MMAE 544 Design Optimization

Fall 2009

Instructor: Prof. Xiaoping Qian

Classroom: E1-242

Lecture Time: M W 8:35 am ~ 9:50 am

Office Hours: M W 3:00 pm ~ 5:00 pm

Course Description: Optimization theory and practice with examples. Finite-dimensional unconstrained and constrained optimization, Kuhn-Tucker theory, linear and quadratic programming, penalty methods, direct methods, approximation techniques, duality. Formulation and computer solution of design optimization problems in structures, manufacturing and thermofluid systems.

Programming using Matlab or Mathematica is required in this course.

Learning Objectives: Understand how to use optimization tools to design structures (size, shape and topology).

Grading Policy

• Homework 30%
• Projects 40%
• Exam 30%

Prerequisites

• Graduate standing
• Knowledge with FEA is desirable, but not required.

Textbook

• J. Arora, Introduction to Optimum Design, 2nd Ed, Elsevier 2004
• M. P. Bendsoe and O. Sigmund, Topology Optimization: Theory, Methods and Applications, Springer 2004.

Topics

Part I: Optimum Design Concepts

Optimum Design Problem Formulation

Optimum Design Concepts

Fundamental concepts: Gradient, Hessian, Taylor series expansion

Unconstrained Optimum Design

Constrained Optimum Design

Global Optimality

Part II: Numerical Methods for Optimization

Unconstrained Optimum Design

One-dimensional minimization, Steepest descent, Conjugate gradient, Newton’s method, Quasi-Newton.

Constrained Optimum Design

SLP, SQP, Method of feasible direction, Gradient projection, Generalized reduced gradient method

Local Approximation

Lagrange duality, Convex linear approximation, Method of moving asymptotes

Part III: Geometric (Size, Shape and Topology) Optimization

Sensitivity Analysis

Optimal Design of Static, Linear Systems

Optimal Design of Dynamic Systems, Eigenvalue Problems

Shape Optimization

Topology optimization

Applications: Compliant mechanism, MEMS, dynamically loaded structures, heat conduction.