Ø. Hjelle,et al.  Triangulations and Applications (Mathematics and Visualization) , 2006 .

[22]  Kiyoshi Ono,et al.  A CONSTITUTIVE EQUATION FOR STRUCTURAL STEELS BASED ON A MONOTONIC LOADING CURVE UNDER CYCLIC LOADING , 1995 .

[23]  V. V. Novozhilov,et al.  Thin shell theory , 1964 .

[24]  Dieter Radaj,et al.  Design and Analysis of Fatigue Resistant Welded Structures , 1990 .

[25]  David Stephenson.  Pipeline design for water engineers , 1989 .

[26]  Anders Eriksson,et al.  Numerical analysis of complex instability behaviour using incremental-iterative strategies , 1999 .

[28]  Paul-Louis George,et al.  Delaunay triangulation and meshing : application to finite elements , 1998 .

[29]  Paul Seide,et al.  Small Elastic Deformations of Thin Shells , 1975 .

[30]  John Lancaster,et al.  Handbook of Structural Welding: Processes, Materials and Methods Used in the Welding of Major Structures, Pipelines and Process Plant , 1992 .

[31]  Ben C. Gerwick,et al.  Construction of Marine and Offshore Structures , 2007 .

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

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

[34]  J. Michael Rotter,et al.  Buckling of Thin Cylindrical Shells Under Locally Elevated Compressive Stresses , 2011 .

[35]  Jin-Guang Teng,et al.  Postbuckling analysis of elastic shells of revolution considering mode switching and interaction , 2006 .

[36]  Mitsuyoshi Akiyama,et al.  Analytical Study on Seismic Performance of Hollow Spiral Steel Pipes under Cyclic Loading , 2011 .

[37]  David J. O'Connor.  Computerised buckling analysis of shells: D. Bushnell. Martinus Nijhoff Publishers, Netherlands, August '85 423 pp. ISBN: 90-247-3099-6 Dfl 240.00 US$ 85.00. £ 60.95 , 1986 .

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

[39]  Jin-Guang Teng,et al.  Imperfection sensitivity and postbuckling analysis of elastic shells of revolution , 2008 .

[40]  Jin-Guang Teng,et al.  Numerical models for nonlinear analysis of elastic shells with eigenmode-affine imperfections , 2001 .

[41]  Anders Eriksson,et al.  Structural instability analyses based on generalised path-following , 1998 .

[42]  Anders Eriksson,et al.  Fold lines for sensitivity analyses in structural instability , 1994 .

[43]  J. Michael Rotter,et al.  Elastic Buckling of Imperfect Cylinders Containing Granular Solids , 1990 .

[44]  Ali Limam.  Flambage de coques cylindriques sous combinaison de chargements : pression interne et compression axiale , 1991 .

[45]  Archibald N. Sherbourne,et al.  Buckling of Cylindrical Shells Under Axial Compression , 1967 .

[46]  A. Eriksson.  On accurate descriptions for primary and secondary paths in equilibrium problems , 1992 .

[47]  Fumio Fujii,et al.  Path-tracing analysis for post-buckling process of elastic cylindrical shells under axial compression , 2012 .

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

[49]  J. M. Rotter,et al.  Compression tests on cylinders with circumferential weld depressions , 2000 .

[50]  J. M. Rotter,et al.  IMPERFECTION SENSITIVITY OF THIN ELASTIC CYLINDRICAL SHELLS SUBJECT TO PARTIAL AXIAL COMPRESSION , 2004 .

[51]  M. J. Jirinec,et al.  Experimental determination of the residual stresses in a spiral weld overlay tube , 1997 .

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

[53]  Wilhelm Flügge,et al.  Statik und Dynamik der Schalen , 1962 .

[54]  J. S. Mason,et al.  Bulk Solids Handling: An Introduction to the Practice and Technology , 2011 .

[55]  Oyvind Hjelle,et al.  Triangulations and applications , 2006 .

[56]  L. Donnell,et al.  Effect of Imperfections on Buckling of Thin Cylinders and Columns under Axial Compression , 1950 .

[57]  J. Williams,et al.  Imperfection Surveys on a 10-ft-Diameter Shell Structure , 1977 .

[58]  B. Yilbas,et al.  Thermal stress analysis of spiral laser-welded tube , 2011 .

[59]  J. Teng,et al.  Elastic Stability of Cylindrical Shells with Weld Depressions , 1989 .

[60]  C. R. Calladine,et al.  Imperfections and buckling in cylindrical shells with consistent residual stresses , 2000 .