Failure analysis of engineering structures in undergraduate courses using optimization

Abstract

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 optimizationbased 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. ß

Improvement of students’ understanding about the phenomena of groundwater pumping by using computer software

“…Simulation models and virtual e‐learning (a learning, training, or education program by electronic means) environments provided the potential for improved learning. The learners literally created the phenomenon of interest . Grunwald et al developed similar a soil‐landscape model implemented in Virtual Reality Modeling Language (VRML) at four different spatial scales in southern Wisconsin.…”

Developing students’ mathematical and computational knowledge to investigate mooring line in ocean engineering

“…When the computational simulations is taken into consideration , it can be said that computational technology have a great role on improving educational processes in the context of both teachers and students. One of the most important advantages of such computational technology is enabling users to experience self‐learning processes.…”

Interactive computer for teaching biot poroelasticity modeling in civil engineering

“…Simulation tools are ideal media to support inquiry and discovery learning [15][16][17]. In addition, simulation models offer a platform for hypothesis testing.…”