Student Handbook

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Dulyachot Cholaseuk Mechanical Engineering
Department Thammasat University
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• Design theories
• Optimum design of mechanical elements
• Optimum and Robust Design
• Representation of a free-form shape using
  non-uniform rational B-spline surface
• Selection of design variables and objective
  functions
• Solution of design optimization problems
• Advanced computer aided design

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Week Date Topics
1 Introduction. Optimum design problem formulation. Review of necessary topics in mathematics. Introduction to computer programming and plotting software.
2 Minimization of unconstrained uni-variate and multivariate functions. Sufficient and necessary conditions for minimization.
3 Numerical method for optimization of unconstrained uni-vatiate functions. Line search bisection, golden section, Newton's method and parabolic interpolation.
4 Numerical method for optimization of unconstrained multivariate functions. Gradient-based method uni-direction search, steepest direction, conjugate gradient method and Newton's method.
5 Numerical method for optimization of unconstrained multivariate functions. Zeroth-order method Grid search, downhill Simplex search, adaptive random search and genetic algorithm.
6 Project presentation. Recap.
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Tentative Schedule
Week Date Topics
9 Introduction to designed experiments and their application to optimization problem. Response functions.
10 Minimization of unconstrained functions. Geometric of a constrain optimization problem. Lagrange multipliers and their geometric meaning. Karush-Khun-Tucker conditions. Introduction to Excel solver module.
11 Basic numerical Method for constrain optimization problem.
12 Optimization of discrete problems. Simulated annealing. Genetic algorithm. Traveling salesman problem.
13 Multi-criteria optimization. Pareto solutions. Minimax method. Weighted objective method.
14 Case study. Black-box concept in solving engineering optimization problem. Mathematical representation of free form geometry. Bezier curves. B-spline curves. Nurbs. Intoduction to commercial software for engineering optimization. Robust design and other design concept. Discussion of advanced topics in optimum design.
15 Project presentation. Course Summary.
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• Arora, J., Introduction to Optimum Design, 2nd
  Edition, McGraw-Hill
• Stoecker, W., Design of Thermal Systems, 3rd
  Edition, McGraw-Hill
• Press, W., et. al., Numerical Recipes in Fortran
  77, Cambridge.

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• 80 ?????????????????? A.

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• Engineering Mechanics
• Statics/Dynamics
• Mechanics of Solids
• Mathematics
• Algebra
• Calculus
• Programming skill

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Design (in engineering context) The management
of constraints Manipulate design variables to
satisfy non-negotiable constraints and optimize
the negotiable constraints Usually, no unique
solution.
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Recognition of Need
Optimization
Problem Formulation
Prototyping
Conceptual Design
Testing
System Design
Manufacturing Process Design
Component Design
Production
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???????????????????????? - Optimization
Maxima
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???????????????????????? - Optimization
Minima
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????????????????? - Objective function ?????? -
Design variables ???????? - Constraints
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Design of a rod under tension
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f
r
g
r
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• Program editor and compiler
• C/C
• Basic
• Fortran
• Optimization tools
• Matlab
• Excel
• Plotting software

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• Matlab
• Gnuplot