Junctions in shell structures: A review

Abstract Many shell structures used in modern technology consist of regular shell parts joined together along their common boundaries. We review different theoretical, numerical, and experimental approaches to modelling, analyses and design of the compound shell structures with junctions. Several alternative forms of boundary, continuity and jump conditions at the singular midsurface curves modelling the shell junction are reviewed. We also analyse the results obtained for special shell structures containing the cylinder–cylinder intersections, cone– , sphere– , and plate–cylinder junctions, tubular joints as well as other special types of junctions appearing in complex multi-shell structures.

[1]  D. A. Danielson,et al.  Nonlinear Shell Theory With Finite Rotation and Stress-Function Vectors , 1972 .

[2]  Jan Błachut,et al.  Strength, Stability, and Optimization of Pressure Vessels: Review of Selected Problems , 2008 .

[3]  T. E. Taylor,et al.  Optimum reinforcement of uniform thickness cone-cylinder intersections in vessels subject to internal pressure , 1983 .

[4]  Jin-Guang Teng,et al.  A stability design proposal for cone–cylinder intersections under internal pressure , 2003 .

[5]  Zhangzhi Cen,et al.  Limit analysis based on a modified elastic compensation method for nozzle-to-cylinder junctions , 2005 .

[6]  A. Khan,et al.  A parametric study of two normally intersecting cylindrical shells subjected to out-of-plane moment , 1986 .

[7]  K. Hwang,et al.  An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation , 2010 .

[8]  Donald Mackenzie,et al.  A method of estimating limit loads by iterative elastic analysis. III—Torispherical heads under internal pressure , 1992 .

[9]  Paweł Romanowicz,et al.  Numerical and Experimental Analysis of Stress and Strains in Flat Ends of High-Pressure Vessels , 2011 .

[10]  Charles R. Steele,et al.  STRESS ANALYSIS OF NOZZLES IN CYLINDRICAL VESSELS WITH EXTERNAL LOAD , 1983 .

[11]  W. Pietraszkiewicz.  Finite Rotations in the Nonlinear Theory of Thin Shells , 1980 .

[12]  Jin-Guang Teng.  Intersections in steel shell structures , 2000 .

[13]  Further three-dimensional stress analysis of an intersection of a cylindrical shell with a plate , 1977 .

[14]  Johann Arbocz,et al.  Computerized buckling analysis of shells , 1985 .

[15]  R. Preiss.  On the shakedown analysis of nozzles using elasto-plastic FEA , 1999 .

[16]  David Mair.  Stress Intensification Factors for Fabricated Lateral Piping Connections , 2014 .

[17]  I. C. Wang,et al.  STRESSES IN JUNCTION OF NOZZLE TO CYLINDRICAL PRESSURE VESSEL FOR EQUAL DIAMETER OF VESSEL AND NOZZLE. , 1967 .

[18]  W. Reidelbach,et al.  Der Spannungszustand im Übergangsgebiet einer rechtwinkligen Rohrabzweigung , 1961 .

[19]  Non-linear problems of connecting composite spatial bodies and thin shells, and variational methods for their solution , 1985 .

[20]  David Bushnell,et al.  STRESS, STABILITY AND VIBRATION OF COMPLEX, BRANCHED SHELLS OF REVOLUTION , 1974 .

[21]  David Bushnell,et al.  Failure of axially compressed frangible joints in cylindrical shells , 1980 .

[22]  Y. V. L. Narasimha Murthy,et al.  Analysis of residual stresses in hemispherical head to cylindrical shell joints of steam generator by weld cycle simulation , 1994 .

[23]  J. Michael Rotter,et al.  Collapse Behavior and Strength of Steel Silo Transition Junctions. Part II: Parametric Study , 1991 .

[25]  J. G. Teng,et al.  Elastic buckling of ring-stiffened cone–cylinder intersections under internal pressure , 1999 .

[26]  H. Hua,et al.  Free Vibration Analysis on Combined Cylindrical-Spherical Shell , 2012 .

[27]  Hamid Ahmadi,et al.  The development of fatigue design formulas for the outer brace SCFs in offshore three-planar tubular KT-joints , 2012 .

[28]  G. E. O. Widera,et al.  Burst Pressure of Pressurized Cylinders With Hillside Nozzle , 2009 .

[29]  John Anderson,et al.  Three-dimensional finite element analysis of sphere/cylinder intersections under axisymmetric loading , 1994 .

[30]  Haofeng Chen,et al.  Calculation of a lower bound ratchet limit part 2: Application to a pipe intersection and dissimilar material join , 2013 .

[31]  V. Skopinsky,et al.  Stress Analysis of Ellipsoidal Shell With Nozzle Under Internal Pressure Loading , 1994 .

[32]  Husain J. Al-Gahtani,et al.  Local pressure testing of spherical vessels , 2014 .

[33]  Alphose Zingoni,et al.  A theoretical formulation for the stress analysis of multi-segmented spherical shells for high-volume liquid containment , 2015 .

[34]  J. L. Zeman,et al.  On bending stresses at longitudinal weld joints of cylindrical shells due to peaking , 1994 .

[35]  Koetsu Yamazaki,et al.  Stress analysis of junction of plate and shell built-up structures via special finite shell element , 1996 .

[36]  Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Non-Central Shell Segment , 2004 .

[37]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model , 1990 .

[38]  G. E. O. Widera,et al.  Parametric FEA Study of Burst Pressure of Cylindrical Shell Intersections , 2010 .

[39]  Alexander Tesar,et al.  The influence of elasticity of joints on the behaviour of thin-walled structures , 2000 .

[40]  J. G. Lekkerkerker.  The determination of elastic stresses near cylinder-to-cylinder intersections , 1972 .

[41]  D. E. Johnson.  Stresses in a Spherical Shell With a Nonradial Nozzle , 1967 .

[42]  Elsadig Mahdi,et al.  Crushing Behavior of Cone-Cylinder-Cone Composite System , 2002 .

[43]  Donald G. LaBounty,et al.  Comparison of Cone-to-Cylinder Junction Reinforcement Requirements Between ASME Section VIII, Division 1 and Code Case 2286-1 , 2008 .

[44]  Jürgen Rudolph,et al.  Finite element analyses concerning the fatigue strength of nozzle-to-spherical shell intersections , 1995 .

[45]  Chen Wang,et al.  Experimental Limit Load of Forged Piping Branch Junctions and Comparison with Existing Solutions , 2005 .

[46]  Ruhr-Universitát Bochum.  On Geometrically Non-Linear Theories for Thin Elastic Shells , 1984 .

[47]  N. Jones,et al.  A Theoretical Study of the Elastic Behavior of Two Normally Intersecting Cylindrical Shells , 1969 .

[48]  V. Ramamurti,et al.  Asymmetric bending of cylindrical conical shell junction , 1970 .

[49]  Fernand Ellyin.  Elastic-Plastic Behavior of intersecting Shells , 1969 .

[50]  G. Li,et al.  A New Connection Structure Between Hydrogen Nozzle and Sphere Head in a Hydrofining Reactor , 2011 .

[51]  Wei Jiang,et al.  Effect of welding sequence on residual stress distribution in a multipass welded piping branch junction , 2012 .

[52]  Peter J. Budden,et al.  Plastic limit loads for thick-walled branch junctions , 2009 .

[53]  M. D. Xue,et al.  Theoretical stress analysis of intersecting cylindrical shells subjected to external loads transmitted through branch pipes , 2005 .

[54]  M.M.K. Lee,et al.  Parametric equations for distributions of stress concentration factors in tubular K-joints under out-of-plane moment loading , 1998 .

[55]  Chihdar Charles Yang,et al.  Stress Analysis of Composite Pipe Joints Under Combined Torsional and Tensile Loading , 2009 .

[56]  K. C. Pan,et al.  Stress and Displacement Analysis of a Shell Intersection , 1970 .

[57]  Jaroslav Mackerle,et al.  Finite element analysis and simulation of welding: a bibliography (1976 - 1996) , 1996 .

[58]  A. C. Eringen,et al.  STRESS DISTRIBUTION AT TWO NORMALLY INTERSECTING CYLINDRICAL SHELLS , 1965 .

[59]  Alphose Zingoni,et al.  Discontinuity effects at cone-cone axisymmetric shell junctions , 2002 .

[61]  James Wood.  Stresses in the vicinity of an unreinforced mitre intersection: An experimental and finite element comparison , 2007 .

[62]  Xiao Xia Guo,et al.  Stress of Spherical Shell with Opening Nozzle , 2012 .

[63]  Victor A. Eremeyev,et al.  Extended non‐linear relations of elastic shells undergoing phase transitions , 2007 .

[64]  Norman Jones.  The collapse pressure of a flush cylindrical nozzle intersecting a conical pressure vessel axisymmetrically , 1969 .

[65]  M. Robinson.  Lower-Bound Limit Pressures for the Cylinder-Cylinder Intersection: A Parametric Survey , 1978 .

[66]  Hossein Showkati,et al.  T-ring stiffened cone cylinder intersection under internal pressure , 2012 .

[67]  V. N Skopinsky,et al.  Parametric study of reinforcement of pressure vessel head with offset nozzle , 2003 .

[68]  Yun-Jae Kim,et al.  Effect of local wall thinning on limit loads for piping branch junctions. Part 1: Internal pressure , 2008 .

[69]  E. C. Rodabaugh,et al.  Stresses in Tapered Transition Joints in Pipelines and Pressure Vessels , 1962 .

[70]  S. E. Reed,et al.  Analytical and Experimental Stress Analysis of a Cylinder-to-Cylinder Structure , 1977 .

[71]  J. L. Zeman.  Ratcheting limit of flat end cylindrical shell connections under internal pressure , 1996 .

[72]  J Zheng,et al.  Unique design of the junction between a thick pressure vessel shell and a thinner hemispherical head , 2001 .

[73]  D G Moffat,et al.  Effective stress factors for piping branch junctions due to internal pressure and external moment loads , 1991 .

[74]  D. N. Moreton,et al.  An Approximate Method for Determining the Limit Pressure of Piping Branch Junctions With d/D ≤ 0.5 , 2007 .

[75]  Jin-Guang Teng,et al.  Buckling experiments on steel silo transition junctions: II: Finite element modeling , 2004 .

[76]  Shu Yang,et al.  Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading , 2012 .

[77]  Philippe G. Ciarlet,et al.  Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis , 1991 .

[78]  Peter J. Budden,et al.  Plastic limit loads for piping branch junctions under out-of-plane bending , 2012 .

[79]  Hans De Backer,et al.  Determining the SCFs of tubular bridge joints with an alternative method , 2014 .

[80]  Akhtar S. Khan,et al.  A comparative study of the stress field around a reinforced and an unreinforced normal intersection of two cylindrical shells , 1984 .

[81]  Y Zhao,et al.  Techniques for buckling experiments on steel silo transition junctions , 2001 .

[82]  K. Hwang,et al.  Stresses at the intersection of two cylindrical shells , 1995 .

[83]  Robert Hamilton,et al.  Simplified lower bound limit analysis of pressurised cylinder/cylinder intersections using generalised yield criteria , 1996 .

[84]  Victor A. Eremeyev,et al.  Thermomechanics of shells undergoing phase transition , 2011 .

[85]  Wenchun Jiang,et al.  A study of the residual stress and deformation in the welding between half-pipe jacket and shell , 2013 .

[86]  Giuseppe Geymonat,et al.  On the rigidity of certain surfaces with folds and applications to shell theory , 1995 .

[87]  Arturs Kalnins,et al.  Effect of Reinforcement on the Strength of Junctions Between Cylindrical and Conical Shells , 1995 .

[89]  R. M. Stone,et al.  THE EFFECT OF NOZZLE SPACING ON THE PRESSURE STRESSES AT THE INTERSECTION OF CYLINDRICAL NOZZLES AND SHELLS. , 1967 .

[90]  Hamid Ahmadi,et al.  Stress concentration factors induced by out-of-plane bending loads in ring-stiffened tubular KT-joints of jacket structures , 2015 .

[91]  Fernand Ellyin,et al.  The effect of yield surfaces on the limit pressure of intersecting shells , 1969 .

[92]  C. Calladine,et al.  Plastic Behaviour of Thin Cylindrical Pressure Vessels with Circular Cutouts and Radial Branches , 1969 .

[93]  B. F. Langer,et al.  Stresses in Thin-Walled Pressure Vessels With Ellipsoidal Heads , 1961 .

[94]  J. Haswell,et al.  A review of fracture mechanics models of tubular joints , 1991 .

[95]  Reinhard Preiss.  Stress concentration factors of flat end to cylindrical shell connection with a fillet or stress relief groove subjected to internal pressure , 1997 .

[96]  L. Varga.  Bestimmung der in der Umgebung der Ausschnitte von innendruckbeanspruchten Druckbehälterdeckeln auftretenden Spannungen , 1963 .

[97]  Michael P. Nemeth,et al.  Axisymmetric shell analysis of the Space Shuttle solid rocket booster field joint , 1990 .

[98]  G. E. O. Widera,et al.  Elastic Behavior of Cylindrical Vessels With Lateral Nozzle Under Internal Pressure , 2009 .

[99]  V. Skopinsky.  Stress concentration in cone–cylinder intersection , 2001 .

[100]  Guang Meng,et al.  A variational method for free vibration analysis of joined cylindrical-conical shells , 2013 .

[101]  J. M. Rotter,et al.  Recent research on the behaviour and design of steel silo hoppers and transition junctions , 1992 .

[102]  V. N. Skopinsky,et al.  Stress Analysis of Shell Intersections With Torus Transition Under Internal Pressure Loading , 1997 .

[103]  Alphose Zingoni,et al.  Liquid-containment shells of revolution: A review of recent studies on strength, stability and dynamics , 2015 .

[104]  Cai Xia Luo,et al.  Research of the Connecting Form about the Spherical Shell and the Nozzle , 2011 .

[105]  Abdel-Hakim Bouzid,et al.  Effect of Creep on the Residual Stresses in Tube-to-Tubesheet Joints , 2010 .

[106]  Toshiyuki Sawa,et al.  FEM stress analysis and strength of adhesive butt joints of similar hollow cylinders under static and impact tensile loadings , 2002 .

[107]  Chi-Yong Park,et al.  Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending , 2006 .

[108]  Wei Wang,et al.  A Simplified Strength Checking Approach for a Header–Nozzle Intersection Under Combined Piping Loads , 2013 .

[109]  W. Pietraszkiewicz,et al.  On unique kinematics for the branching shells , 2011 .

[110]  Darcy Holderness,et al.  Effective Expansion and Repair of Tube-to-Tubesheet Joints in a High Pressure Feedwater Heater , 2010 .

[111]  K. Hwang,et al.  An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part II: Design Method , 2010 .

[112]  J. Chróścielewski,et al.  Four‐node semi‐EAS element in six‐field nonlinear theory of shells , 2006 .

[113]  J. N. Flavin.  Concerning elastic cylinders bonded to rigid end plates , 1979 .

[114]  W. Pietraszkiewicz,et al.  Singular curves in the resultant thermomechanics of shells , 2014 .

[115]  P. Myler,et al.  Limit analysis of intersecting conical pressure vessels , 1985 .

[116]  A. Koizumi,et al.  Buckling of cylindrical shells with longitudinal joints under external pressure , 2010 .

[117]  I Mangerig,et al.  Ermuedungsverhalten geschweisster Rohrknoten von Fachwerkverbundbruecken / Fatigue behaviour of welded pipe intersections in steel-concrete composite bridges , 2009 .

[118]  P. Chellapandi,et al.  Parametric study of pull-out radius for steam generator shell nozzle junction for fast breeder reactor , 2013 .

[119]  J. Michael Rotter,et al.  Collapse Behavior and Strength of Steel Silo Transition Junctions. Part I: Collapse Mechanics , 1991 .

[120]  J.A.M. Ferreira,et al.  Influence of weld and plate geometry on the fatigue strength of cruciform joints , 1988 .

[121]  S. B. Lambert,et al.  Stress intensity factors for a pipe-plate welded joint , 1993 .

[122]  F. Flores,et al.  Post-buckling of elastic cone-cylinder and sphere-cylinder complex shells , 1991 .

[123]  Shunji Kataoka,et al.  Study on Collapse Characteristics and CSRF Method for 45 Deg Cylinder-to-Cylinder Intersections , 2012 .

[124]  V. Maz'ya,et al.  Asymptotic representation of elastic fields in a multi-structure , 1995 .

[125]  J. Haswell.  SIMPLE MODELS FOR PREDICTING STRESS INTENSITY FACTORS FOR TUBULAR JOINTS , 1991 .

[126]  E. C. Rodabaugh,et al.  Approximate Analysis of the Plastic Limit Pressures of Nozzles in Cylindrical Shells , 1968 .

[127]  W C Schnobrich,et al.  Nonlinear Analysis of Intersecting Cylinders by the Finite Element Method , 1976 .

[128]  E. M. Haseganu,et al.  LOW FREQUENCY VIBRATIONS OF A THIN CYLINDRICAL SHELL JOINED WITH AN ANNULAR THIN PLATE , 2003 .

[129]  David R Hayhurst,et al.  The creep behaviour of sphere-cylinder shell intersections subjected to internal pressure , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[131]  Markus Feldmann,et al.  Friction connection vs. ring flange connection in steel towers for wind converters , 2015 .

[132]  V. Skopinsky,et al.  Effect of Pad Reinforcement on the Plastic Limit Load for Nozzle Connection of Cylindrical Vessel , 2015 .

[133]  Hany F. Abdalla,et al.  Determination of Shakedown Limit Loads for a Cylindrical Vessel–Nozzle Intersection via a Simplified Technique , 2011 .

[134]  J. G. Teng.  Collapse Strength of Complex Metal Shell Intersections by the Effective Area Method , 1998 .

[135]  Yun-Jae Kim,et al.  Effect of local wall thinning on limit loads for piping branch junctions. Part 2: In-plane bending , 2008 .

[136]  W. Pietraszkiewicz.  On Using Rotations as Primary Variables in The Non-linear Theory of Thin Irregular Shells , 2001 .

[137]  M. Bernadou,et al.  Some Finite Element Methods for Linear Thin Shell Problems , 1987 .

[138]  Reza Fotouhi,et al.  Welded T-joint connections of square thin-walled tubes under a multi-axial state of stress , 2010 .

[139]  Martin Ruess,et al.  Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures , 2015 .

[140]  M. A. Kouchakzadeh,et al.  Free vibration analysis of joined conical shells: Analytical and experimental study , 2014 .

[141]  Farid Taheri,et al.  An Engineering Approach for Design and Analysis of Metallic Pipe Joints Under Torsion by the Finite Element Method , 2006 .

[142]  J. G. Teng,et al.  Sleeved Cone-Cylinder Intersection under Internal Pressure , 1998 .

[143]  M. Robinson.  Some Further Comments on Limit Pressures for the Cylinder-Cylinder Intersection , 1980 .

[144]  A. B. Sabir.  Strain-based finite elements for the analysis of cylinders with holes and normally intersecting cylinders , 1983 .

[145]  Jin-Guang Teng.  Cone‐Cylinder Intersection under Pressure: Axisymmetric Failure , 1994 .

[146]  Chi King Lee,et al.  Residual stress study of welded high strength steel thin-walled plate-to-plate joints, Part 1: Experimental study , 2012 .

[147]  Robin S. Langley.  Elastic Wave Transmission Coefficients and Coupling Loss Factors for Structural Junctions Between Curved Panels , 1994 .

[148]  Michel Bernadou,et al.  Numerical Analysis of Junctions between Thin Shells, Part 2 : Approximation by Finite Element Methods , 1998 .

[149]  Yeping Xiong,et al.  Free and forced vibration analysis of coupled conical–cylindrical shells with arbitrary boundary conditions , 2014 .

[150]  J. M. Rotter,et al.  Plastic buckling of rings at steel silo transition junctions , 1991 .

[151]  Young-Shin Lee,et al.  Free Vibrations of Circular Cylindrical Shells with AN Interior Plate Using the Receptance Method , 2001 .

[152]  J G Bouwkamp,et al.  Analytical Study of Tubular Tee-Joints , 1970 .

[153]  G. D. Galletly,et al.  Influence Coefficients and Pressure Vessel Analysis , 1960 .

[154]  J. Lyell Sanders,et al.  Analysis of a mitered joint in a cylindrical shell in bending , 1980 .

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

[156]  Limit pressure for a spherical vessel with a circumferential slot at its junction with a radial cylindrical protruding branch , 1987 .

[157]  M. D. Xue,et al.  A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments , 2005 .

[158]  V. Skopinsky.  A comparative study of three-dimensional and two-dimensional finite element analyses for intersecting shells , 2001 .

[159]  Deformational boundary quantities in the nonlinear theory of shells with transverse shears , 1998 .

[160]  H. Lakshminarayana.  Finite element analysis of laminated composite shell junctions , 1976 .

[161]  Shunji Kataoka,et al.  Study on Collapse Characteristics and CSRF Method for Cylinder-to-Cylinder Intersections by Plastic Analysis , 2010 .

[162]  V. N. Skopinsky,et al.  Numerical Stress Analysis of Intersecting Cylindrical Shells , 1993 .

[163]  Yang Zhao,et al.  Buckling Experiments on Cone-Cylinder Intersections under Internal Pressure , 2001 .

[164]  W. Pietraszkiewicz,et al.  Work-Conjugate Boundary Conditions in the Nonlinear Theory of Thin Shells , 1989 .

[166]  T. Ahmad,et al.  FEM Stress Analysis of Tee Intersections With LTA , 2008 .

[167]  G. E. O. Widera,et al.  Study of Elastic Strength for Cylinders With Hillside Nozzle , 2009 .

[168]  W. Pietraszkiewicz.  Finite rotations and Lagrangean description in the non-linear theory of shells , 1979 .

[169]  W. T. Koiter,et al.  Foundations of shell theory , 1973 .

[170]  Donald Mackenzie,et al.  Limit and shakedown analysis of nozzle/cylinder intersections under internal pressure and in-plane moment loading , 1996 .

[171]  Ya. M. Grigorenko,et al.  Linear and Nonlinear Problems on the Elastic Deformation of Complex Shells and Methods of Their Numerical Solution , 2000 .

[172]  Wei Jiang,et al.  Finite element prediction of residual stress distributions in a multipass welded piping branch junction , 2007 .

[173]  Adnan Ibrahimbegovic,et al.  Thermomechanical coupling in folded plates and non-smooth shells , 2005 .

[174]  A. A. El Damatty,et al.  Dynamic characteristics of combined conical-cylindrical shells , 2005 .

[175]  J Zamani,et al.  Analytical Investigation of Elastic Thin-Walled Cylinder and Truncated Cone Shell Intersection Under Internal Pressure. , 2014, Journal of pressure vessel technology.

[176]  D. Redekop,et al.  Approximate Prediction of Hoop Stresses at Major Sections of Tee Intersections of Cylindrical Shells Subjected to Internal Pressure , 1979 .

[177]  J. Mąkowski,et al.  Statyka i dynamika powłok wielopłatowych : nieliniowa teoria i metoda elementów skończonych , 2004 .

[178]  M. D. Xue,et al.  A Universal Design Method Based on Analysis for Cylindrical Shells With Nozzles Due to Internal Pressure, External Forces and Moments: Part I , 2009 .

[179]  H Fessler,et al.  Stress distribution in a tee junction of thick pipes , 1956 .

[180]  Michael A. Porter,et al.  A Suggested Shell∕Plate Finite Element Nozzle Model Evaluation Procedure , 2008 .

[181]  Junction reinforced pressurized spherical shell with a conical nozzle , 1985 .

[182]  D. Redekop,et al.  SCF analysis of a pressurized vessel–nozzle intersection with wall thinning damage , 2009 .

[184]  Michel Bernadou,et al.  Numerical analysis of junctions between thin shells Part 1: Continuous problems , 1998 .

[185]  A L Petrovic,et al.  Oblique nozzle loaded by the torque moment–stress state in the cylindrical shells on the pressure vessel , 2012 .

[186]  W. Pietraszkiewicz,et al.  Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells , 2007 .

[187]  J. L. Zeman.  On the problem of angular misalignment at longitudinal weld joints of cylindrical shells , 1994 .

[188]  Akhtar S. Khan.  A study of flexibility factors of integrally reinforced shell to shell intersections , 1987 .

[189]  Alain Nussbaumer,et al.  On the low-cycle fatigue capacity of unanchored steel liquid storage tank shell-to-base connections , 2012, Bulletin of Earthquake Engineering.

[190]  J. Schroeder,et al.  Lower bounds to limit pressures of a tee-intersection of cylindrical shells based on a three-dimensional stress field , 1977 .

[191]  V. I. Weingarten,et al.  Vibrations of segmented shells , 1973 .

[192]  W. D. Dover,et al.  Prediction of stress distributions along the intersection of tubular Y and T-joints , 1999 .

[193]  W. Pietraszkiewicz.  Development of Intrinsic Formulation of W.-Z. Chien of the Geometrically Nonlinear Theory of Thin Elastic Shells , 2011 .

[194]  Jong Bum Kim,et al.  Thermal Ratcheting Behavior of a Cylindrical Structure with Plate-to-Shell Junction , 2003 .

[195]  Osama Bedair,et al.  Analysis and Limit State Design of Stiffened Plates and Shells: A World View , 2009 .

[196]  K. Munaswamy,et al.  Numerical stress analysis of internal ring-stiffened tubular T-joints , 1995 .

[197]  Lin Seng Ong,et al.  Bending Stresses at Longitudinal Weld Joints of Pressurized Cylindrical Shells due to Angular Distortion , 1996 .

[198]  G D T Carmichael,et al.  Finite element stress analysis of an equal diameter branch pipe intersection subjected to out-of-plane and twisting moments , 1986 .

[199]  Alain Nussbaumer,et al.  Fatigue analysis of liquid-storage tank shell-to-base connections under multi-axial loading , 2012 .

[200]  Donald Mackenzie,et al.  A method of estimating limit loads by iterative elastic analysis. II—Nozzle sphere intersections with internal pressure and radial load , 1992 .

[201]  Dong-Seong Sohn,et al.  FREE VIBRATION OF CLAMPED–FREE CIRCULAR CYLINDRICAL SHELL WITH A PLATE ATTACHED AT AN ARBITRARY AXIAL POSITION , 1998 .

[202]  Jin Jiang,et al.  Residual stress study of welded high strength steel thin-walled plate-to-plate joints, part 2 : numerical modeling , 2012 .

[203]  W. Pietraszkiewicz.  Refined resultant thermomechanics of shells , 2011 .

[204]  M. D Xue,et al.  Stress analysis of cylindrical shells with nozzles due to external run pipe moments , 2000 .

[205]  Jean-Luc Akian,et al.  Asymptotic analysis of bending-dominated shell junctions , 2005 .

[206]  M. D. Xue,et al.  Theoretical Stress Analysis of Intersecting Cylindrical Shells Subjected to External Forces on Nozzle , 2006 .

[207]  Jin-Guang Teng,et al.  Shell restraint to ring buckling at cone-cylinder intersections , 1997 .

[208]  A. N. Sherbourne,et al.  The collapse of cylinder/sphere intersecting pressure vessels , 1965 .

[209]  D. F. Li,et al.  Analytical solution of two intersecting cylindrical shells subjected to transverse moment on nozzle , 2004 .

[210]  F. Z. Xuan,et al.  Evaluation of plastic limit load of piping branch junctions subjected to out-of-plane moment loadings , 2003 .

[211]  Karl Schweizerhof,et al.  COMBINATION OF ADAPTIVITY AND MESH SMOOTHING FOR THE FINITE ELEMENT ANALYSIS OF SHELLS WITH INTERSECTIONS , 1997 .

[212]  V N Skopinsky,et al.  Theoretical analysis of composite shell intersections , 1999 .

[213]  W. Pietraszkiewicz,et al.  On modelling and non‐linear elasto‐plastic analysis of thin shells with deformable junctions , 2011 .

[214]  W. Chien,et al.  The intrinsic theory of thin shells and plates. III. Application to thin shells , 1944 .

[215]  J. G. Simmonds,et al.  The Nonlinear Theory of Elastic Shells , 1998 .

[216]  T. Christopher,et al.  Finite element analysis of cylindrical pressure vessels having a misalignment in a circumferential joint , 2010 .

[217]  John F. Harvey,et al.  Pressure vessel design : nuclear and chemical applications , 1963 .

[218]  Jae-Han Lee,et al.  Progressive inelastic deformation characteristics of cylindrical structure with plate-to-shell junction under moving temperature front , 2003 .

[219]  Koetsu Yamazaki,et al.  A stress analysis technique for plate and shell built-up structures with junctions and its application to minimum-weight design of stiffened structures , 1997 .

[220]  B. P. Patel,et al.  Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical-cylindrical shells , 2006 .

[221]  E. Oñate,et al.  A rotation‐free shell triangle for the analysis of kinked and branching shells , 2007 .

[222]  Yegao Qu,et al.  Vibrations characteristics of joined cylindrical-spherical shell with elastic-support boundary conditions , 2013 .

[223]  W. Pietraszkiewicz,et al.  Jump Conditions in the Non-linear Theory of Thin Irregular Shells , 1999 .

[224]  Abdel-Hakim Bouzid,et al.  Flanged Joints of Multi-Pass Shell-and-Tube Heat Exchangers Subjected to Non-Axisymmetric Thermal Loading , 2010 .

[225]  Hiroyuki Fujiki,et al.  Study on the Effects of Switching Temperature on the Thermal Fatigue Life of the Shell-to-Skirt Junction of Coke Drum , 2011 .

[226]  Numerical modeling of nonlinear deformation and buckling of composite plate-shell structures under pulsed loading , 1999 .

[227]  S. Bao,et al.  Comparative studies on buckling behaviors of T joint and pipe by varying geometric parameters and analysis methods , 2015 .

[228]  J. L. Zeman,et al.  The flat end to cylindrical shell connection—limit load and creep design , 1998 .

[229]  C. Hsiao,et al.  Strain field in straight cylindrical shells due to applied forces on an attached shell. Part I: No hole in the intersection region , 1984 .

[230]  F. Xuan,et al.  Constraint-Dependent J-R Curves of a Dissimilar Metal Welded Joint for Connecting Pipe-Nozzle of Nuclear Pressure Vessel , 2015 .

[231]  G. E. O. Widera,et al.  Investigation of Fatigue Strength of Welded Tube-to-Tubesheet Joint , 2009 .

[232]  R. Grossi.  Boundary value problems for anisotropic plates with internal line hinges , 2012 .

[233]  Jin-Guang Teng,et al.  Buckling experiments on steel silo transition junctions: I: Experimental results , 2004 .

[234]  Wojciech Pietraszkiewicz,et al.  The Nonlinear Theory of Elastic Shells with Phase Transitions , 2004 .

[235]  G. E. O. Widera,et al.  Limit and burst pressures for a cylindrical shell intersection with intermediate diameter ratio , 2002 .

[236]  Victor A. Eremeyev,et al.  Phase transitions in thermoelastic and thermoviscoelastic shells , 2008 .

[237]  Ei Damatt,et al.  Simplified Procedure for Design of Liquid-Storage Combined Conical Tanks , 2009 .

[238]  W. Flügge.  Stresses in Shells , 1960 .

[239]  E. Baker,et al.  Structural analysis of shells , 1972 .

[240]  V. Luzin,et al.  Effect of residual stress on the integrity of a branch connection , 2012 .

[241]  Kenneth M. Will,et al.  A FINITE ELEMENT TECHNIQUE FOR THE ULTIMATE STRENGTH ANALYSIS OF TUBULAR JOINTS , 1992 .

[243]  Alphose Zingoni,et al.  Stresses and deformations in egg-shaped sludge digestors: discontinuity effects , 2001 .

[244]  D Bowness,et al.  A finite element study of stress fields and stress intensity factors in tubular joints , 1995 .

[247]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part VII: Shell intersections with -DOF finite element formulations , 1993 .

[248]  Jin-Guang Teng,et al.  On the buckling failure of a pressure vessel with a conical end , 2000 .

[249]  P. Chellapandi,et al.  Investigations on shell–nozzle junction of steam generator for LBB justification , 2007 .

[250]  Tommy Vilhelmsen.  Reference stress solutions of flat end to cylindrical shell connection and comparison with design stresses predicted by codes , 2000 .

[251]  V. N. Skopinsky,et al.  Stress analysis of nonradial cylindrical shell intersections subjected to external loading , 1996 .

[252]  M. A. Kouchakzadeh,et al.  Free vibration analysis of joined cross-ply laminated conical shells , 2014 .

[253]  I. Harik,et al.  AXISYMMETRIC GENERAL SHELLS AND JOINTED SHELLS OF REVOLUTION , 1992 .

[254]  Shan Tung Tu,et al.  Limit Load Interaction of Welded Piping Branch Junctions Subjected to Combined Internal Pressure and Bending , 2005 .

[255]  Wei Jiang,et al.  Influence of Cooling Rate on Predicted Weld Residual Stress Buildup in a Thick-Walled Piping Intersection , 2010 .

[256]  Wojciech Pietraszkiewicz,et al.  Intrinsic equations for non-linear deformation and stability of thin elastic shells ? , 2004 .

[257]  B. P. Patel,et al.  Analysis of parametrically excited laminated composite joined conical–cylindrical shells , 2001 .

[258]  Jaap Wardenier,et al.  Current static design guidance for hollow-section joints , 2010 .

[259]  Alphonse Zingoni,et al.  Shell structures in civil and mechanical engineering , 1997 .

[260]  Matthew Walter,et al.  An Investigation Into the Effects of Modelling Cylindrical Nozzle to Cylindrical Vessel Intersections Using 2D Axisymmetric Finite Element Models and a Proposed Method for Correcting the Results , 2011 .

[261]  Asif Israr,et al.  To Analyze the Effects of Geometric Misalignment in a Cylindrical Pressure Vessel , 2012 .

[262]  A. A. El Damatty,et al.  Experimental study conducted on a liquid-filled combined conical tank model , 2005 .

[263]  Tsutomu Hayashi,et al.  Theory of Stress Concentration of Two Normally Intersecting Cylindrical Shells , 1969 .

[264]  C. A. Laberge,et al.  The Effect of Corner Radius on Plate-Cylinder Intersections , 1980 .

[265]  Jaroslav Mackerle,et al.  Finite element analysis of fastening and joining: A bibliography (1990–2002) , 2003 .

[266]  A. Biron,et al.  On limit analysis of cylinder-cylinder intersections subjected to internal pressure , 1976 .

[267]  J. Hanna,et al.  Jump conditions for strings and sheets from an action principle , 2014, 1406.5175.

[268]  A. Biron.  Review of Lower-Bound Limit Analysis for Pressure Vessel Intersections , 1977 .

[269]  Masashi Daimaruya,et al.  Effect of Hot Feed Injection Time on Thermal Fatigue Life of Shell-to-Skirt Junction Area of Coke Drums , 2010 .

[270]  Jin-Guang Teng.  Cone-cylinder intersection under internal pressure : nonsymmetric buckling , 1995 .

[271]  W. J. Koves,et al.  A Finite Element for the Analysis of Shell Intersections , 1996 .

[272]  Ingbert Mangerig,et al.  Ermüdungsverhalten geschweißter Rohrknoten von Fachwerkverbundbrücken , 2009 .

[273]  Shan-Tung Tu,et al.  Limit load analysis for the piping branch junctions under in-plane moment , 2006 .

[274]  Norman Jones.  An Approximate Rigid-Plastic Analysis of Shell Intersections Loaded Dynamically , 1973 .

[275]  Md. Wahhaj Uddin,et al.  Stresses at the junctions of axisymmetric shells under axially varying load , 1998 .

[276]  J. Teng.  Elastic buckling of cone-cylinder intersection under localized circumferential compression , 1996 .

[277]  J. Chróścielewski,et al.  Finite element analysis of smooth, folded and multi-shell structures , 1997 .

[278]  Akhtar S. Khan.  A study of stress intensification factors of integrally reinforced shell to shell intersections , 1987 .

[280]  Colin H. Hansen,et al.  Wave propagation through cylinder/plate junctions , 1995 .

[281]  D. Redekop.  Vibration analysis of a torus–cylinder shell assembly , 2004 .

[282]  Jeffrey A. Packer,et al.  Numerical study and design of T-type branch plate-to-circular hollow section connections , 2012 .

[283]  G. E. O. Widera,et al.  Study of Plastic Limit Load on Pressurized Cylinders With Lateral Nozzle , 2008 .

[284]  F. A. Leckie.  Shakedown Pressures for Flush Cylinder-Sphere Shell Intersections , 1965 .

[285]  A. N. Sherbourne,et al.  Limit analysis of axisymmetric intersecting shells of revolution , 1965 .

[286]  Inge Lotsberg,et al.  Stress concentration factors at welds in pipelines and tanks subjected to internal pressure and axial force , 2008 .

[287]  D G Moffat,et al.  Experimental Stress Analysis of Four Fabricated Equal Diameter Branch Pipe Intersections Subjected to Moment Loadings and the Implications on Branch Junction Design , 1985 .

[288]  R. C. Gwaltney,et al.  Experimental Stress Analysis of Cylinder-to-Cylinder Shell Models and Comparisons With Theoretical Predictions , 1976 .