This paper proposes a simultaneous optimal design method of asymmetric large-scale space frames with tuned mass dampers (TMDs). The objective function is defi ned by the maximum absolute acceleration response of the structure to input ground motions of sine waves. Sine waves of periods with the fi ve natural periods having large modal participation factors of the structure are input, and the maximum responses are calculated by time–history response analysis to evaluate the objective function. The shape of the space frame, i.e. nodal coordinates of the space frame’s joints, is described by a Bézier surface to reduce the number of design variables. The change from the initial values of the nodal coordinates is constrained to preserve the initial design shape, which is provided by an architect. The method employs a genetic algorithm in optimization. In addition, a case study is conducted for an asymmetric steel space frame of a vault-like shape. The results confi rm the reduction of maximum absolute acceleration responses in the optimal shapes not only to the fi ve sine waves but also to four scaled ground motion records. Moreover, the presence of TMDs enables the reduction of the peak response value and maintains similarity to the initial shape.
architectural design, Bézier surface, earthquake engineering, genetic algorithm, optimization, seismic control, structural engineering, structural shape, space frame, tuned mass damper
 Architecture Institute of Japan, Report on the Hanshin-Awaji Earthquake Disaster, Building Series, Volume 3: Structural Damage to Steel Buildings, Structural Damage to Shell and Spatial Structures, Structural Damage to Storage Tanks and Their Supports, 1998 (in Japanese).
 Architecture Institute of Japan, Preliminary Reconnaissance Report of the 2011 Tohoku-Chiho Taiheiyo-Oki Earthquake. Springer, 2012.
 Kaynia, A.M., Veneziano, D. & Biggs, J.M., Seismic effectiveness of tuned mass damp-ers. Journal of the Structural Division, 107(8), pp. 1465–1484, 1981.
 Lin, C.-C., Hu, R.-Y. & Wang, J.-J., Optimal design of passive tuned mass dampers for seismic structures. 33rd Structures, Structural Dynamics and Materials Conference, Vol. 33, pp. 1497–1503, 1992.
 Johnson, J.G., Reavelley, L.D. & Pantelides, C., A rooftop tuned mass damper frame. Earthquake Engineering & Structural Dynamics, 32(6), pp. 965–984, 2003. doi: http:// dx.doi.org/10.1002/eqe.257
 Kusunoki, T., Xue, S. & Yamada, M., Study of seismic response and vibration control of single-layer latticed domes using TMD. Journal of Structural Engineering, 41B, pp. 17–22, 1995 (in Japanese).
 Yoshinaka, S. & Kawaguchi, K., Vibration control of spatial structures using spatially distributed MTMDs. Memoirs of the Faculty of Engineering, Osaka City University, 49, pp. 19–28, 2008.
 Ramm, E., Bletzinger, K.U. & Reitinger, R., Shape optimization of shell structures. Revue Européenne des Éléments, 2(3), pp. 377–398, 1993.
 Ohsaki, M., Nakamura, T. & Kohiyama, M., Shape optimization of a double-layer space truss described by a parametric surface. International Journal of Space Structures, 12(2), pp. 109–119, 1997.
 Goldberg, D.E., Genetic Algorithm in Search Optimization and Machine Learning. New York: Addison-Wesley, 1989.
 Jenkins, W.M., Towards structural optimization via the genetic algorithm. Computers & Structures, 40(5), pp. 1321–1327, 1991. doi: http://dx.doi.org/10.1016/00457949(91)90402-8
 Rajeev, S. & Krishnamoorthy, C., Discrete optimization of structures using genetic algorithms. Journal of Structural Engineering, 118(5), pp. 1233–1250, 1992. doi: http://
 Rajan, S.D., Sizing, shape, and topology design optimization of trusses using genetic algorithm. Journal of Structural Engineering, 121(10), pp. 1480–1487, 1995. doi: http://dx.doi.org/10.1061/(ASCE)0733-9445(1995)121:10(1480)
 Ohsaki, M., Genetic algorithm for topology optimization of trusses. Computers & Structures, 57(2), pp. 219–225, 1995. doi: http://dx.doi.org/10.1016/0045-7949(94)00617-C
 Camp, C., Pezeshk, S. & Cao, G., Optimized design of two-dimensional structures using a genetic algorithm. Journal of Structural Engineering, 124(5), pp. 551–559, 1998. doi: http://dx.doi.org/10.1061/(ASCE)0733-9445(1998)124:5(551)
 Erbatur, F., Hasançebi, O., Tütüncü, I. & Kılıç, H., Optimal design of planar and space structures with genetic algorithms. Computers & Structures, 75(2), pp. 209–224, 2000. doi: http://dx.doi.org/10.1061/(ASCE)0733-9445(1998)124:5(551)
 Dan, M. & Kohiyama, M., Simultaneous optimization of structural shape and control system of large-scale space frame. WIT Transactions on the Built Environment, 132, 2013, ISSN 1743-3509, doi.10.2495/ERES130141.
 Den Hartog, J.P., Mechanical Vibration, 4th edn, McGraw-Hill: New York, 1956.
 Ikago, K., Saito, K. & Inoue, N., Seismic control of single-degree-of-freedom structure using tuned viscous mass damper. Earthquake Engineering and Structural Dynamics, 41, pp. 453–474, 2011. doi: http://dx.doi.org/10.1002/eqe.1138
 Kato, S., Nakazawa, S., Uchikoshi, M. & Mukaiyama, Y., Response reducing effect of seismic isolation system installed between large dome and lower structure. Proceedings of 6th Asian Pacifi c Conference on Shell and Spatial Structures, Seoul, Korea, pp. 323–330, 2001.