Keywords: earthquake architecture, structural optimization, topology, shape, mixed-integer nonlinear programming, trusses, seismic analysis, pushover analysis, N2 method, earthquake resistant design.

The paper presents the application of a structural optimization approach in earthquake architecture. The structural optimization is considered not only as a means of reducing the structure's weight or volume, but also, by including topology and shape optimization, as a method for finding interesting solutions from the aesthetic point of view. Truss-like structures are considered as vertical structural elements resisting horizontal loads in multi-storey buildings. The optimization is proposed to represent a part of the preliminary stage of the building design and it is thus performed using a simplifed structural and load model. The combined topology, shape and sizing optimization of trusses gives rise to a mixed discrete or continuous optimization problem. The mixed-integer nonlinear programming (MINLP) approach was applied. A numerical example is presented where the optimization was performed at different levels, namely the sizing optimization combined with/without shape and/or topology optimization. In order to obtain a more accurate information about the seismic performance of the optimal solutions a subsequent re-analysis was performed.

The assessment of the inelastic seismic performance of the optimal truss structures obtained was based on global criteria related to inter-storey drifts which have been selected in accordance with the FEMA-356 code [1]. A non-linear static (pushover) analysis has been employed for assessing the seismic response [2]. The target displacement (indicating the so called "earthquake demand") of the models analysed has been obtained using the N2 method, introduced by Fajfar [3].

In terms of structural optimization it has been concluded that performing only sizing optimization yields the best results regarding the inter-storey drift ratios, while the downside of this solution is that it lacks sufficient ductility and additional strength for seismic input higher that the prescribed design input. When considering the sizing optimization together with shape optimization a better base shear force to self-weight ratio is achieved, while sizing optimization coupled with topology optimization allows for some local stiffness redistribution around damaged elements, resulting in an increase of the ultimate lateral load capacity and in a higher ductility level. The best seismic response has been achieved by performorming the simultaneous topology, shape and sizing optimization of the structure. This solution does not only provide the highest base shear force to self-weight ratio, but also possesses an adequate amount of ductility as well as additional strength to account for seismic events larger than the design seismic input.

The study has shown that the structural optimization approach can be successfully applied as a part of the preliminary stage of building design. However, there is still room for improvement, especially in terms of upgrading the optimization models in order that higher quality preliminary solutions can be obtained.

1

FEMA, "FEMA 356 - Prestandard and commentary for the seismic rehabilitation of buildings", Federal Emergency Management Agency, Washington (DC), 2000.

2

H. Krawinkler, G.D.P.K. Seneviratna, "Pros and cons of a pushover analysis of seismic performance evaluation", Engineering Structures, 20(4-6), 452-464, 1998. doi:10.1016/S0141-0296(97)00092-8

3

P. Fajfar, "A nonlinear analysis method for performance based seismic design", Earthquake Spectra, 16(3), 573-592, 2000. doi:10.1193/1.1586128

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £130 +P&P)