CIE514 - Introduction to Advanced Mechanics and Mathematics
Principles of mechanics underlie many activities in engineering, and this is particularly so in civil engineering.
We have undoubtedly evidenced this in our undergraduate curricula.
Mathematics provides the logic infrastructure to assert these principles in a manner
such that they can be understood holistically, and not as isolated facts.
A computer program is a perfect vehicle to express this logical understanding unambiguously;
computer programs also enable exploration and intuition-building.
Hence (in my view), mechanics, mathematics and computer programming go hand-in-hand.
In this course, we will look at some engineering problems,
taking an approach that combines mechanics, mathematics and computer programming (using MATLAB),
building on ideas from undergraduate mechanics and mathematics courses, and emphasizing unifying themes.
This course is centered around assignments, each resembling a mini-project more than a homework,
and tied to certain learning outcomes.
Assignments are not organized by topic; rather, each assignment is built around a theme,
and could invoke multiple mechanics/mathematics concepts.
Most assignments will lead to software code or an executable mode,
and have a degree of open-endedness both in approach and final results.
Sequences of videos and other resources are grouped with each assignment to provide tools and suggest approaches,
assignments will be direct applications of results or formulas from the videos.
They will involve significant thought and reflection beyond the provided resources.
Syllabus
Syllabus for 2022 offering
Assignments and resources
- Matrix structural analysis
- The structure of mechanics problems (Tonti diagram)
- Static stability: mechanisms and prestress modes
- Elastic stability: column buckling and beam lateral torsional buckling
- Optimization applications in mechanics: energy theorems and limit analysis
- Computation of torsional constant: membrane analogy, Fourier series and finite elements