An Experimental Buckling Study of Column supported Cylinder Procedia Engineering 172 ( 2017 ) 823 – 830 Available online at www sciencedirect com 1877 7058 © 2017 The Authors Published by Elsevier Ltd[.]
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 172 (2017) 823 – 830 Modern Building Materials, Structures and Techniques, MBMST 2016 An experimental buckling study of column-supported cylinder Olgerts Ozolins*a, Kaspars Kalninsa a Riga Technical University, Institute of Materials and Structures, Riga, LV-1048, Latvia Abstract An accuracy of numerical prediction of buckling load of axially or locally loaded thin-walled circular shells was always been a challenge for engineers With the introduction of new materials and manufacturing methods, well known design rules can be too conservative in the case of buckling performance New advanced or more sophisticated analyses/design methods should be considered to fully utilize buckling load capacity of modern structural design The major factors which can affect numerical prediction of buckling load are combination of initial geometrical imperfections and shell imperfection sensitivity Shells having high imperfection to wall thickness ratio a/t are most affected, in contrast thicker shells are less sensitive The current study deals with less sensitive shell, subjected to combined axial/bending loading introduced by three support posts which acts locally introducing local skin buckling Prediction accuracy obtained by employing detailed finite element modeling of real case boundary conditions and interaction of involved components Combination of shell elements with 3D solid elements and utilization of contact algorithm for sliding spherical ball supports produce highly reliable buckling load experimental and numerical prediction © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license © 2016 The Authors Published by Elsevier Ltd (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-reviewunder under responsibility oforganizing the organizing committee of MBMST Peer-review responsibility of the committee of MBMST 2016 2016 Keywords: Buckling, composite cylindrical shells, numerical analyses Introduction A typical local buckling of column supports one may observe in frame supported silos design or in launcher structures, where booster loads form a specific compression load path to primary structure These structures by the scale and size is rarely tested and reported in literature with sufficient level of details thus designers are exposed to over conservative designs as nor does aerospace nor building design codes give a detailed estimate of such a load *Corresponding author: Olgerts Ozolins E-mail address: olgerts.ozolins@rtu.lv 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of MBMST 2016 doi:10.1016/j.proeng.2017.02.130 824 Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 cases An extensive review on shell buckling and particularly on the case covered by this paper is given by Teng [1] There were conducted number of studies in the 90`s covering mainly steel silos structures More recent study of column supported steel cylindrical structure was analyzed numerically by Hotała et al [2] Extensive studies on silos buckling problems was covered by Rotter [3] and integrated in Eurocodes Design of silos under various load conditions considering shell buckling was assessed by Zhao [4] As well as studies on eccentric discharge related buckling [5] In general observations from referred studies are summarized in Eurocode [6], but in relation to composite design there are the only option of Eurocode [7] on concrete structures Composite structures, in this case composite silos, should be designed according to specified Eurocode [8] section on silos Nevertheless Eurocode design practice explicitly allows designer to address material, loading imperfections and non-linearity as well as manufacturing process related issues as design criteria which properly treated may reduce the over conservative designs Therefore a study which address all those issues has been conducted and obtained numerical experimental validation show capacity potential for higher load carrying capacity or lighter/less expensive designs for the future Nomenclature ܲ ܲ LVDT ܴ ݐ ܧ௧ ܧ ܩଵଶ ݒଵଶ S1T/C SG Axial compressive load Critical buckling load for a perfect shell Linear variable differential transformer Radius Thickness Elastic modulus along the fiber / transverse direction, tension Elastic modulus along the fiber / transverse direction, compression Shear modulus Poisson`s ratio Strength along the fiber / transverse direction, tension and compression Strain gauge General description and manufacturing A tested specimen representing scaled down model of the free standing silos/reservoir type structure, considering three stand support, was manufactured of IM7/8552 pre-preg system General lay-up considered for shell consisted of 18 plies [0°/45°/-45°/90°/0°/90°/-45°/45°/0°]sym for shell structure with additional 12 plies [60°/0°/-60°/60°/0°/60°]sym for reinforcement area under the load support structure General geometry of shell shown on Fig.1 Fig Geometry of the shell Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 Instead of standard curing practice for IM7/8552 system, out-of-autoclave curing employed, skipping autoclave phase Different stages of manufacturing shown on Fig Shell made of IM7/8552 was manufactured employing stage intermediate debulking, with the purpose to eliminate slack in consecutive layers generated by entrapped air Three equally spaced reinforcement patches consisting of 12 additional layers were prepared and located on the shell before final vacuum bagging and curing Curing cycle for IM7/8552 system was carried out as specified by manufacturer, except autoclave and longer hold time at 180°C, Fig.3 Cure cycle temperature readings are carried out with two thermocouples, located on inside surface of the mandrel close to the top and in the middle, manufacturer cure curve shown on graph as green curve Fig Shell manufacturing on different stages Fig Curing cycle for shell made of IM7/8552 Reinforcement placed on the outside only, due to manufacturing aspects, such pre-preg co-curing and use of internal mandrel Height of the reinforcement patch was 200 mm Lower edge of the shell was not reinforced and left free during testing Support structures were CNC machined from EN AW 6082 aluminum blocks to desired shape, formed as concave and convex two piece structure matching shell geometry, attached to the shell structure on both outside and inside with PU (polyurethane) two component adhesive and bolted by DIN 912 M6 10.8 class bolts, Fig Quality control and thickness measurements were performed by employing ultrasound inspection equipment, as well as, initial geometry scan was performed by employing industrial 3D measurement system EXAscan scanner More detailed imperfection scanning results are given by Kalnins et al [9] 825 826 Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 Fig Shell structure with attached support blocks and casted upper boundary Experimental set-up To obtain desirable test height for shell a custom-made support frame for testing on INSTRON 8002 test frame was designed and produced Support ball bearing joints consists of 40 mm bearing ball and two conical seats at each side at each support point, see Fig Figure 5, shows FE analyses of deformations for design load of 125 kN Support frame mounted on INSTRON 8002 test frame allowed to obtain extra space for data acquisition by hiding lower grip/load cell assembly inside the cylindrical shell Fig Support frame for shell specimen, considers two out of three adjustable height seats to compensate non-parallel machine plates Shell was tested on servo hydraulic test frame, considering incremental displacement loading with rate of mm/min Shell was equipped with strain gauges equally spaced along the circumference near the top loading edge used to check uniform load distribution, Fig Additionally back to back strain gauges were located at predicted buckle spots - 45 mm at the center above support reinforcement patch upper edge, Fig 6, and used to detect buckling of the shell Shell were equipped with three LVDT located in-line with the supports, Fig Two adjustable support columns allowed to align shell upper edge to the machine plate, to allow simple shimming of the interface Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 827 Fig Strain gauge arrangement for tested specimen shell Fig Test set-up Experimental results and numerical validation Experimental and numerical load-shortening curves were compared on Fig Measured strain gauge readings are shown on Fig Due to non-uniform support translation it was considered to involve non-uniform loading in the finite element analyses It should be noted that only minor improvement in buckling load prediction was achieved, see Table whereas the complexity of numerical solution raise rapidly Numerical models 100 80 Load, kN EXPERIM ENT 60 FEM perfect model 40 20 0,00 0,50 1,00 1,50 2,00 Shortening, mm 2,50 3,00 Fig Load-shortening curve for experimental test and numerical analysis 828 Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 Table Experimental vs numerical predictions Load (kN) KDF Experimental test 93.57 0.96 FEM perf 97.45 FEM perf + loading imp 95.68 0.98 Fig.10 lower edge shows photogrammetry based buckling shape captured in comparison to the numerical analyses obtained for finite element model containing loading asymmetry It should be noted that photogrammetry approach can produce some scattered results due to presence of column support structure in point cloud caused by cleaning out support block and SG wiring In order to improve visualization of deformed state the reinforcement patch should be cut out too from the point cloud in order to provide as uniform surface as possible (patch was considered as out-ofplane deformation by 3-D processing software Autocad Recap 360 [10]) So photogrammetry based buckling shape captures can be used only for buckling shape observation, not actual out-of-plane deflection measurements Fig Loading edge SG readings and back-to-back SG readings for tested shell Numerical simulations were carried out on commercially available ANSYS [11] finite element code Additionally numerical model was corrected for non-uniform load distribution by applying actually measured LVDT translations to the corresponding supports, causing non-linear reaction force to develop associated to individual supports, Fig Obtained buckling predictions was presented in Table 1, as well as corresponding knockdown factors Numerical analyses was carried out with non-linear (Newton-Raphson large deformation solver) analyses under displacement control Numerical model represents FEM composed of SHELL281 shell elements used for shell structure blended with 3D solid elements SOLID186 employed for support structures made of aluminum/steel, Fig 11 Table Material properties used for the shell Strength Stiffness Mean value Mean value Std Deviation [%] T Std Deviation [%] E1 T 171.5 GPa 2.6 S1 2300 MPa 13.8 E1C 150.2 GPa 4.6 S1C 857 MPa 10.1 T E2 T 8.9 GPa 4.2 S2 40 MPa 20.4 E2C 9.4 GPa 10.9 S2C 203 MPa 3.9 G12 5.1 GPa 7.8 S12 51 MPa 8.4 v12 0.32 13 tply 0.1308 mm Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 829 Nodal plane of shell elements was shifted to cylinder inner surface to represent actual reinforcement patch and to connect with solid elements, Fig 11 Connection between shell and solid elements was realized as merging on coincident nodes Table 2, summarizes material properties used for finite element model Compression material properties were used for finite element analyses which even though produced in out of autoclave method [12] correlate with material properties provided in product data sheet [13,14] Fig 10 Buckling mode shape for shell – numerical versus photogrammetry measurements Three supports are realized as 3D solid modelled support block with spherical joint, which incorporate surface to surface sliding contact between concave conical support surface and support semi-sphere surface, with the reason to reproduce actual boundary conditions as precisely as possible Fig 11 3D solid support block and half of the spherical ball For model simplification both support block and semi-sphere were considered represented of steel, since this elements are deformation free Bottom surface of the spherical support (semi-sphere) is clamped (UX=UY=ROTX=ROTY=ROTZ=0), except loading direction UZ, via the coupled nodes for UZ Bottom surface of 830 Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 the spherical support (semi-sphere) is clamped (UX=UY=ROTX=ROTY=ROTZ=0), except loading direction UZ, via the coupled nodes for UZ Upper edge of the shell considered clamped (UX=UY=UZ=ROTX=ROTY=ROTZ=0) Coupled set UZ applied for the loading edge nodes for load extraction from single pilot node reaction force Bottom edge of the shell was left free Loading was considered as displacement controlled and applied equally for all three semi-sphere pilot nodes This was done with the purpose of capacity to apply non-uniform loading in accordance with LVDT displacement measurements during experimental test campaign Buckling load was extracted as a reaction force (FZ) for the upper edge coupled set master node Conclusions Even though the complexity of column support introduced buckling numerical and experimental tests are high the current research highlight that very good agreement between experimental and numerical prediction has been achieved This involved complex finite element model implementation which took into account the sensitivity to precise load application off-set eccentricity, which was not achieved during the preliminary studies employing simplified point support approach It was shown that structural robustness is relatively high as application of the loading imperfection didn`t cause structure to change the load/displacement pattern It was visually shown that photogrammetry may be a powerful tool for buckled mode shape extraction even though the capture could be partly blocked by adjacent structure References [1] J Teng, Buckling of Thin Shells: Recent Advances and Trends ASME Appl Mech Rev 49(4) (1996) 263-274 [2] E Hotała, Ł Skotny, Journal of Constructional Steel Research 96 (2014) 81–94 [3] Bulk Solids Handling: Equipment Selection and Operation Edited by Don McGlinchey [4] Y.Zhao et al., Thin-Walled Structures73 (2013) 337–349 [5] Adam J Sadowski and J Michael Rotter, A study of buckling in steel silos under eccentric discharge flows of stored solids, ASCE Journal of Engineering Mechanics 136(6) 769-776 [6] Eurocode 3: Design of steel structures - Part 1-6: Strength and stability of shell structures (2007) Comite Europeen de Normalisation (CEN) [7] Eurocode 4: Design of composite steel and concrete structures (2004) Comite Europeen de Normalisation (CEN) [8] Eurocode 3: Design of steel structures - Part 4-1: Silos (2007) Comite Europeen de Normalisation (CEN) [9] K Kalnins, O Ozoliņš, M.A Arbelo, R Degenhardt, S.G.P Castro, Verification study on buckling behaviour of composite cylinder with eccentric supports, 54th Israel Annual Conference on Aerospace Sciences (2014) 1216-1221 [10] Autodesk® ReCap 360™ [11] ANSYS® Academic Research, Release 16.2 [12] M.A Arbelo, K Kalnins, O Ozolins, E Skukis, S.G.P Castro, Degenhardt, R Experimental and numerical estimation of buckling load on unstiffened cylindrical shells using a vibration correlation technique, Thin-Walled Structures 94 (2015) 273-279 [13] E Clarkson, A comparison of Equivalence Criteria and Basis Values for HEXCEL 8552 IM7 Unidirectional Tape computed from the NCAMP shared database, NCP-RP-2013-015 N/C [14] G Jacobsen, Mechanical characterization of stretch broken carbon fiber materials – IM7 fiber in 8552 resin HEXCEL corp ... out-ofplane deformation by 3-D processing software Autocad Recap 360 [10]) So photogrammetry based buckling shape captures can be used only for buckling shape observation, not actual out -of- plane... down model of the free standing silos/reservoir type structure, considering three stand support, was manufactured of IM7/8552 pre-preg system General lay-up considered for shell consisted of 18 plies... for experimental test and numerical analysis 828 Olgerts Ozolins and Kaspars Kalnins / Procedia Engineering 172 (2017) 823 – 830 Table Experimental vs numerical predictions Load (kN) KDF Experimental