George F. Corliss
Electrical and Computer Engineering
Marquette University
Milwaukee, WI 53201-1881, USA
email: George.Corliss@Marquette.edu
"If the only tool you have is a hammer, the whole world looks like a nail." - Mark Twain. Our tool is optimization. Is structural engineering a nail?
A typical modern office building is supported by steel columns and beams arranged in bays (horizontally) and stories (US) (vertically). The structure must support static (weight) and dynamic (storms and earthquakes) loads, at modest construction costs. If the structure fails under extreme conditions, we want to control its failure. For example, we prefer failures that can be repaired, and we prefer an inward collapse to toppling over. Members under extreme loads exhibit multiple modes of failure, which must be understood and modeled.
Increasingly, software tools used by practicing structural engineers augment or replace engineering experience and rules-of-thumb by careful mathematical modeling and analysis to support rapid exploration of the design space. Optimization and nonlinear systems problems abound, and their reliable solution is life-critical. Many problems have nonlinear finite element formulations. Parameter values are known approximately, at best. Problems such as beam buckling are extremely sensitive to initial conditions. Problems such as selection of suitable members are discrete because we want to specify members from a catalogue in stock. Some problems have broad, flat minimal regions, and some admit continua of solutions. Are we having fun yet?
This talk is accessible to anyone who remembers how to solve calculus max-min problems in two variables. I assume no structural engineering beyond the fact that the lecture hall has not collapsed. I report a little on work that has been done, but mostly speculate on opportunities. Is your hammer in your hand?