Topology Optimization
ME 5512
This course delves into the fundamentals and applications of topology optimization, which refers to the application of mathematical optimization techniques to the design of lightweight structures. Topology optimization techniques determine an optimal distribution of material within a prescribed region with regard to structural performance, mass, and geometric criteria. A characteristic of topology optimization problems is that the evaluation of the structural performance requires the numerical solution of a boundary value problem, typically through the finite element method (FEM). The course will discuss fundamental techniques used in topology optimization and its application in several fields such as solid mechanics, fluids, and heat transfer. Topics include density-based and level-set techniques, ground-structure methods, evolutionary and machine learning methods, and feature-mapping techniques. Multi-scale, multi-material, and multi-component applications are also discussed.
Introduction to the Finite Element Method
ME 3295 / ME 4895
The primary goal of this course is for students to develop a fundamental understanding of the mathematical and numerical underpinnings of the FEM by formulating and programming the method for linear problems. While we will solve simple, representative problems using a commercial FEM code towards the end of the semester in order to connect the concepts to the practical application of the method, the emphasis of the course is on mathematical and numerical aspects. The method will be presented in a general way as a means to solve partial differential equations and not focused on a particular physical domain. Examples in structural, heat transfer, and diffusion analysis will be presented throughout the course. This course aims at making students better users of commercial finite element software by understanding the fundamentals of the method and providing a foundation for students wishing to develop their own codes for research purposes.
Principles of Optimal Design
ME 5511/ ME 3295
In this course, we study the application of mathematical optimization concepts to the numerical solution of engineering design problems. We also examine heuristic methods for the solution of optimization problems for which efficient gradient-based solution methods cannot be used. We briefly cover the use of Matlab to solve optimization problems; however, the focus of the course is not on the tools but on understanding the underlying concepts behind optimal design to make intelligent use of these tools (and others that you may encounter throughout your career). This understanding includes identifying when and how to cast a design problem into an optimization problem, how to choose the most (or an) appropriate algorithm to solve it, how to interpret the results of the optimization, and how to diagnose problems when things go wrong.
Computational Mechanics
ME 3255
Topics include elementary numerical analysis, finite differences, initial value problems, ordinary and partial differential equations, and finite element techniques. Applications include structural analysis, heat transfer, and fluid flow.