Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effects of longitudinal and transverse curvatures on optimal design of shell footbridge

  • Liu, Shiming (School of Civil Engineering and Communication, North China University of Water Resources and Electric Power) ;
  • Huang, Bin (School of Civil Engineering and Communication, North China University of Water Resources and Electric Power) ;
  • Xie, Yi Min (Centre for Innovative Structures and Materials, School of Engineering, RMIT University)
  • Received : 2021.03.26
  • Accepted : 2021.07.15
  • Published : 2021.10.10
⟨ Previous Next ⟩

Abstract

Shell bridges have attracted extensive interest in engineering research and practice. This paper aims to evaluate the effects of longitudinal and transverse curvatures on the optimal design of the shell bridge. For this purpose, a slant-legged steel shell footbridge with the same initial and target volumes of steel was chosen to build parametric geometric models with different curvature radii, and then topology optimization was carried out using the bi-directional evolutionary structural optimization (BESO) technique to obtain optimized designs with high structural stiffness. Furthermore, linear static analysis and eigenvalue analysis demonstrate that the displacement, von Mises effective stress, and the first-order vertical vibration frequency satisfied all the requirements of design regulations. Numerical results indicate that not only the longitudinal curvature but also the transverse curvature have a significant effect on the optimized designs of steel shell footbridge. While the mean compliance increased with the transverse curvature radius, it first decreased and then increased with the longitudinal curvature radius.

Keywords

Acknowledgement

This study was funded by the National Natural Science Foundation of China (51508189) and the China Scholarship Council (201808410438).

References

  1. Ansola, R., Canales, J., Tarrago, J.A. and Rasmussen, J. (2002), "An integrated approach for shape and topology optimization of shell structures", Comput. Struct., 80(5-6), 449-458. https://doi.org/10.1016/S0045-7949(02)00019-6.
  2. Artar, M., Catar, R. and Daloglu, A.T. (2017), "Optimum design of steel bridges including corrosion effect using TLBO", Struct. Eng Mech., 63(5), 607-615. https://doi.org/10.12989/sem.2017.63.5.607.
  3. Artar, M. and Daloglu, A.T. (2019), "Optimum design of steel space truss towers under seismic effect using Jaya algorithm", Struct. Eng Mech., 71(1), 1-12. https://doi.org/10.12989/sem.2019.71.1.001.
  4. Avetisyan, Z., Harutyunyan, D. and Hovsepyan, N. (2021), "Rigidity of a thin domain depends on the curvature, width, and boundary conditions", Appl. Math. Optim., 1-26. https://doi.org/10.1007/s00245-021-09746-y.
  5. Aydogdu, I. and Akin, A. (2014), "Optimum design of geodesic aluminum domes using firefly algorithm", Proceedings of the ACE 2014 11th International Congress on Advances in Civil Engineering, Istanbul, Turkey.
  6. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Meth. Appl. Mech. Eng., 71, 197-224. https://doi.org/10.1016/0045-7825(88)90086-2.
  7. Bendsoe, M.P. and Sigmund, O. (1995), Optimization of Structural Topology, Shape, and Material, Springer.
  8. Bendsoe, M.P. and Sigmund, O. (2007), Topology Optimization, World Scientific.
  9. Bertetto, A.M., Gabriele, S., Marmo, F. and Micheletti, A. (2020), "Shell and spatial structures: Between new developments and historical aspects", Curv. Layer. Struct., 7(1), 186-187. https://doi.org/10.1515/cls-2020-0015.
  10. Bletzinger, K.U. and Ramm, E. (1993), "Form finding of shells by structural optimization", Eng. Comput., 9(1), 27-35. https://doi.org/10.1007/BF01198251.
  11. Bourdin, B. (2001), "Filters in topology optimization", Int. J. Numer. Meth. Eng., 50(9), 2143-2158. https://doi.org/10.1002/nme.116.
  12. Briseghella, B., Fenu, L., Feng, Y., Mazzarolo, E. and Zordan, T. (2013), "Topology optimization of bridges supported by a concrete shell", Struct. Eng. Int., 23(3), 285-294. https://doi.org/10.2749/101686613X13363929988214.
  13. Congiu, E., Fenu, L. and Briseghella, B. (2021), "Comparison of form-finding methods to shape concrete shells for curved footbridges", Struct. Eng. Int., 1-9. https://doi.org/10.1080/10168664.2021.1878974.
  14. Dede, T. (2018), "Jaya algorithm to solve single objective size optimization problem for steel grillage structures", Steel Compos. Struct., 26(2), 163-170. https://doi.org/10.12989/scs.2018.25.2.163.
  15. Dede, T., Grzywinski, M. and Selejdak, J. (2020), "Continuous size optimization of large-scale dome structures with dynamic constraints", Struct. Eng. Mech., 73(4), 397-405. https://doi.org/10.12989/sem.2020.73.4.397.
  16. Ding, L., Shi, J., Wang, X., Sun, S. and Wu, Z. (2019), "Optimisation of a prestressed fibre-reinforced polymer shell for composite bridge deck", Struct. Infrastr. Eng., 15(4), 454-466. https://doi.org/10.1080/15732479.2018.1559866.
  17. Eirgash, M.A., Togan, V. and Dede, T. (2019), "A multi-objective decision-making model based on TLBO for the time-cost trade-off problems", Struct. Eng. Mech., 71(2), 139-151. https://doi.org/10.12989/sem.2019.71.2.139.
  18. Fauche, E., Adriaenssens, S. and Prevost, J.H. (2010), "Structural optimization of a thin-shell bridge structure", J. Int. Assoc. Shell Spat. Struct., 51(2), 153-160.
  19. Fenu, L., Briseghella, B. and Zordan, T. (2015), "Curved shell-supported footbridges", IABSE Conference on Structural Engineering, Geneva, The Netherlands, September.
  20. Fenu, L., Congiu, E., Lavorato, D., Briseghella, B. and Marano, G.C. (2019), "Curved footbridges supported by a shell obtained through thrust network analysis", J. Traff. Tran. Eng. (English Ed.), 6(1), 65-75. https://doi.org/10.1016/j.jtte.2018.10.007.
  21. Fenu, L., Congiu, E., Marano, G.C. and Briseghella, B. (2020), "Shell-supported footbridges", Curv. Layer. Struct., 7(1), 199-214. https://doi.org/10.1515/cls-2020-0017.
  22. Fujino, Y. and Siringoringo, D.M. (2016), "A conceptual review of pedestrian-induced lateral vibration and crowd synchronization problem on footbridges", J. Bridge Eng., 21(8), C4015001. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000822.
  23. Grzywinski, M., Dede, T. and Ozdemir, Y.I. (2019), "Optimization of the braced dome structures by using Jaya algorithm with frequency constraints", Steel Compos. Struct., 30(1), 47-55. https://doi.org/10.12989/scs.2019.30.1.047.
  24. Hassani, B., Tavakkoli, S.M. and Ghasemnejad, H. (2013), "Simultaneous shape and topology optimization of shell structures", Struct. Multidisc. Optim., 48(1), 221-233. https://doi.org/10.1007/s00158-013-0894-9.
  25. Huang, X. and Xie, M. (2010), Evolutionary Topology Optimization of Continuum Structures: Methods And Applications, John Wiley & Sons.
  26. Huang, X. and Xie, Y. (2007), "Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method", Finite Elem. Anal. Des., 43(14), 1039-1049. https://doi.org/10.1016/j.finel.2007.06.006.
  27. Kaveh, A. and Ilchi Ghazaan, M. (2018), "A new hybrid meta-heuristic algorithm for optimal design of large-scale dome structures", Eng. Optim., 50(2), 235-252. https://doi.org/10.1080/0305215X.2017.1313250.
  28. Kaveh, A. and Rezaei, M. (2015), "Optimum topology design of geometrically nonlinear suspended domes using ECBO", Struc. Eng. Mech., 56(4), 667-694. https://doi.org/10.12989/sem.2015.56.4.667.
  29. Kaveh, A. and Rezaei, M. (2016), "Topology and geometry optimization of different types of domes using ECBO", Adv. Comput. Des., 1(1), 1-25. https://doi.org/10.12989/acd.2016.1.1.001.
  30. Kaveh, A. and Talatahari, S. (2010), "An improved ant colony optimization for the design of planar steel frames", Eng. Struct., 32(3), 864-873. https://doi.org/10.1016/j.engstruct.2009.12.012.
  31. Kaveh, A. and Talatahari, S. (2010), "A novel heuristic optimization method: charged system search", Acta Mechanica, 213(3), 267-289. https://doi.org/10.1007/s00707-009-0270-4.
  32. Kaveh, A. and Talatahari, S. (2010), "Optimal design of Schwedler and ribbed domes via hybrid Big Bang-Big Crunch algorithm", J. Constr. Steel Res., 66(3), 412-419. https://doi.org/10.1016/j.jcsr.2009.10.013.
  33. Kaveh, A. and Talatahari, S. (2010), "Optimal design of skeletal structures via the charged system search algorithm", Struct. Multidisc. Optim., 41(6), 893-911. https://doi.org/10.1007/s00158-009-0462-5.
  34. Kaveh, A. and Talatahari, S. (2011), "Geometry and topology optimization of geodesic domes using charged system search", Struct. Multidisc. Optim., 43(2), 215-229. https://doi.org/10.1007/s00158-010-0566-y.
  35. Keil, A. and Straub, K. (2011), "Leicht und transparent-eine Glasbrucke in Lissabon", Stahlbau, 80(S1 1), 24-30. https://doi.org/10.1002/stab.201120004.
  36. Kimura, T. and Ohmori, H. (2008), "Computational morphogenesis of free form shells", J. Int. Assoc. Shell Spat. Struct., 49(3), 175-180.
  37. Kromoser, B. and Kollegger, J. (2020), "Efficient construction of concrete shells by pneumatic forming of hardened concrete: construction of a concrete shell bridge in Austria by inflation", Struct. Concrete, 21(1), 4-14. https://doi.org/10.1002/suco.201900169.
  38. Kutylowski, R. and Rasiak, B. (2014), "Application of topology optimization to bridge girder design", Struct. Eng. Mech., 51(1), 39-66. https://doi.org/10.12989/sem.2014.51.1.039.
  39. Lee, S.J. and Bae, J.E. (2008), "A study on the structural optimization for geodesic dome", J. Korean Assoc. Spat. Struct., 8(4), 47-55.
  40. Leissa, A. and Kadi, A. (1971), "Curvature effects on shallow shell vibrations", J. Sound Vib., 16(2), 173-187. https://doi.org/10.1016/0022-460X(71)90482-2.
  41. Li, Y. and Xie, Y.M. (2021), "Evolutionary topology optimization for structures made of multiple materials with different properties in tension and compression", Compos. Struct., 259, 113497. https://doi.org/10.1016/j.compstruct.2020.113497.
  42. Machelski, C. (2019), "Effects of surrounding earth on shell during the construction of flexible bridge structures", Studia Geotechnica et Mechanica, 41(2), 67-73. https://doi.org/10.2478/sgem-2019-0002.
  43. Maleska, T. and Beben, D. (2019), "Numerical analysis of a soil-steel bridge during backfilling using various shell models", Eng. Struct., 196, 109358. https://doi.org/10.1016/j.engstruct.2019.109358.
  44. Manko, Z.Z. and Beben, D. (2005), "Research on steel shell of a road bridge made of corrugated plates during backfilling", J. Bridge Eng., 10(5), 592-603. https://doi.org/10.1061/(ASCE)1084-0702(2005)10:5(592).
  45. Marmo, F., Demartino, C., Candela, G., Sulpizio, C., Briseghella, B., Spagnuolo, R., Xiao, Y., Vanzi, I. and Rosati, L. (2019), "On the form of the Musmeci's bridge over the Basento river", Eng. Struct., 191, 658-673. https://doi.org/10.1016/j.engstruct.2019.04.069.
  46. Mashayekhi, M. and Yousefi, R. (2021), "Topology and size optimization of truss structures using an improved crow search algorithm", Struct. Eng. Mech., 77(6), 779-795. https://doi.org/10.12989/sem.2021.77.6.779.
  47. Miskiewicz, M., Pyrzowski, L. and Sobczyk, B. (2020), "Short and long term measurements in assessment of FRP composite footbridge behavior", Mater., 13(3), 525. https://doi.org/10.3390/ma13030525.
  48. Nguyen, T.N., Hien, T.D., Nguyen-Thoi, T. and Lee, J. (2020), "A unified adaptive approach for membrane structures: Form finding and large deflection isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 369, 113239. https://doi.org/10.1016/j.cma.2020.113239.
  49. Papapetrou, V.S., Tamijani, A.Y., Brown, J. and Kim, D. (2019), "Correction to: Design optimization of hybrid FRP/RC bridge", Appl. Compos. Mater., 26(1), 271-271. https://doi.org/10.1007/s10443-018-9704-2.
  50. Picelli, R., Sivapuram, R. and Xie, Y.M. (2021), "A 101-line MATLAB code for topology optimization using binary variables and integer programming", Struct. Multidisc. Optim., 63(2), 935-954. https://doi.org/10.1007/s00158-020-02719-9.
  51. Popescu, M., Reiter, L., Liew, A., Van Mele, T., Flatt, R.J. and Block, P. (2018), "Building in concrete with an ultra-lightweight knitted stay-in-place formwork: prototype of a concrete shell bridge", Struct., 14, 322-332. https://doi.org/10.1016/j.istruc.2018.03.001.
  52. Quagliaroli, M. and Malerba, P.G. (2013), "Flexible bridge decks suspended by cable nets. A constrained form finding approach", Int. J. Solid. Struct., 50(14-15), 2340-2352. https://doi.org/10.1016/j.ijsolstr.2013.03.009.
  53. Saka, M. (2007), "Optimum geometry design of geodesic domes using harmony search algorithm", Adv. Struct. Eng., 10(6), 595-606. https://doi.org/10.1260/136943307783571445.
  54. Schlaich, M. (2018), "Shell bridges-and a new specimen made of stainless steel", J. Int. Assoc. Shell Spat. Struct., 59(3), 215-224. https://doi.org/10.20898/j.iass.2018.197.027.
  55. Sigmund, O. and Petersson, J. (1998), "Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima", Struct. Optim., 16(1), 68-75. https://doi.org/10.1007/BF01214002.
  56. Smits, J., Eigenraam, P., Gkaidatzis, R., Visser, D.R., Wong, K. and Wassermann-Fry, S. (2018), "Shaping forces; review of two bridge design methodologies towards architectural and structural symbiosis", J. Int. Assoc. Shell Spat. Struct., 59(2), 152-164. https://doi.org/10.20898/j.iass.2018.196.884.
  57. Sulpizio, C., Fiore, A., Demartino, C., Vanzi, I. and Briseghella, B. (2020), "Optimal design criteria for form-finding of double-curved surfaces", Procedia Manuf., 44, 28-35. https://doi.org/10.1016/j.promfg.2020.02.201.
  58. Tamplin, R. and Iuorio, O. (2018), "Challenges in designing and fabrication of a thin concrete shell", Proceedings of IASS Annual Symposia.
  59. Teimouri, M. and Asgari, M. (2019), "Multi-objective BESO topology optimization for stiffness and frequency of continuum structures", Struct. Eng. Mech., 72(2), 181-190. https://doi.org/10.12989/sem.2019.72.2.181.
  60. Topbas, A., Tulen, F.O., Marasli, M. and Kohen, B. (2019), "A Prefabricated UHPC Shell Pedestrian Bridge", Proceedings of IASS Annual Symposia.
  61. Tugrul, T. (2012), "Multiobjective size and topolgy optimization of dome structures", Struct. Eng. Mech., 43(6), 795-821. https://doi.org/10.12989/sem.2012.43.6.795.
  62. Wang, M.Y., Wang, X. and Guo, D. (2003), "A level set method for structural topology optimization", Comput. Meth. Appl. Mech. Eng., 192(1-2), 227-246. https://doi.org/10.1016/S0045-7825(02)00559-5.
  63. Xie, Y.M., Zuo, Z.H., Huang, X., Black, T. and Felicetti, P. (2014), "Application of topological optimisation technology to bridge design", Struct. Eng. Int., 24(2), 185-191. https://doi.org/10.2749/101686614X13830790993366.