International journal of steel structures (국제강구조저널)

Korean Society of Steel Construction (한국강구조학회)
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Study on the Shape Optimization of Cable-Stiffened Single-Layer Latticed Shells

  • Wang, Hao (Department of Structural Engineering, Tongji University) ;
  • Wu, Minger (Department of Structural Engineering, Tongji University)
  • Received : 2016.12.18
  • Accepted : 2018.01.29
  • Published : 2018.09.30
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Abstract

The cable-stiffened single-layer latticed shell is a new type of spatial structure. In this paper, a shape optimization method is proposed for two kinds of cable-stiffened single-layer latticed shells. Firstly, an optimization algorithm is proposed to minimize the strain energy of shell. Interior-point method, conjugate gradient method and golden section method are adopted as the approach of constraint optimization, the minimization algorithm and the line search strategy, respectively. Secondly, the derivatives of stiffness matrixes of two kinds of cable-stiffened systems are discussed. Finally, optimization program is programmed in MATLAB and a numerical example is carried out. The linear buckling load, the displacement and the stress distribution of the optimized shells are investigated. According to numerical results, the structural behaviours of cable-stiffened single-layer latticed shells are improved significantly. The optimization method suggested in this paper is valid.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Bletzinger, K. U., Wuchner, R., Daoud, F., et al. (2005). Computational methods for form finding and optimization of shells and membranes. Computer Methods in Applied Mechanics and Engineering, 194(30-33), 3438-3452. https://doi.org/10.1016/j.cma.2004.12.026
  2. Cui, C. Y., Jiang, B. S., & Wang, Y. B. (2014). Node shift method for stiffness-based optimization of single-layer reticulated shells. Journal of Zhejiang University Science A, 15(2), 97-107. https://doi.org/10.1631/jzus.A1300239
  3. Feng, R. Q., & Ge, J. M. (2013). Shape optimization method of freeform cable-braced grid shells based on the translational surfaces technique. International Journal of Steel Structures, 13(3), 435-444. https://doi.org/10.1007/s13296-013-3004-3
  4. Feng, R. Q., Yao, B., & Ye, J. H. (2013a). Stability of lamella cylinder cable-braced grid shells. Journal of Constructional Steel Research, 88(9), 220-230. https://doi.org/10.1016/j.jcsr.2013.05.019
  5. Feng, R. Q., Ge, J. M., & Ye, J. H. (2013b). Shape optimization of free-form cable-braced grid shells. China Civil Engineering Journal, 46(4), 64-70(in Chinese).
  6. Feng, R. Q., Zhang, L. L., & Ge, J. M. (2015). Multi-objective morphology optimization of free-form cable-braced grid shells. International Journal of Steel Structures, 15(3), 681-691. https://doi.org/10.1007/s13296-015-9014-6
  7. Fujimoto, M., Kushima, S., Imai, K., et al. (2010). Numerical study on buckling behavior of single layer two-way grid dome with tension member as diagonal. In Proceeding of the IASS 2010 symposium, Shanghai, China, 8-12 November.
  8. Fujita, S., & Ohsaki, M. (2009). Shape optimization of free-form shells considering strain energy and algebraic invariants of parametric surface. In Proceeding of IASS 2009 symposium, Valencia, Spain, 28 September-2 October.
  9. Fujita, S., & Ohsaki, M. (2010). Shape optimization of free-form shells using invariants of parametric surface. International Journal of Space Structures, 25(3), 143-157. https://doi.org/10.1260/0266-3511.25.3.143
  10. Ikeya, K., Shimoda, M., & Shi, J. X. (2016). Multi-objective free-form optimization for shape and thickness of shell structures with composite materials. Composite Structures, 135, 262-275. https://doi.org/10.1016/j.compstruct.2015.09.011
  11. Li, P. C., Wu, M., & Xing, P. J. (2014). Novel cable-stiffened singlelayer latticed shells and their stabilities. Journal of Constructional Steel Research, 92, 114-121. https://doi.org/10.1016/j.jcsr.2013.10.008
  12. Li, P. C., Wu, M., Wang, H., et al. (2016). Experimental and numerical analysis of cable-stiffened single-layer spherical latticed shells. Advances in Structural Engineering, 19(3), 488-499. https://doi.org/10.1177/1369433216630120
  13. Nocedal, J., & Wright, S. J. (2006). Numerical optimization (2nd ed.). United States of America: Springer.
  14. Ohmori, H., & Hamada, H. (2006). Computational morphogenesis of shells with free curved surface considering both designer's preference and structural rationality. In Proceeding of IASS - APCS 2006, Beijing, China, 16-19 October.
  15. Ohsaki, M., Ogawa, T., & Tateishi, R. (2004). Shape optimization of curves and surfaces considering fairness metrics and elastic stiffness. Structural and Multidisciplinary Optimization, 27(4), 250-258. https://doi.org/10.1007/s00158-004-0382-3
  16. Schlaich, J., & Schober, H. (1996). Glass-covered grid-Shells. Structural Engineering International, 6(2), 88-90. https://doi.org/10.2749/101686696780495716
  17. Schlaich, J., & Schober, H. (1997). Glass roof for the hippo house at the Berlin Zoo. Structural Engineering International, 7(4), 252-254. https://doi.org/10.2749/101686697780494581
  18. Shimoda, M., Okada, T., Nagano, T., et al. (2016). Free-form optimization method for buckling of shell structures under out-of-plane and in-plane shape variations. Structural and Multidisciplinary Optimization, 54(2), 275-288. https://doi.org/10.1007/s00158-016-1402-9
  19. Umezawa, R., Hiraoka, S., Takahashi, K., et al. (2003). On design of Kumagaya Dome of a super large single layer reticular dome with membrane roof recently constructed in Japan. In Proceedings of IASS - APCS 2003, Taipei, Taiwan, 22-25 October.
  20. Vizotto, I. (2010). Computational generation of free-form shells in architectural design and civil engineering. Automation in Construction, 19(8), 1087-1105. https://doi.org/10.1016/j.autcon.2010.09.004
  21. Winslow, P., Pellegrino, S., & Sharma, S. B. (2010). Multi-objective optimization of free-form grid structures. Structural and Multidisciplinary Optimization, 40(1-6), 257-269. https://doi.org/10.1007/s00158-009-0358-4
  22. Wu, M., Ohmori, H., & Sasaki, M. (2001). Pre-stress introduction analysis of a lattice shell stiffened by tensile system. In Proceedings of the IASS 2001 symposium, Nagoya, Japan, 9-13 October.
  23. Yang, D. B., Guo, B., Chong, C. C., et al. (2015). Modeling and structural behavior of cable-stiffened single-layer latticed domes of hexagonal meshes. Journal of Constructional Steel Research, 114, 237-246. https://doi.org/10.1016/j.jcsr.2015.08.003
  24. Zhang, Z., & Fujimoto, M. (2010). Effect of tension member on buckling and strength behaviour of single layer two-way grid cylindrical shell roof. In Proceeding of the IASS 2010 symposium, Shanghai, China, 8-12 November.

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