Failure analysis of engineering structures in undergraduate courses using optimization

In the design process for engineering structures, it is often of interest to determine the largest magnitude of a given form of load that can be applied on a structure before causing failure. This gives the factor of safety against failure. Determining the factor of safety entails analysis of a structure on the verge of failure, and is known as limit analysis. It is well known that limit analysis can be formulated as a constrained optimization problem. With robust computational tools for optimization having become readily available, it is possible to introduce the optimization-based approach to limit analysis at various stages in the undergraduate civil engineering curriculum. In this article, we present three instances of limit analysis using an optimization-based approach from (i) a sophomore level Statics course, (ii) a junior level Structural Analysis course, and (iii) a senior level Advanced Solid Mechanics course. These are based on materials presented by the author in undergraduate mechanics courses at the University of Colorado at Boulder. In each case, we develop a mathematical formulation and implement the computations in MATLAB. We use two optimization tools, one from the MATLAB Optimization Toolbox and the other called SeDuMi. Classroom experience has shown that the optimization-based approach helps students recognize the underlying thread in seemingly disparate limit analysis problems.