# Introduction to Structural Optimization

## ME 5512

This is an introductory course on structural optimization, which refers to the application of mathematical optimization techniques to the design of structures modeled via the ﬁnite element method (FEM). The main types of structural optimization techniques are studied, including size, shape, and topology optimization. To use eﬃcient gradient-based optimization methods, we require derivatives of the optimization functions with respect to the design variables, which cannot be explicitly evaluated for functions computed using the FEM. Therefore, one particular area of study is the mathematical derivation and computational implementation of material and shape sensitivities that can be used for shape and topology optimization of structures.

# 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.