Topology Optimization of Engineering Systems

Abstract

The goal of the course is to offer a rather exhaustive introduction on the field of topology optimization and its most recent emerging trends.

Objective

Topology optimization is a field focusing on the computation of optimized designs for various engineering applications, including weight reduction of mechanical structure, aerodynamic designs, or enhanced cooling in thermomechanical systems. In this course, we will mainly focus on nonparametric shape optimization based on the boundary variation method of Hadamard. Three sessions will be dedicated to project presentations made by the students, either on the presentation of some recent work related to the field, or on their own applicative project. Project will be written in FreeFEM based on a ready-to-use code. Webpage of the course: https://people.math.ethz.ch/~ffeppon/topopt_course/index.html

Content

The lecture will outline as follows. 0. Topology optimization and automated generative design : perspectives and applications in the context of additive manufacturing (2 hours) 1. Common physical models in mechanical and aeronautic engineering. PDE and variational forms. Formulation of shape optimization problems. (2 hours) 2. Nonlinear constrained optimization. Nullspace gradient flows. (2 hours) 3. General results about shape optimization. Homogenization, relaxed designs. The SIMP method (2 hours). 4. Shape differential calculus. Shape derivatives and shape gradients. The adjoint method. (4 hours). 5. Numerical shape evolution algorithms : moving mesh methods, implicit surfaces and body-fitted meshes (2 hours). 6. Projects : numerical implementation in FreeFEM++. (4 hours) 7. Advanced methods : geometric constraints. (2 hours). 8. Project presentations. (6 hours)

Resources