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Then, the effects of factors such as the prestress level, original imperfection size, original imperfection distribution, and addition of hoop tension rods on the stability of the TBCD model are investigated. The results show that the unstable loads of the TBCD are arranged from small to large in the following order: doubly nonlinearity with an original imperfection, geometry nonlinearity with an original imperfection, geometry nonlinearity without an original imperfection, and eigen buckling. In this case, the effects of geometry nonlinearity, material nonlinearity, and original imperfections must be comprehensively analyzed. The unstable mode of the TBCD depends on the loading form. Torsional buckling of the overall structure occurs under the symmetric load of \u2018Full live + full dead\u2019, while local out-of-plane buckling appears with the asymmetric load of \u2018Half live + full dead\u2019. With 2\u20133 times the loading integrations, the innermost tension beams change from stretch bending to pressurized bending, which causes the overall TBCD to become unstable. A small prestress level clearly decreases the stability of the TBCD, while a relatively large prestress level has little effect. When the original imperfection is greater than 1\/400 of the span, the stability of the TBCD is problematic. Comprehensively considering the impact of multiple defects is needed when analyzing the buckling of the TBCD. Adding hoop tension beams between the top ends of rods can effectively improve the integrity and stability of the TBCD.<\/jats:p>","DOI":"10.3390\/sym15091690","type":"journal-article","created":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T02:14:50Z","timestamp":1693793690000},"page":"1690","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Study on the Nonlinear Stability and Parametric Analysis of a Tensile\u2013Beam Cable Dome"],"prefix":"10.3390","volume":"15","author":[{"given":"Jianchen","family":"Guo","sequence":"first","affiliation":[{"name":"College of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingmin","family":"Ding","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Libin","family":"Wang","sequence":"additional","affiliation":[{"name":"Faculty of Architecture and Civil Engineering, Huaiyin Institute of Technology, Huaian 223001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yangjie","family":"Ruan","sequence":"additional","affiliation":[{"name":"National Prestress Engineering Research Center, Key Laboratory of C & PC Structures of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9455-1847","authenticated-orcid":false,"given":"Bin","family":"Luo","sequence":"additional","affiliation":[{"name":"National Prestress Engineering Research Center, Key Laboratory of C & PC Structures of Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113627","DOI":"10.1016\/j.engstruct.2021.113627","article-title":"Form-finding of tessellated tensegrity structures","volume":"252","author":"Song","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109159","DOI":"10.1016\/j.tws.2022.109159","article-title":"Control method for determining feasible pre-stresses of cable-struts structure","volume":"174","author":"Zhao","year":"2022","journal-title":"Thin-Walled Struct."},{"key":"ref_3","first-page":"134","article-title":"Nonlinear Numerical Analysis of Cable Dome Structure with Rigid Roof","volume":"26","author":"Zong","year":"2009","journal-title":"Eng. Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.ijsolstr.2019.01.035","article-title":"Multi-objective optimization for prestress design of cable-strut structures","volume":"165","author":"Ma","year":"2019","journal-title":"Int. J. Solids Struct."},{"key":"ref_5","first-page":"61","article-title":"Mechanical performance study of three joints tension-beam Geiger type cable dome structure","volume":"37","author":"Luo","year":"2016","journal-title":"J. Build. Struct."},{"key":"ref_6","unstructured":"Zuo, Q. (2017). Research on the Performance Analysis and the Key Technology of Construction of Levy-Patterned Tensile-Beam Cable Dome. [Master\u2019s Thesis, Southeast University]."},{"key":"ref_7","unstructured":"Pan, J. (2014). Initial Form and Structural Behavior Analysis on Cable Dome of Rigid Roof Supported by Single-Layer Cable. [Master\u2019s Thesis, Southeast University]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1739","DOI":"10.1007\/s40999-018-0331-y","article-title":"Experimental Study and Comparative Analysis of a Geiger-type Ridge-beam Cable Dome Structure","volume":"16","author":"Ding","year":"2018","journal-title":"Int. J. Civ. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Dong, F., and Zhang, H. (2022). Probabilistic Safety Factor Calculation of the Lateral Overturning Stability of a Single-Column Pier Curved Bridge under Asymmetric Eccentric Load. Symmetry, 14.","DOI":"10.3390\/sym14081534"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Dong, F., Gao, J., Hao, A., Wei, Y., Huang, X., Shi, F., and Zheng, K. (2022). A New Approach to Symmetry Reliability: Combination of Forward and Inverse Reliability Principle and Its Application to Frame Structures and Bamboo Bridges. Symmetry, 14.","DOI":"10.3390\/sym14020318"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106226","DOI":"10.1016\/j.aml.2020.106226","article-title":"A domain-decomposition generalized finite difference method for stress analysis in three-dimensional composite materials","volume":"104","author":"Wang","year":"2020","journal-title":"Appl. Math. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.compstruct.2019.01.041","article-title":"A robust B\u00e9zier based solution for nonlinear vibration and post-buckling of random checkerboard graphene nano-platelets reinforced composite beams","volume":"212","author":"Kabir","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/S0263-8223(97)00112-8","article-title":"Differential quadrature: A powerful new technique for analysis of composite structures","volume":"39","author":"Bert","year":"1997","journal-title":"Compos. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"108874","DOI":"10.1016\/j.tws.2021.108874","article-title":"Stability design of axially loaded stringer-stiffened moderately-thick cylindrical shells in steel tubular transmission towers","volume":"172","author":"Chen","year":"2022","journal-title":"Thin-Walled Struct."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Duan, M., Suo, X., Dong, F., Li, J., and Li, G. (2022). Research on the Control Method for the Reasonable State of Self-Anchored Symmetry Suspension Bridge Stiffening Girders. Symmetry, 14.","DOI":"10.3390\/sym14050935"},{"key":"ref_16","unstructured":"(2017). Code for Design of Steel Structures. Standard No. GB 50017-2017. (In Chinese)."},{"key":"ref_17","first-page":"1","article-title":"A Simplified Calculation Method for Initial Prestress of Levy Cable Domes with the Consideration of Self-Weight","volume":"26","author":"Dong","year":"2009","journal-title":"Eng. Mech."},{"key":"ref_18","first-page":"7","article-title":"Stability Analysis of Large Rise-span Ratio Special-shaped Single Layer Spherical Shells with Defects","volume":"38","author":"Jiang","year":"2022","journal-title":"Build. Sci."},{"key":"ref_19","unstructured":"(2010). Technical Specification for Spatial Grid Structure. Standard No. JGJ 7-2010. (In Chinese)."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1690\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:45:31Z","timestamp":1760129131000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1690"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,2]]},"references-count":19,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["sym15091690"],"URL":"https:\/\/doi.org\/10.3390\/sym15091690","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,2]]}}}