Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

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• 作者：Lei Zhang 张磊 ; Zhen-cai Zhu 朱真懿/a> ; Gang Shen 沈刚…
• 刊名：Journal of Central South University
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：22
• 期：11
• 页码：4219-4227
• 全文大小：1,116 KB
• 参考文献：[1]LASHGARI A, FOULADGAR M M, YAZDANI-CHAMZINI A, SKIBNIEWSKI M J. Using an integrated model for shaft sinking method selection [J]. Journal of Civil Engineering and Management, 2011, 17(4): 569–580.CrossRef
  [2]GUY J, THABANE M. Technology, ethnicity and ideology: Basotho miners and shaft-sinking on the South African gold mines [J]. Journal of Southern African Studies, 1988, 14(2): 257–278.CrossRef
  [3]KIM Y Y, KIM J H. Thin-walled closed box beam element for static and dynamic analysis [J]. International Journal for Numerical Methods in Engineering, 1999, 45(4): 473–490.MATH CrossRef
  [4]PAGANI A, BOSCOLO M, BANERJEE J R, CARRERA E. Exact dynamic stiffness elements based on one-dimensional higher-order theories for free vibration analysis of solid and thin-walled structures [J]. Journal of Sound and Vibration, 2013, 332(23): 6104–6127.CrossRef
  [5]HAMDOUNI A, KATILI I, MAKNUN I J, MILLET O. Analytical and experimental analysis of an asymptotic thin-walled beam model [J]. European Journal of Environmental and Civil Engineering, 2013, 17(1): 1–18.CrossRef
  [6]SARAVIA M C, MACHADO S P, CORTINEZ V H. A consistent total Lagrangian finite element for composite closed section thin walled beams [J]. Thin-walled Structures, 2012, 52(3): 102–116.CrossRef
  [7]SARAVIA M C, MACHADO S P, CORTÍNEZ V H. A consistent total Lagrangian finite element for composite closed section thin walled beams [J]. Thin-Walled Structures, 2012, 52(1): 102–116.CrossRef
  [8]ABAMBRES M, CAMOTIM D, SILVESTRE N, ROSMUSSEN K J R. GBT-based structural analysis of elastic-plastic thin-walled members [J]. Computers & Structures, 2014, 136(3): 1–23.CrossRef
  [9]RADOS J S A J. A critical review of Vlasov’s general theory of stability of in-plane bending of thin-walled elastic beams [J]. Meccanica, 2001, 36(2): 177–190.MATH MathSciNet CrossRef
  [10]ZHANG S H, LYONS L P R. A thin-walled box beam finite element for curved bridge analysis [J]. Computers & Structures, 1984, 18(6): 1035–1046.MATH CrossRef
  [11]AMBROSINI R D, RIERA J D, DANESI R F. A modified Vlasov theory for dynamic analysis of thin-walled and variable open section beams [J]. Engineering Structures, 2000, 22(8): 890–900.CrossRef
  [12]LUO Q Z, LI Q S. Shear lag of thin-walled curved box girder bridges [J]. Journal of Engineering Mechanics-ASCE, 2000, 126(10): 1111–1114.CrossRef
  [13]YU W, HODGES D H, VOLOVOI V V, FUCHS E D. A generalized Vlasov theory for composite beams [J]. Thin-Walled Structures, 2005, 43(9): 1493–1511.CrossRef
  [14]PIOVAN M T, CORTINEZ V H, ROSSI R E. Out-of-plane vibrations of shear deformable continuous horizontally curved thin-walled beams [J]. Jornal of Sound and Vibration, 2000, 237(1): 101–118.CrossRef
  [15]FU C C, HSU Y T. The development of an improved curvilinear thin-walled Vlasov element [J]. Computers & Structures, 1995, 54(1): 147–159.MATH CrossRef
  [16]WALDRON P. Elastic analysis of curved thin-walled girders including the effects of warping restraint [J]. Engineering Structures, 1985, 7(2): 93–104.CrossRef
  [17]BAO S H, ZHOU J. Structural mechanics of thin-walled bars [M]. Beijing: China Architecture & Building Press, 2005: 93–99. (in Chinese)
  [18]HUANG J Y. Torsional analysis of thin-walled structures: Curved beams and skewly supported box beams [M]. Beijing, China Railway Publishing House, 1983: 54–60. (in Chinese)
  [19]CHAN S L. Geometric and material non-linear analysis of beamcolumns and frames using the minimum residual displacement method [J]. International Journal for Numerical Methods in Engineering, 1988, 26(12): 2657–2669.MATH CrossRef
  [20]ZHANG Y H, LIN L X. Initial parameter method for analyzing shear lag effect of thin-walled box girders [J]. Engineering Mechanics, 2013, 30(8): 205–211.
  [21]SCHAFER B W, ÁDÁNY S. Buckling analysis of cold-formed steel members using CUFSM: Conventional and constrained finite strip methods [C]// Eighteenth International Specialty Conference on Cold-formed Steel Structures. Orlando: University of Missouri-Rolla, 2006: 39–54.
  [22]LUO Q Z, TANG J, LI Q S. Finite segment method for shear lag analysis of cable-stayed bridges [J]. Journal of Structural Engineering, 2002, 128(12): 1617–1622.CrossRef
  [23]ZHOU B W, JIANG L Z, LIU Z J, LIU X J. Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag [J]. Journal of Central South University, 2012, 19(9): 2650–2655.CrossRef
  [24]CHANG S T, YUN D. Shear lag effect in box girder with varying depth [J]. Journal of Structural Engineering-ASCE, 1988, 114(10): 2280–2292.CrossRef
  [25]LOFRANO E, PAOLONE A, RUTA G. A numerical approach for the stability analysis of open thin-walled beams [J]. Mechanics Research Communications, 2013, 48(1): 76–86.CrossRef
  [26]TIMOSHENKO S, GOODIER J N. Theory of elasticity [M]. New York: McGraw-Hill, 1951: 61–66.
  [27]YOON K Y, PARK N H, CHOI Y J, KANG Y J. Natural frequencies of thin-walled curved beams [J]. Finite Elements in Analysis and Design, 2006, 42(13): 1176–1186.CrossRef
  
• 作者单位：Lei Zhang 张磊 (1)
  Zhen-cai Zhu 朱真才 (1) (2)
  Gang Shen 沈刚 (1) (2)
  Guo-Hua Cao 曹国华 (1) (2)
  
  1. School of Mechanical and Electrical Engineering, China University of Mining & Technology, Xuzhou, 221008, China
  2. Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining & Technology, Xuzhou, 221008, China
  
• 刊物类别：Engineering
• 刊物主题：Engineering, general
  Metallic Materials
  Chinese Library of Science
  
• 出版者：Central South University, co-published with Springer
• ISSN：2227-5223

文摘

For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.