Vol. 21, No. 1, pp. 64-72 (2025)
METHOD OF IMPERFECTION RANDOM FIELD CONSTRUCTION FOR
WELDED CYLINDRICAL SHELL BASED ON SMALL SAMPLE
Hong-Fei Fu 1, Yu-Hong Shi 1, *, Wei-Xiu Xv 1, Fan Yang 1, Hao Yang 2 and Liang-Liang Jiang 1
1 Beijing Institute of Astronautical Systems Engineering, Beijing 100076, China
2 State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment,
Dalian University of Technology, Dalian 116023, China
*(Corresponding author: E-mail:This email address is being protected from spambots. You need JavaScript enabled to view it.)
Received: 14 July 2024; Revised: 15 December 2024; Accepted: 16 December 2024
DOI:10.18057/IJASC.2025.21.1.6
 View Article |
Export Citation: Plain Text | RIS | Endnote |
ABSTRACT
The initial geometrical imperfections of thin-walled cylindrical shell structures are important factors that cause the actual bearing capacity of such products to deviate from the theoretical value. In recent years, with the development of digital image measurement technology, it is possible to obtain geometric imperfections(GIs) through the measurement of the real geometric shape of the product, and it is possible to accurately predict the structural load-bearing capacity by considering the imperfections. On this basis, the initial GIs random field can then be considered to carry out thin-walled cylindrical shell load carrying capacity simulation targeting to obtain the strength distribution, and the lower limit of structural strength can be determined scientifically through a probabilistic approach..In this paper, based on Fourier series method, a modeling method of imperfection random field considering geometrical imperfection features is proposed for welded plates of carrier rocket tank. In the first stage, in order to solve the problem of large GIs characterization parameters, a GIs characterization method based on simplified Fourier coefficients is proposed, and an evaluation criterion based on determination coefficient (R2) and characterization accuracy (RP) is established. In the second stage, according to the simplified GIs, a dual construction method based on the waveform and amplitude of the distribution of sample GIs is innovatively proposed. And according to the structural characteristics, a single panel is used as a sample to achieve sample expansion. It solves the problem of uncertain random field construction of such structure morphology under the condition of small sample. Finally, the method is applied to the actual engineering structure, and the accuracy of the method is verified by the bearing capacity test data.
KEYWORDS
Plate welding, Thin-walled cylindrical shell, Geometric imperfections, Random field, Small sample
REFERENCES
[1] Chan S.L. and Chui P.T., Non-Linear Static and Cyclic Analysis of Steel Frames with Semi-Rigid Connections, Elsevier, New York, 2000.
[2] Liu S.W., Chan T.M., Chan S.L. and So. D.K.L., “Direct analysis of high-strength concrete-filled-tubular columns with circular & octagonal sections”, Journal of Constructional Steel Research, 129, 301-314, 2017.
[1] Shi, Y.H., Fu, H.F., Xv, W.X. and Yang, F., “Research status and prospects on the strength variation coefficient of large diameter thin-walled structures” , Structure and Environment Engineering, 51, 1-12, 2024. (in Chinese)
[2] Jiao, P., Chen, Z., Tang, X., Su, W., and Wu, J., “Design of axially loaded isotropic cylindrical shells using multiple perturbation load approach–Simulation and validation”, Thin-Walled Structures, 133, 1-16, 2018.
[3] Naraykin, O., Sorokin, F., and Kozubnyak, S., “Numerical Determination of the Splitting of Natural Frequencies of a Thin-Walled Shell with Small Nonaxisymmetric Imperfections of the Middle Surface”, Mathematical Models and Computer Simulations, 15(5), 850-862, 2023.
[4] Teter, A., and Kolakowski, Z., “Interactive buckling of wide plates made of Functionally Graded Materials with rectangular stiffeners”, Thin-Walled Structures, 171, 108750, 2022.
[5] Weingarten, V. I., Seide, P., and Peterson, J. P., “Buckling of thin-walled circular cylinders”, No. NASA-SP-8007, 1968.
[6] Hilburger, M. W., Nemeth, M. P., and Starnes Jr, J. H., “Shell buckling design criteria based on manufacturing imperfection signatures”, AIAA journal, 44(3), 654-663, 1968.
[7] Wang, B., Zhu, S., Hao, P., Bi, X., Du, K., Chen, B., Ma, X.,and Chao, Y. J., “Buckling of quasi-perfect cylindrical shell under axial compression: a combined experimental and numerical investigation”, International Journal of Solids and Structures, 130, 232-247, 1968.
[8] Hühne, C., Rolfes, R., Breitbach, E., and Teßmer, J., “Robust design of composite cylindrical shells under axial compression—simulation and validation”, Thin-walled structures, 46(7-9), 947-962, 2008.
[9] Wang, B., Hao, P., Li, G., Fang, Y., Wang, X., and Zhang, X., “Determination of realistic worst imperfection for cylindrical shells using surrogate model”, Structural and Multidisciplinary Optimization, 48, 777-794, 2013.
[10] Schmidt, H., “Stability of steel shell structures: General Report”, Journal of Constructional Steel Research, 55(1-3), 159-181, 2000.
[11] Arbocz, J., and Williams, J. G., “Imperfection surveys on a 10-ft-diameter shell structure”, AIAA Journal, 15(7), 949-956, 1977.
[12] Elishakoff, I., and Arbocz, J. [1982] “Reliability of axially compressed cylindrical shells with random axisymmetric imperfections”, International Journal of Solids and Structures, 18(7), 563-585.
[13] Wagner, H. N. R., Hühne, C., and Elishakoff, I., “Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression”, Thin-Walled Structures, 146, 106451, 2020.
[14] Kepple, J., Herath, M. T., Pearce, G., Prusty, B. G., Thomson, R., and Degenhardt, R., “Stochastic analysis of imperfection sensitive unstiffened composite cylinders using realistic imperfection models”, Composite Structures, 126, 159-173, 2015.
[15] Zhang, D., Chen, Z., Li, Y., Jiao, P., Ma, H., Ge, P., and Gu, Y., “Lower-bound axial buckling load prediction for isotropic cylindrical shells using probabilistic random perturbation load approach”, Thin-Walled Structures, 155, 106925, 2020.
[16] Arbocz, J., and Hol, J. M. A. M., “Collapse of axially compressed cylindrical shells with random imperfections”, AIAA journal, 29(12), 2247-2256, 1991.
[17] Gray, A., Wimbush, A., de Angelis, M., Hristov, P. O., Calleja, D., Miralles-Dolz, E., and Rocchetta, R., “From inference to design: A comprehensive framework for uncertainty quantification in engineering with limited information”, Mechanical Systems and Signal Processing, 165, 108210, 2022.
[18] Hotelling, H. “Analysis of a complex of statistical variables into principal components”, Journal of educational psychology, 24(6), 417, 1933.
[19] Ghanem, R. G., and Spanos, P. D., “Spectral stochastic finite-element formulation for reliability analysis”, Journal of Engineering Mechanics, 117(10), 2351-2372, 1991.
[20] Li, C. C., and Der Kiureghian, A., “Optimal discretization of random fields”, Journal of engineering mechanics, 119(6), 1136-1154, 1993.
[21] Lauterbach, S., Fina, M., and Wagner, W., “Influence of stochastic geometric imperfections on the load-carrying behaviour of thin-walled structures using constrained random fields”, Computational Mechanics, 62, 1107-1125, 2018.
[22] Luo, Y., Zhan, J., Xing, J., and Kang, Z., “Non-probabilistic uncertainty quantification and response analysis of structures with a bounded field model”, Computer Methods in Applied Mechanics and Engineering, 347, 663-678, 2019.
[23] Li, Z., Pasternak, H., and Geißler, K., “Buckling Analysis of Cylindrical Shells using Stochastic Finite Element Method with Random Geometric Imperfections”, ce/papers, 5(4), 653-658, 2022.
[24] Yang, H., Feng, S., Hao, P., Ma, X., Wang, B., Xu, W., and Gao, Q., “Uncertainty quantification for initial geometric imperfections of cylindrical shells: A novel bi-stage random field parameter estimation method”, Aerospace Science and Technology, 124, 107554, 2022.
[25] Fina, M., Weber, P., and Wagner, W., “Polymorphic uncertainty modeling for the simulation of geometric imperfections in probabilistic design of cylindrical shells”, Structural Safety, 82, 101894, 2020.
[26] Schenk, C. A., and Schuëller, G. I., “Buckling analysis of cylindrical shells with random geometric imperfections”, International journal of non-linear mechanics, 38(7), 1119-1132, 2003.
[27] Jianyu, L., Kun, Y., Bo, W., and Lili, Z., “A maximum entropy approach for uncertainty quantification of initial geometric imperfections of thin-walled cylindrical shells with limited data”, Chinese Journal of Theoretical and Applied Mechanics, 55(4), 1028-1038, 2023.
[28] Wu, J., Luo, Y. F., and Wang, L., “Inversion algorithm for the geometric imperfection distribution of existing reticulated structures”, Journal of Zhejiang University, 52(5), 864-872, 2018.
[29] Arbocz, J., and Hilburger, M. W., “Toward a probabilistic preliminary design criterion for buckling critical composite shells”, AIAA journal, 43(8), 1823-1827, 2005.
[30] Hilburger, M. W. [2018] “On the development of shell buckling knockdown factors for stiffened metallic launch vehicle cylinders,” In 2018 AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference , pp. 1990.
[31] Lovejoy, A. E., Hilburger, M. W., and Gardner, N. W., “Test and analysis of full-scale 27.5-foot-diameter stiffened metallic launch vehicle cylinders”, In 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2018.
[32] Hilburger, M., Haynie, W., Lovejoy, A., Roberts, M., Norris, J., Waters, W., and Herring, H., “Sub-scale and full-scale testing of buckling-critical launch vehicle shell structures,” In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, 2012.
[33] Hilburger, M., Lovejoy, A., Thornburgh, R., and Rankin, C., “Design and analysis of subscale and full-scale buckling-critical cylinders for launch vehicle technology development”, In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA , 2012.
[34] Hilburger, M. W., “Buckling of thin-walled circular cylinders”, No. NASA/SP-8007-2020/REV 2, 2020.