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Integrating probabilistic performance-based design into topology optimization for the conceptual design of structures

Recently there has been a significant move towards the use of probabilistic Performance-Based Design (PBD) techniques during the structural design process. These techniques are more commonly used in later design stages to fine-tune structures to meet performance requirements; however, as noted by Krawinkler et al. (2006), in order to obtain efficient designs PBD techniques should be incorporated into the design process during the conceptual design stage. This research illustrates the usefulness and versatility of probabilistic PBD during the conceptual design of structures through the integration of the Pacific Earthquake Engineering Research (PEER) Center’s probabilistic PBD framework (Porter 2003) with topology optimization techniques. The resulting framework considers the topology optimization of uncertain building systems while rigorously accounting for the stochastic nature of the external excitation and resulting structural response within a setting described by the PEER methodology. A novel method is presented to decouple the performance-based analysis from the topology optimization using a series of approximate sub-problems that are defined from the results of a single probabilistic analysis carried out in the current design point and are solved sequentially. The approximate sub-problems are constructed using an Auxiliary Variable Vector that conveniently simplifies the governing equilibrium equations and therefore allows the approximate sub-problems to be solved using established algorithms for static, deterministic topology optimization problems. The successive definition and solution of the sub-problems until convergence leads to a final topology that satisfies the original probabilistic constraints. Examples will be presented to illustrate the proposed method.

REFERENCES

Krawinkler, H., Zareian, F., Medina, R.A., and Ibarra, L.F. (2006). Decision support for conceptual performance-based design. Earthquake Engng. Struct. Dyn. 35:115-133.

Porter, K.A. (2003). An overview of PEER’s performance-based earthquake engineering methodology. In Proc. of the Ninth International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP9).

Author(s):

Sarah Bobby    
University of Notre Dame
United States

Seymour M.J. Spence    
University of Michigan
United States

Ahsan Kareem    
University of Notre Dame
United States