BiOPT, a method for shape and discrete member sizing optimization of steel truss structures [electronic resource]

Advancements in finite element methods (FEM) and computing over the past thirty years enable engineers to accurately simulate the behavior of complex steel building and civil structures in a matter of seconds. Despite this technological progress, engineers today continue to rely on heuristics and rules of thumb to support many design decisions. Chapter 1 of this dissertation measures the efficiency of conventional structural design processes based on industry survey data. For large steel structures with at least 1,000 constituent members, it takes on average 13 man-hours to evaluate a single structural shape configuration and four hours to evaluate a single configuration of member sizes; engineers typically evaluate fewer than 50 shape and sizing alternatives per project. Chapter 2 presents the results of an experiment that measured the effectiveness of conventional design processes. The subjects of the experiment solved a series of parameter design problems that varied in terms of scale (number of design variables) and coupling (interactions between variables). The results show an exponential decrease in the quality of the solution produced as the scale of the problem increases. The average loss of solution quality was 6.4% for a two variable problem and 25.0% for a six variable problem—approximately a fourfold increase. Coupling has a comparable impact on solution quality for problems involving two to three variables, but becomes less significant as the scale of the problem increases. I discuss these findings in the context of information processing models for human cognition and explore the implications for current design theories and methodologies. Chapters 3 and 4 present a computational method for optimizing the shape and member sizes of steel truss structures that aims to efficiently and effectively handle large variable sets involving both discrete and continuous variables that are common in industry practice. The proposed method known as BiOPT utilizes a unique combination of algorithms that are organized hierarchically: the Fully Constrained Design (FCD) method for discrete sizing optimization is nested within SEQOPT, a gradient-based optimization method that operates on continuous shape variables. Based on the optimality criteria approach, FCD features a distinct approach to constraint handling and the generation of new designs that is easily understood by practicing engineers without a background in optimization and independent of the problem objective and constraint functions. Therefore, the FCD algorithm does not require modification to conform to local regulatory requirements and varied stakeholder preferences, making it relatively easy to apply to a wide variety of industry problems compared to optimality criteria. SEQOPT is an existing gradient-based method that uses surrogate models and has been shown to be robust and efficient for problems with continuous variables, particularly when the objective and/or constraint functions are computationally expensive to evaluate. Both the BiOPT and FCD methods are benchmarked against existing computational approaches using a series of standard truss structures found in the literature. FCD produces superior quality solutions (> 5% difference) compared to optimality criteria and comparable quality solutions (< 2% difference) to leading heuristic methods, but requires approximately two orders of magnitude fewer iterations. BiOPT compares favorably to all existing techniques in terms of solution quality (2.8% less steel weight on average). The computational efficiency of BiOPT is also superior to existing techniques, except for Hansen and Vanderplaat's gradient-based approach which, however, produced solutions of inferior quality. The improved efficiency and effectiveness of the BiOPT method can be attributed to the method's unique combination of algorithms as well as the particular way in which the FCD algorithm handles constraints and generates new designs. The FCD and BiOPT methods are also compared to conventional structural optimization methods based on two parallel industry case studies involving stadium roof structures. In both cases, these methods yielded design solutions that required significantly less structural material, resulting in project structural steel cost savings of greater than 18%. The proposed methods also reduced design cycle time more than two orders of magnitude complete compared to conventional design methods and reduced the total duration of the design process. The theoretical and practical contributions of this dissertation are summarized in Chapter 5.

Advisor: Fischer Martin
Deierlein Gregory G. (Gregory Gerard)
Shea Kristina