Structural Engineering and Mechanics

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Parametric modeling and shape optimization of four typical Schwedler spherical reticulated shells

  • Wu, J. (Geotechnical and Structural Engineering Research Center, Shandong University) ;
  • Lu, X.Y. (Institute of Engineering Mechanics, Shandong Jianzhu University) ;
  • Li, S.C. (Geotechnical and Structural Engineering Research Center, Shandong University) ;
  • Xu, Z.H. (Geotechnical and Structural Engineering Research Center, Shandong University) ;
  • Li, L.P. (Geotechnical and Structural Engineering Research Center, Shandong University) ;
  • Zhang, D.L. (Shandong Agriculture and Engineering University) ;
  • Xue, Y.G. (Geotechnical and Structural Engineering Research Center, Shandong University)
  • Received : 2014.12.05
  • Accepted : 2015.11.09
  • Published : 2015.12.10
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Abstract

Spherical reticulated shells are widely applied in structural engineering due to their good bearing capability and attractive appearance. Parametric modeling of spherical reticulated shells is the basis of internal analysis and optimization design. In the present study, generation methods of nodes and the corresponding connection methods of rod elements are proposed. Modeling programs are compiled by adopting the ANSYS Parametric Design Language (APDL). A shape optimization method based on the two-stage algorithm is presented, and the corresponding optimization program is compiled in FORTRAN environment. Shape optimization is carried out based on the objective function of the minimum total steel consumption and the restriction condition of strength, stiffness, slenderness ratio, stability. The shape optimization of four typical Schwedler spherical reticulated shells is calculated with the span of 30 m~80 m and rise to span ratio of 1/7~1/2. Compared with the shape optimization results, the variation rules of total steel consumption along with the span and rise to span ratio are discussed. The results show that: (1) The left and right rod-Schwedler spherical reticulated shell is the most optimized and should be preferentially adopted in structural engineering. (2) The left diagonal rod-Schwedler spherical reticulated shell is second only to left and right rod regarding the mechanical behavior and optimized results. It can be applied to medium and small-span structures. (3) Double slash rod-Schwedler spherical reticulated shell is advantageous in mechanical behavior but with the largest total weight. Thus, this type can be used in large-span structures as far as possible. (4) The mechanical performance of no latitudinal rod-Schwedler spherical reticulated shell is the worst and with the second largest weight. Thus, this spherical reticulated shell should not be adopted generally in engineering.

Keywords

References

  1. Chai, S. and Sun, H.C. (1996), "A two-level delimitative and combinatorial algorithm for a kind of (0, 1, 2) programing", J. Dalian Univ. Tech., 36(3), 258-263.
  2. Chiu, M.C. (2010), "Shape optimization of multi-chamber mufflers with plug-inlet tube on a venting process by genetic algorithms", Appl. Acoust., 71(6), 495-505. https://doi.org/10.1016/j.apacoust.2010.01.008
  3. Deng, H. and Dong, S.L. (1999), "Shape optimization of spatial reticulated shell structures", J. Zhejiang Univ. (Eng. Sci.), 33(4), 371-375.
  4. Dong, S.L. and Yao, J. (2003), "Future and prospects of reticulated shells", Spatial Struct., 9(1), 31-34.
  5. Dietl, J.M. and Garcia, E. (2010), "Beam shape optimization for power harvesting", J. Intel. Mater. Syst. Struct., doi: 10.1177/1045389X10365094.
  6. Durgun, I. and Yildiz, A.R. (2012), "Structural design optimization of vehicle components using cuckoo search algorithm", Mater. Test., 54(3), 185-188. https://doi.org/10.3139/120.110317
  7. Emmanuel Nicholas, P., Padmanaban, K.P. and Vasudevan, D. (2014), "Buckling optimization of laminated composite plate with elliptical cutout using ANN and GA", Struct. Eng. Mech., 52(4), 815-827. https://doi.org/10.12989/sem.2014.52.4.815
  8. Fraternali, F., Marino, A., Sayed, T E. and Cioppa, A.D. (2011), "On the structural shape optimization through variational methods and evolutionary algorithms", Mech. Adv. Mater. Struct., 18(4), 225-243. https://doi.org/10.1080/15376494.2010.483319
  9. Gholizadeh, S and Barzegar, A. (2013), "Shape optimization of structures for frequency constraints by sequential harmony search algorithm", Eng. Optim., 45(6), 627-646. https://doi.org/10.1080/0305215X.2012.704028
  10. Jenkins, W.M. (1991), "Towards structural optimization via the genetic algorithm", Comput. Struct., 40(5), 1321-1327. https://doi.org/10.1016/0045-7949(91)90402-8
  11. Jenkins, W.M. (1991), "Structural optimization with the genetic algorithm", Struct. Eng., 69(24), 418-422.
  12. Jenkins, W.M. (1997), "On the application of natural algorithms to structural design optimization", Eng. Struct., 19(4), 302-308. https://doi.org/10.1016/S0141-0296(96)00074-0
  13. Kaveh, A. and Ahmadi, B. (2014), "Sizing, geometry and topology optimization of trusses using force method and supervised charged system search", Struct. Eng. Mech., 50(3), 365-382. https://doi.org/10.12989/sem.2014.50.3.365
  14. Kaveh, A. and Zolghadr, A. (2014), "A new PSRO algorithm for frequency constraint truss shape and size optimization", Struct. Eng. Mech., 52(3), 445-468. https://doi.org/10.12989/sem.2014.52.3.445
  15. Lipson, S.L. and Gwin, L.B. (1977), "Discrete sizing of trusses for optimal geometry", J. Struct. Div., 103(5), 1031-1046.
  16. Lu, X.Y., Zhao, X.W. and Huang, L.L. (2012), "Shape optimizing design of kiewiti spherical reticulated shell", Adv. Mater. Res., 424, 324-329.
  17. Luo, Z., Zhang, N., Gao, W. and Ma, H. (2012), "Structural shape and topology optimization using a meshless Galerkin level set method", Int. J. Numer. Meth. Eng., 90(3), 369-389. https://doi.org/10.1002/nme.3325
  18. Pedersen, N.L. (2010), "Improving bending stress in spur gears using asymmetric gears and shape optimization", Mech. Machine Theor., 45(11), 1707-1720. https://doi.org/10.1016/j.mechmachtheory.2010.06.004
  19. Qian, X. (2010), "Full analytical sensitivities in NURBS based isogeometric shape optimization", Comput. Meth. Appl. Mech. Eng., 199(29), 2059-2071. https://doi.org/10.1016/j.cma.2010.03.005
  20. Rajan, S.D. (1995), "Sizing, shape, and topology design optimization of trusses using genetic algorithm", J. Struct. Eng., 121(10), 1480-1487. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:10(1480)
  21. Rahami, H., Kaveh, A. and Gholipour, Y. (2008), "Sizing, geometry and topology optimization of trusses via force method and genetic algorithm", Eng. Struct., 30(9), 2360-2369. https://doi.org/10.1016/j.engstruct.2008.01.012
  22. Svanberg, K. (1987), "The method of moving asymptotes-a new method for structural optimization", Int. J. Numer. Meth. Eng., 24(2), 359-373. https://doi.org/10.1002/nme.1620240207
  23. Sun, H.C., Wang, Y.F. and Huang, J.F. (1995), "Shape optimization designs of trusses with discrete variables", J. Dalian Univ. Tech., 35(1), 10-16.
  24. Saka, M.P. and Kameshki, E.S. (1998), "Optimum design of nonlinear elastic framed domes", Adv. Eng. Softw., 29(7), 519-528. https://doi.org/10.1016/S0965-9978(98)00018-0
  25. Salajegheh, E. and Vanderplaats, G.N. (1993), "Optimum design of trusses with discrete sizing and shape variables", Struct. Optim., 6(2), 79-85. https://doi.org/10.1007/BF01743339
  26. Salajegheh, E. (2000), "Optimum design of structures with high-quality approximation of frequency constraints", Adv. Eng. Softw., 31(6), 381-384. https://doi.org/10.1016/S0965-9978(00)00002-8
  27. Vyzantiadou, M.A., Avdelas, A.V. and Zafiropoulos, S. (2007), "The application of fractal geometry to the design of grid or reticulated shell structures", Comput. Aid. Des., 39(1), 51-59. https://doi.org/10.1016/j.cad.2006.09.004
  28. Yildiz, A.R. (2013), "Comparison of evolutionary-based optimization algorithms for structural design optimization", Eng. Appl. Artif. Intel., 26(1), 327-333. https://doi.org/10.1016/j.engappai.2012.05.014
  29. Wu, W., Petrini, L., Gastaldi, D., Villa, T., Vedani, M., Lesma, E. and Migliavacca, F. (2010), "Finite element shape optimization for biodegradable magnesium alloy stents", Ann. Biomed. Eng., 38(9), 2829-2840. https://doi.org/10.1007/s10439-010-0057-8
  30. Wu, J., Lu, X.Y., Li, S.C., Zhang, D.L., Xu, Z.H., Li, L.P. and Xue, Y.G. (2015), "Shape optimization for partial double-layer spherical reticulated shells of pyramidal system", Struct. Eng. Mech., 55(3), 555-581. https://doi.org/10.12989/sem.2015.55.3.555
  31. Xu, J., Yang, S.S. and Diao, Y.S. (2006), "Optimized design of single - layer reticulated shell", Spat. Struct., 12(3), 35-37.
  32. Xia, Q., Shi, T., Liu, S. and Wang, M.Y. (2012), "A level set solution to the stress-based structural shape and topology optimization", Comput. Struct., 90, 55-64.
  33. Yas, M.H., Shakeri, M. and Ghasemi-Gol, M. (2007), "Two-objective stacking sequence optimization of a cylindrical shell using genetic algorithm", Scientia Iranica, 14(5), 499-506.
  34. Chen, Z.H. and Liu, H.B. (2009), APDL Parametric Calculation and Analysis, China Water Power Press, Beijing, China.
  35. Gong, S.G. and Xie, G.L. (2010), ANSYS Parametric Programming and Command Manual, China Machine Press Beijing, China.
  36. Lu, X.Y., Zhao, X.W. and Chen, S.Y. (2013), The Optimization of Reticulated Shell Structures Based On Discrete Variables, Building Industry Press, Beijing, China.
  37. Sun, H.C., Chai, S. and Wang, Y.F. (2002), Structural Optimization with Discrete Variables, Dalian University of Technology Press, Dalian, China.
  38. Shen, Z.Y. and Chen, Y.J. (1996), Grid and Lattice Shell, Tongji University Press, Shanghai, China.
  39. Shang, X.J. and Qiu, F. (2005), ANSYS Structural Finite Element Senior Analysis Method and Sample Applications, China Water Power Press, Beijing, China.
  40. Wu, J. (2013), "Parametric modeling and shape optimization of four typical schwedler reticulated shells", Mater Dissertation, Shandong Jianzhu University, Jinan.

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