Buckling Of Stiffened Thin-Walled Cylindrical Shells Under Axial .
Journal of Structural Engineering and Geotechnics,Journal of Structural Engineering and Geotechnics,2 (2),19-28,20121 (1),1-5,SummerSpring 2011QIAUBuckling of Stiffened Thin-Walled Cylindrical Shells under AxialCompression with Symmetrical ImperfectionsA. Nobakht Namin*aaQazvin Branch, Islamic Azad University, Qazvin, IranReceived 14 September 2012, Accepted 18 November 2012AbstractThis study aimed to investigate the effects of stiffeners on buckling of thin cylindrical shells under uniform axial compression. To this end,more than 300 finite element models of stiffened cylindrical shells were prepared. The variables considered are shell thickness, number,dimension and the location of the vertical and horizontal stiffeners as well as circular symmetrical imperfections. Results show that thestiffeners can increase buckling of the stiffened cylindrical shells under axial compression. It is also shown that buckling of the cylindricalshells is susceptible to some circular imperfection patterns. In this context, buckling graph of the models are compared with each other;obviously, the stiffened shells with more stiffeners have upper buckling graph in force - displacement curves.Key words:Cylindrical shell, Thin-walled, Stiffener, Buckling, Axial compressioncollapse in axially compressed cylindrical shells.Stringers, the longitudinal stiffeners, are most effective inincreasing the axial bending strength of cylindrical shellsand their optimization has resulted in closely spacedstiffening, which generates general instability failure [5].But rings, latitudinal stiffeners, can show more influenceon shells strength against internal pressures. Moredetailed experimental and theoretical studies have beenconducted by Singer et al. [6-13] for the buckling ofstringer stiffened cylindrical shells including effects suchas load eccentricity, stiffener eccentricity and geometry,boundary conditions, prebuckling deformations andgeometric imperfections. In 1993, Shen, et al. [14]investigated the buckling and postbucklingbehavior ofperfect and imperfect, stringer and ring stiffenedcylindrical shells of finite length subject to combinedloading of external pressure and axial compression. In2003, Park and Park [15] developed an efficient nonlinearfinite element method that covers both initialdeformations and initial stresses of general distribution incalculating the ultimate strength of ring-stiffenedcylinders. Also early works were done byKrasovskyandKostyrko (2007) [16]. They tested thebuckling capacity of inside and outside stiffened shells atsimply supported and clamped edges.This project aimed to access the effects of the stiffenerson buckling of the cylindrical shells under uniform axialcompression and also the circular symmetricalimperfections influences are checked.1. IntroductionCylindrical thin-walled shells are common components ofindustries, especially in pressure vessels, liquid storagetanks and silos. During the past decades, severalcylindrical shells were damaged due to the extreme loadssuch as tornados, explosions and earthquakes.Performance of shell structures during pas events showedthat shell buckling is the most common failure mode ofthin-walled cylindrical shells. Although there is not aunique borderline between thin and thick cylindricalshells, thin shells usually have the radius to thickness ratioof 100 to 2000 [1]. Shell Buckling depends on severalparameters such as geometric specifications, loadingcondition and imperfections [2]. Shariati et al. [3]presented experimental and numerical investigations onthe effects of length, sector angle and boundary conditionson the buckling and postbucklingbehavior of cylindricalshells. In order to increase the shell strength one can usehorizontal and vertical stiffeners that can be used alone orby a combination of both. Generally stiffener sections arein T, L and Z Figures. Stiffened cylindrical shellssubjected to axial compression can fail in one of threemodes: local shell buckling, global instability or localstiffener buckling [4]. When the stiffeners are morewidely spaced, local shell instability will proceed global*Corresponding Author Email: armin n86@yahoo.com19
A. Nobakht Namin3. Numerical analysis2. Modeling AssumptionsIn this context, stiffened shells have been modeled byANSYS and have been analyzed under axial compression.Here is the some of the assumptions:1.Nonlinear Static analysis with large displacements andclamped edges are considered here.2.Yieldstress and elastic modules are respectivelyassumed to be 240 MPa and E 2.1*1011 ( N ) .Buckling of ring-stiffened and stringer-stiffenedcylindrical shells by moving the stiffeners.In this part, twocylindrical shells with radius of 2.5 & 5m and the heightof 10m were modeled. For each of them ring stiffenersand stringer stiffeners with the 10 cm width in thedistance of 0.5, 1 & 2 meter were considered. The axialbuckling loads of the stiffened cylindrical shells withdifferent thicknesses are presented in Figs. s2 and 3s: Stiffeners width(cm)l: Distance of the stiffeners(m)r: Shell radius(m)t: Shell thickness(m)T: Loading stepsPcr: Axial critical buckling load(Newton)m23.Nonlinear slope are considered as 2% of the linear slopeof the steel stress-strain graph.4.Four node Shell181 elements (Fig. 1) with three degreesof freedom at each node were used to model stiffenedcylindrical shells. The elements were capable ofconsidering material nonlinearity and large deformations.A bilinear elastic-plastic model was considered formodeling material properties of cylindrical shell.Fig.1. Specification of shell elementsTable 1. Axial buckling loads of the ring- stiffened cylindrical shells under axial compression(r 2.5&5 m)6Buckling of Ring-Stiffened shells(10 N)Ring-S ffened shell (r 167208250313417Pcr(l 2,s 7849.6198441.2100832.9323225.5648Pcr(l 1,s 850.267241.8153634.1124825.28384Ring-S ffened shell (r 5)Pcr(l 0.5,s r(l 2,s 694.3401677.1609654.3497625.732544Pcr(l 1,s 1532894.2822476.7785653.7926439.36Pcr(l 0.5,s 0928100.8614482.7987264.4409646.13952
Journal of Structural Engineering and Geotechnics,2 (2), 19-28, Summer 2012Table 2. Axial buckling loads of the stringer- stiffened cylindrical shells under axial compression(r 2.5&5 m)Buckling of Stringer-Stiffened shells(106 N)Stringer-S ffened shell (r 2.5)Stringer-Stiffened shell (r 5.0)rtr/tPcr(l 2,s 10)Pcr(l 1,s 10)Pcr(l 0.5,s 10)rtr/tPcr(l 2,s 10)Pcr(l 1,s 10)Pcr(l 0.5,s 33672.6035256.781888Table 1 shows that when the distance of the ring stiffenersreduces, the shell buckling strength increases but it doesn'thave much effect unless the stiffeners are too close toeach other. But in stringer-stiffened shells the morestiffeners used, the more buckling strength is expectedbecause the section area increases(see Table 2). Alsobuckling figures are mentioned which indicate thatnumber of the stiffeners doesn’t have any effects on linearand nonlinear buckling slopes(see Figs. 2 and 3).Fig. 3. Buckling of the Stringer-stiffened cylindrical shells by changingthe number of stiffeners(t 2.0 cm)3.1. Shell buckling by changing the stiffeners widthIn order to investigate the effects of the stiffeners widthon the buckling of the shells, a cylindrical shell withradius of 2.5 and the height of 10m and thickness 2cmwas modeled. The stiffeners with the distance of 0.5 mFig. 2. Buckling of the ring-stiffened cylindrical shells by changing thenumber of stiffeners(t 1.5 cm)21
A. Nobakht Naminwere considered. The axial buckling loads of the ring andstringer stiffened cylindrical shells with different widthare presented in Fig. 4.Fig. 4 shows that increasing stiffeners’ width doesn’t haveenough effect on the buckling strength of the ringstiffened shells duo to uniform axial compression, So thatthe width of 5 cm to 20 cm only 8 percent of bucklingresistance increased. On the other hand, stiffeners widthdoesn’t have any effects on linear and nonlinear bucklingslope (see Fig. 5).In stringer-stiffened shells, the stiffeners’ width additionincreases the axial load buckling strength (see Fig. 4). Asthe stiffeners’ width increases, more destruction appearsin stringer-stiffened shells because the postbuckling zoneslope becomes less. As a result more instability isobserved(see Figs. 6 and 7).Fig. 6. Buckling and postbuckling of the stringer- stiffenedcylindrical shells with different width(a)Fig. 4. Buckling loads of the ring- stiffened and stringer-stiffenedcylindrical shells with different width(b)Fig. 5. Buckling and postbuckling of the ring- stiffened cylindrical shellswith different widthFig. 7. (a) Buckling of the stringer- stiffened cylindrical shell with5 cm width. (b) Buckling of the stringer- stiffened cylindrical shellwith 15 cm width.22
Journal of Structural Engineering and Geotechnics, 2 (2), 19-28, Summer 2012external stiffened cylindrical shells with differentthicknesses are presented in Table 3. It indicates thatusing ring-stiffeners inside or outside the cylindricalshells doesn’t change the axial buckling load. But instringer-stiffened cylindrical shells using internalstiffeners have more buckling strength under axialcompression against outside ones (see Table 4).3.2. Buckling of internal ring-stiffened and stringerstiffened cylindrical shellsIn order to compare the internal and external ringstiffened and stringer-stiffened cylindrical shells, twocylindrical shells with radius of 2.5 & 5m and the heightof 10m were modeled. For each of them, stiffeners withthe 10 cm width in the distance of 1 meter wereconsidered. The axial buckling loads of internal andTable 3. Buckling load of internal and external ring-stiffened cylindrical shells under axial compression(r 2.5&5 m)Buckling of Ring-Stiffened shells(106 N)insideoutsideinsideoutsidePcr(l 1,s 10)Pcr(l 1,s 10)Pcr(l 1,s 10)Pcr(l 1,s 0849.911842.50.012502.50.0082.50.006Fig. 8. Axial buckling loads of the internal and external ring- stiffenedcylindrical shells under axial compression (r 2.5m)Fig. 9. Axial buckling loads of the internal and external ring- stiffenedcylindrical shells under axial compression (r 5.0m)23
A. Nobakht NaminTable 4. Buckling load of internal and external stringer-stiffened cylindrical shells under axial compression(r 2.5&5 m)6Buckling of Stringer-S ffe ned shells (10 N)rtr/tInsideOutsidePcr(l 1,s 10)Pcr(l 1,s 10)rtr/tInsideOutsidePcr(l 1,s 10)Pcr(l 1,s 0336load of models are presented in Table 5 and Fig. 12. It isobvious that imperfections can reduce the buckling loadof ring-stiffened cylindrical shells and also as the radiusof the shells increases, Circular symmetricalimperfections have more effect on buckling strength.Herein W denotes the imperfection amplitude (m).Table 5.Buckling load of imperfect ring-stiffened cylindrical shellsunder axial compressionL 2 ,s 10imprefect Ring-stiffened shell(imperfection between stiffners)r 2.5 mFig. 10. Axial buckling loads of the internal and external stringerstiffened cylindrical shells under axial compression (r 2.5m)Fig. 11. Axial buckling loads of the internal and external stringerstiffened cylindrical shells under axial compression (r 5m)2.5, 5, 7.5 m and the height of 10m and thickness 2cmwere modeled. For each of them, stiffeners with the 10 cmwidth in the distance of 2 meter were considered. Circularsymmetrical imperfections at the height of 1, 3, 5, 7 and 9m with different amplitude are applied. Axial buckling24tww/t0.020.0250.020.02r 5 m6r 7.5 mPcr(10N)6Pcr(10 241.0080.020086.09536165.1453241.355526151.32
Journal of Structural Engineering and Geotechnics, 2 (2), 19-28, Summer 2012Fig. 13. Buckling load of the stringer-stiffened cylindrical shells withsymmetrical imperfections between stiffenersTo investigate the effects of symmetrical imperfectionsbetween stiffeners on the buckling of the stringerstiffened shells, two cylindrical shell with radius of 2.5, 5m and the height of 10m and thickness 2cm weremodeled. For each of them, stiffeners with the 10 cmwidth in the distance of 1 meter were considered.Symmetrical imperfections between stiffeners withdifferent amplitude are applied. Buckling loads arepresented in Table 6 and Fig. 13. Results shows thatsymmetrical imperfections between stiffeners doesn’thave much effect on buckling load of the stringerstiffened cylindrical shellsFig. 12. Buckling load of the ring-stiffened cylindrical shells withsymmetrical imperfections between stiffenersTable 6. Buckling load of imperfect stringer-stiffened cylindrical shellsunder axial compressionL 1,s 10imperfect Stringer-stiffened shell(imperfection between 1.251.110.90.750.60.50.40.30r 2.563.3.2. Imperfection between stiffeners and shellr 5.0To study the effects of symmetrical imperfectionsbetween stiffeners and shell on the buckling of the ringstiffened shells, two cylindrical shells with radius of 2.5, 5m and the height of 10m and thickness 2cm weremodeled. For each of them, stiffeners with the 10 cmwidth in the distance of 1 and 2 meter were considered.Symmetrical imperfections between stiffeners and shellwith different amplitude are applied. Buckling load of themodels are presented in Tables7 and 8. Results indicatesthat as the radius of the shells increases, symmetricalimperfections have more effect on buckling strength(seeFig. 14) and also the more stiffeners are used, the lesssensitivity observed in buckling load of shells despite ofimperfections are increased(see Fig. 15).6Pcr(10 N)Pcr(10 78.239325
A. Nobakht NaminTable 7. Buckling load of imperfect ring-stiffened cylindrical shellsunder axial compression (L 2 m)Table 8. Buckling load of imperfect ring-stiffened cylindrical shellsunder axial compression (L 1 m)L 2 ,s 10L 1 ,s 10imperfect Ring-stiffened shell(imperfection between stiffeners and .110.90.750.60.50.40.30r 2.5 m6Pcr(10 83.92486.1668886.0201686.09536imperfect Ring-stiffened shell(imperfection between shell and stiffeners)r 5 m6Pcr(10 50.0120.010.0080.00601.251.110.90.750.60.50.40.30r 2.5 m6r 5 m6Pcr(10 N)Pcr(10 037166.0166Fig. 14. Buckling load of the ring-stiffened cylindrical shells withsymmetrical imperfections between stiffeners and shellTo study the effects of symmetrical imperfectionsbetween stiffeners and shell on the buckling of thestringer-stiffened shells, two cylindrical shell with radiusof 2.5, 5 m and the height of 10m and thickness 2cm weremodeled. For each of them, stiffeners with the 10 cmwidth in the distance of 2 meter were considered. Circularsymmetrical imperfections between stiffeners and shell atthe height of 1, 3, 5, 7 and 9 m with different amplitudeare applied. Buckling load of the models is presented inTable 9. Results show that imperfections betweenstiffeners and shell can reduce the buckling load ofstringer-stiffened cylindrical shells and also as the radiusof the shells increases, symmetrical imperfections havemore effect on buckling strength(see Fig. 16).Fig. 15. Buckling load of the ring-stiffened cylindrical shells withsymmetrical imperfections between stiffeners and shell4.ConclusionNonlinear static analyses were carried out to investigatethe effects of ring and stringer stiffeners with symmetricalimperfections on axial buckling of cylindrical shells.Results show that:When the distance of the ring stiffeners reduces, the shellbuckling strength increases but it doesn't have much effectunless the stiffeners are too close to each other. However,in stringer-stiffened shells the more stiffeners is used, themore buckling strength is observed.26
Journal of Structural Engineering and Geotechnics, 2 (2), 19-28, Summer 2012Increasing stiffeners’ width doesn’t have enough effect onthe buckling strength of the ring-stiffened shells duo touniform axial compression but in stringer-stiffened shells,the stiffeners’ width addition increases the axial loadbuckling strength.stiffeners have more buckling strength under axialcompression against outside ones.Imperfections between stiffeners can reduce the bucklingload of ring-stiffened cylindrical shells as the radius of theshells increases. Also symmetrical imperfections betweenstiffeners do not have much effect on buckling load of thestringer-stiffened cylindrical shells.As the radius of the shells increases, symmetricalimperfections between ring stiffeners and shell have moreeffects on buckling strength but they reduce when themore stiffeners are used. In stringer-stiffened shells,imperfections between stiffeners and shells are effectivewhen the shell radius increases.Table 9. Buckling load of imperfect stringer-stiffened cylindrical shellsunder axial compressionL 2 ,s 10Imperfect Stringer-stiffened shell(imperfection in 1.251.110.90.750.60.50.40.30r 2.56r 5.06Pcr(10 N)Pcr(10 67.3363References[1] NimaRahmania, Mehran S. Razzaghi*b, Mahmoud Hosseinic.“Buckling of cylindrical steel shells with randomimperfections due to Global Shear”. Journal of structuralengineering and geotechnics, Fall 2011, 1(2), 39-43.[2] Rotter J.M (2004), “Cylindrical shells under axialcompression”; Buckling of Thin Metal Shells; pp 42-87sponpress, London.[3] M. Shariati, M. Sedighi, J. Saemi, H.R. Eipakchi, H.R.Allahbakhsh. Exprimental study on ultimate strength ofCK20 “steel cylindrical panels subjected to compressiveaxial load.” Archives of civil and mechanical engineering(2010), Vol X, No. 2.[4] Das P.K., Thavalingam A., Bai Y.(2003). “Buckling andultimate strength criteria of stiffened shells under combinedloading for reliability analysis.” Thin-Walled Structures 41, .69–88.[5] Rotter J.M (2004), “Stiffened Cylindrical Shells”; Bucklingof Thin Metal Shells; 286-343 spon press, London.[6] Singer, J., M. Baruch and O. Harari, “On the stability ofeccentrically stiffened cylindrical shells under axialcompression”, Internat. J. Solids Structures, 3 (1967), 445470.[7] Singer, J., J. Arbocz and C. D. Babcock, Jr., “Buckling ofimperfect stiffened cylindrical shells under axialcompression”, AIAA J., 9 (1971), 68 - 75.[8] Weiler, T., J. Singer and S. C. Batterman,“ Influence ofeccentricity of loading on buckling of stringer-stiffenedcylindrical shells”, Thin-Shell Structures, Theory,Experiment, and Design, Ed. Y. C. Fung and E. E. Sechler(1974), 305-324.[9] Rosen, A. and J. Singer, “Vibrations and buckling ofeccentricaUy loaded stiffened cylindrical shells”, Exp.Mech., 16 (1976), 88-94.[10] Singer, J. and A. Rosen, “The influence of boundaryconditions on the buckling of stiffened cylindrical shells,Buckling of Structures”, Ed. B. Budiansky (1976), 225- 250.[11] Rosen, A. and J. Singer, “Vibrations and buckling of axiallyloaded stiffened cylindrical shells with elastic restraints”,Internet J. Solids Structures, 12 (1976), 577-588.[12] Weller, T. and J. Singer, “Experimental studies on thebuckling under axial compression of integrally stringerstiffened circular cylindrical shells”, J. Appl. Mech., 44(1977), 721 - 730.[13] Singer, J. and H. Abramovich, “vibration techniques fordefinition of practical boundary conditions in stiffenedshells”, AIAA J., 17 (1979), 762-769.Fig. 16. Buckling load of the stringer-stiffened cylindrical shells withsymmetrical imperfections between stiffeners and shellUsing ring-stiffeners inside or outside the cylindricalshells doesn’t change the axial buckling load. But instringer-stiffened cylindrical shells using internal27
A. Nobakht Namin[14] ShenHui-shen, Pin Zhou & Tie-yun Chen, “PostbucklingAnalysis of Stiffened Cylindrical Shells under CombinedExternal Pressure and Axial Compression”.Thin - WalledStructures 15 (1993) 43-63.[15] Park Chi-Mo and Dong-MinPark.“Ultimate StrengthAnalysis of Ring-stiffened Cylinders with InitialImperfections.” The Thirteenth International Offshore andPolar Engineering Conference. Honolulu, Hawaii, USA,May 2003. 435-440.[16] Krasovsky V.L. and Kostyrko V.V., “Experimentalstudying of buckling of stringer cylindrical shells underaxial compression. Thin”-Walled Structures 45 (2007) 877–882.[17]ANSYS (Ver 5.4), User manual, ANSYS INC.28
in stringer-stiffened shells because the postbuckling zone slope becomes less. As a result more instability is observed(see Figs. 6 and 7). Fig. 4. Buckling loads of the ring- stiffened and stringer-stiffened cylindrical shells with different width Fig. 5. Buckling and postbuckling of the ring- stiffened cylindrical shells with different width
DIC is used to capture buckling and post-buckling behavior of large composite panel subjected to compressive loads DIC is ideal for capturing buckling modes & resulting out-of-plane displacements Provides very useful insight in the transition regime from local skin buckling to global buckling of panel
numerical post-buckling critical load is more conservative than that obtained in physical tests [4,5,6].Typical load-shorting of stiffened structure undergoing buckling and post-buckling response are shown in Figure 3 where corresponding simplifications have been overlaid indicating the k1 pre-buckling, k2 post-buckling, k3 collapse
Fig. 13.1 Normalized buckling moment vs. buckling mode half-wavelength for a lipped channel 13.1.2 Local buckling via plate stability As discussed at length in Chapter 4, the classical method for determining local stability of thin-walled cross-sections is to break the
sustain dynamic pulse loadings based on difierent dynamic stability criteria is discussed as well. Keywords: Thin{walled plate structures, dynamic buckling, pulse load 1. Introduction The problem of dynamic buckling of thin walled structures such as shells and plates subjected to in{plan
post-buckling conditions. The results without considering any kind of imperfection, are closed and in good agreement with the tests in terms of buckling and post-buckling stiffness, as well as of collapse loads. Jiang et al. [13] studied the buckling of panels subjected to compressive stress using the differential quardrature element method.
written by Simitses [39] or Grybos [40]. It seems that the analysis of dynamic buckling of thin-walled structures, especially structures with flat walls is not sufficiently investigated. There is a lack of both single-and multimodal analysis of dynamic buckling of columns with complex cross-sections made of thin flat walls.
Accurate Simulation of Collapse) [2], was carried out to explore the accurate and reliable analysis methods of post-buckling up to collapse, and a series of simulation principles for buckling behaviours were investigated. Furthermore, numerous experimentations on stiffened panels [3-5] and closed
Keywords with the- Agile software development, Scrum I. INTRODUCTION Scrum [16, 29] is the most often used [6, 30, 31] agile [10] software development methodology among teams that utilize an agile methodology. A large-scale survey [31] deployed in the software engineering industry from June/July 2008 received 3061 respondents from 80 different countries. For the question “Which Agile .
