Abstract
In this study, we use a large-scale parameter analysis and linear regression method to characterize the static stability of Kiewitt-sunflower-type single-layer reticulated spherical shell. Based on more than 15,000 numerical cases of elastic–plastic load–displacement process, and the investigations on the influence of buckling and instability mode, rise-span and ring-numbers ratio, efficiency of the structure, load distribution, support conditions, size of the initial geometric imperfection and distribution patterns are proceeded. We summarize the key effect for stable performance of structure, and develop the formulation to calculate the ultimate capacity of stability. The results show that Kiewitt-sunflower type single-layer reticulated spherical shell is sensitive to defect, and different distribution patterns of geometry defect lead to different structural buckling. The ultimate stability bearing capacity can be improved by increasing the rise-span and ring-numbers ratio. The asymmetrical load distribution has little effect on the stability. The most unfavorable eigenmode is arbitrary, and it is generally not the lowest order. We summarize the key effect for stable performance of structure, and develop the formulation to calculate the ultimate capacity of stability.
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References
Bruno, L., Sassone, M., & Venuti, F. (2016). Effects of the Equivalent Geometric Nodal Imperfections on the stability of single layer grid shells. Engineering Structures, 112, 184–199.
Chen, G., Zhang, H., Rasmussen, K. J. R., et al. (2016). Modeling geometric imperfections for reticulated shell structures using random field theory. Engineering Structures, 126, 481–489.
Chen, X., & Shen, S. Z. (1993). Complete load-deflection response and initial imperfection analysis of single-layer lattice dome. International Journal of Space Structures, 8(4), 271–278.
Fan, F., Cao, Z., & Shen, S. (2010b). Elasto-plastic stability of single-layer reticulated shells. Thin-Walled Structures, 48(10–11), 827–836.
Fan, F., Wang, D., Zhi, X., et al. (2010a). Failure modes of reticulated domes subjected to impact and the judgment. Thin-Walled Structures, 48(2), 143–149.
Fan, F., Yan, J., & Cao, Z. (2012a). Elasto-plastic stability of single-layer reticulated domes with initial curvature of members. Thin-Walled Structures, 60, 239–246.
Fan, F., Yan, J., & Cao, Z. (2012b). Stability of reticulated shells considering member buckling. Journal of Constructional Steel Research, 77, 32–42.
Feng, R., Liu, F., Yan, G., et al. (2017). Mechanical behavior of Ring-sleeve joints of single-layer reticulated shells. Journal of Constructional Steel Research, 128, 601–610.
Ge, H. B., Wan, H. P., Zheng, Y. F., et al. (2020). Experimental and numerical study on stability behavior of reticulated shell composed of plate members. Journal of Constructional Steel Research, 171, 106102.
Guan, Y., Virgin, L. N., & Helm, D. (2018). Structural behavior of shallow geodesic lattice domes. International Journal of Solids and Structures, 155, 225–239.
Han, Q., & Liu, X. (2004). Ultimate bearing capacity of the welded hollow spherical joints in spatial reticulated structures. Engineering Structures, 26(1), 73–82.
He, Y. J., Wang, J. X., Zhou, X. H., et al. (2020). Static properties and stability of segmentally prestressed cylindrical reticulated mega-structures. Thin-Walled Structures, 155, 106949.
He, Y., Zhou, X., & Liu, D. (2014). Research on stability of single-layer inverted catenary cylindrical reticulated shells. Thin-Walled Structures, 82, 233–244.
JGJ7-2010. (2010). Technical specification for space frame structures. China Architecture Building Press.
Kashani, M., & Croll, J. G. A. (1994). Lower bounds for overall buckling of spherical space domes. Journal of Engineering Mechanics, 120(5), 949–970.
Li, W., Zhi, X., Wang, D., et al. (2019). Static stability analysis of a reticulated shell with a roofing system. Engineering Structures, 185, 315–331.
Li, X. L., & Ji, J. (2012). Nonlinear stability analysis for schwedler reticulated dome. Applied Mechanics and Materials, 182–183, 1609–1612.
Liu, H., Ding, Y., & Chen, Z. (2017). Static stability behavior of aluminum alloy single-layer spherical latticed shell structure with Temcor joints. Thin-Walled Structures, 120, 355–365.
Liu, H., Zhang, W., & Yuan, H. (2016). Structural stability analysis of single-layer reticulated shells with stochastic imperfections. Engineering Structures, 124, 473–479.
Luo, Y. F., Shen, Z. Y., & Hu, X. R. (1995). Experimental study on elastoplastic stability of single layer reticulated shells. China Civil Engineering of Journal, 28(4), 33–40. [in Chinese].
Ma, H., Yu, L., Fan, F., et al. (2019). Mechanical performance of an improved semi-rigid joint system under bending and axial forces for aluminum single-layer reticulated shells. Thin-Walled Structures, 142, 322–339.
Ma, J., Fan, F., Zhang, L., et al. (2018). Failure modes and failure mechanisms of single-layer reticulated domes subjected to interior blasts. Thin-Walled Structures, 132, 208–216.
Shan, Z. W., Ma, H. H., Yu, Z. W., et al. (2020). Dynamic failure mechanism of single-layer reticulated (SLR) shells with bolt-column (BC) joint. Journal of Constructional Steel Research, 169, 106042.
Shen, S. Z. (1999). Design formulas for stability analysis of Reticulated shells. In S. L. Chan & J. G. Teng (Eds.), Advances in steel structures (ICASS ’99) (pp. 51–62). Elsevier.
Tian, L., Li, Q., Zhong, W., et al. (2019). Effects of the rise-to-span ratio on the progressive collapse resistance of Kiewitt-6 single-layer latticed domes. Engineering Failure Analysis, 106, 104158.
Wang, D. Z., Zhi, X. D., Fan, F., et al. (2017). The energy-based failure mechanism of reticulated domes subjected to impact. Thin-Walled Structures, 119, 356–370.
Wu, Q. Y., Wang, H. J., Qian, H. L., et al. (2020). Effect of insufficient screwing depth of bolt on mechanical behavior of bolt-ball joint and stability of single-layer reticulated shell. Engineering Structures, 213, 110590.
**ong, Z., Guo, X., Luo, Y., et al. (2017a). Elasto-plastic stability of single-layer reticulated shells with aluminium alloy gusset joints. Thin-Walled Structures, 115, 163–175.
**ong, Z., Guo, X., Luo, Y., et al. (2017b). Experimental and numerical studies on single-layer reticulated shells with aluminium alloy gusset joints. Thin-Walled Structures, 118, 124–136.
Yamada, S., Takeuchi, A., Tada, Y., et al. (2001). Imperfection-sensitive overall buckling of single-layer lattice domes. Journal of Engineering Mechanics, 127(4), 382–386.
Yamashita, T., & Kato, S. (2001). Elastic buckling characteristics of two-way grid shells of single layer and its application in design to evaluate the non-linear behavior and ultimate strength. Journal of Constructional Steel Research, 57(12), 1289–1308.
Yan, J., Qin, F., Cao, Z., et al. (2016). Mechanism of coupled instability of single-layer reticulated domes. Engineering Structures, 114, 158–170.
Zhang, Q., Zhang, Y., Yao, L., et al. (2017). Finite element analysis of the static properties and stability of a 800 m Kiewitt type mega-latticed structure. Journal of Constructional Steel Research, 137, 201–210.
Zheng, Y., Luo, Y., Yang, C., et al. (2019). Analysis of stability against rotation of a spherical shell structure subjected to buoyancy. Thin-Walled Structures, 43, 106236.
Zhou, X., He, Y., & Xu, L. (2009). Formation and stability of a cylindrical ILTDBS reticulated mega-structure braced with single-layer latticed membranous shell substructures. Thin-Walled Structures, 47(5), 537–546.
Zhu, S. J., Ohsaki, M., Guo, X. N., et al. (2020). Shape optimization for non-linear buckling load of aluminum alloy reticulated shells with gusset joints. Thin-Walled Structures, 154, 106830.
Funding
This study was funded by Guangxi Natural Science Foundation (2018JJB160052), Application of key technology in building construction of prefabricated steel structure (BB30300105), Research grant for 100 Talents of Guangxi Plan, The starting research grant for High-level Talents from Guangxi University, Science and Technology Major Project of Guangxi Province (AA18118055), and the Luxembourg National Research Fund for Intuitive modeling and SIMulation platform (IntuiSIM) (PoC17/12253887).
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Yu, P., Yun, W., Bordas, S. et al. Static Stability Analysis of Single-Layer Reticulated Spherical Shell with Kiewitt-Sunflower Type. Int J Steel Struct 21, 1859–1877 (2021). https://doi.org/10.1007/s13296-021-00539-1
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DOI: https://doi.org/10.1007/s13296-021-00539-1