۱- Introduction

۲- Problem formulation

۳- Optimization procedure

۴- Numerical study

۵- Conclusion

References

Abstract

In this paper an efficient first-order multi-objective optimization scheme is adopted for the design of linear viscous dampers for the seismic retrofitting of frame buildings. A retrofitting cost function serves as one objective while the expected losses serve as the other objective. These two objectives are well understood by decision makers that may not be engineers. Furthermore, with the Pareto front for these two objectives at hand, the decision maker can make his decisions with the whole picture at hand. To allow achieving the Pareto front with a reasonable computational effort, a first-order multi-objective optimization approach is adopted. The gradients of the expected loss function, required for the optimization, are analytically derived using the very efficient Adjoint Variable method. This considerably improves the computational efficiency of the methodology. The efficacy of the framework is illustrated with a 2D four storey frame and an eight-storey 3D asymmetric building.

Introduction

Recent seismic events have shown that, when it comes to modern countries with modern seismic codes, loss of human lives due to collapse of buildings is considerably smaller compared to that in the past. For example, the 1994 Northridge and the 2011 Christchurch earthquakes caused a total of 57 and 185 deaths, respectively. As saving human lives has been the major task of earthquake engineering, this is indeed an achievement for the structural engineering community. However, with the relatively small number of deaths due to these events, came huge monetary losses. The 1994 Northridge and 2011 Christchurch led to losses estimated at ∼ US $44 billion and NZ $40 billion (corresponds to approximately 20% of the GDP), respectively (direct and indirect). This motivates a design considering expected losses in parallel to reducing loss of human lives [2]. Adopting such a design approach is necessary for new buildings, where new technologies to limit damage could be easily included. One such loss based design approach is the Loss Optimization Seismic Design, commonly referred as LOSD [3,4]. This may highly affect the losses to be expected in the far future. Nonetheless, in the foreseen future, most buildings to experience earthquakes are ones that have already been designed and built based on the sole goal of saving human lives. Thus, new technologies and design approaches for their retrofitting are required to reduce expected losses.