57:021 Principles of Design I



57:021 Principles of Design I

Fall 2000

2000Catalog Data: 57:021 Principles of Design I. 3 credit hours.

Description Two-to-three week projects involving identification, modeling, and analysis of design problems using optimization principles, methodology and computer-aided design. Junior standing required. Prerequisites: 57:007, 22M:40.

Textbook: Arora, J.S., Introduction to Optimum Design, McGraw Hill Book Co., New York, 1989.

References: Bhatti, M. A., Practical Optimization Methods with Mathematica Applications, Springer-Verlag, 2000.

Belegundu, A.D. and Chandrupatla, T.R., Optimization Concepts and Applications in Engineering, Prentice Hall, New Jersey, 1999.

Coordinator: J.S. Arora, Civil and Environmental Engineering, and Mechanical Engineering

Goals: Goal of the course is to teach the students basic ideas of designing optimum systems. Formulation of a design problem as an optimization problem is covered. Basic concepts of optimization and optimality conditions are covered in class with simple examples. Numerical process of finding roots of nonlinear equations is introduced. Simplex method for linear design optimization problems is covered. Post-optimality analysis is discussed. Numerical methods for solving unconstrained optimization problems are presented and illustrated. Two numerical methods for solving constrained optimization problems are discussed and illustrated. Students use the material learned in the class on 4 team projects and produce written reports.

Learning Objectives:

• Overall process of designing new systems or improving existing systems

• Economic considerations in the design process

• Formulation of a design problem as an optimization problem

• Graphical solution of design optimization problems to illustrate some basic concepts

• Basic principles of optimum design for unconstrained and constrained problems and their illustration using simple design examples: Optimality conditions

• Methods for optimum design for linear problems: Linear programming using Simplex method

• Methods for optimum design for nonlinear unconstrained problems: One dimensional search, steepest descent, conjugate directions, Newton's method

• Methods for optimum design for nonlinear constrained problems: Nonlinear programming, sequential linear programming, and constrained steepest descent method

• Team Work: Students work on four group projects and produce written reports

Prerequisites by Topic: 1. Linear algebra. 2. Calculus of several variables. 3. FORTRAN/Use of Network computers

Topics (Class Hours): 1. Economic analysis (3)

2. Design optimization problem formulation (3)

3. Graphical Optimization (4)

4. Unconstrained Design Concepts (4)

5. Constrained Design Concepts (10)

6. Design of linear systems (LP) (10)

7. Design of nonlinear systems (NLP) (11)

TOTAL (45)

Computer Usage: Computer is extensively used in the course. Three programs are introduced:

1. MATHEMATICA for graphical optimization, and roots of nonlinear equations

2. LINDO for linear programming problems

3. IDESIGN for nonlinear programming problems

Team Projects: 1. Graphical Optimization. 2. Optimality conditions. 3. Design of Linear Systems (LP)

4. Design of Nonlinear Systems (NLP)

Principles of Design I 57:021

|Contribution to |ABET Outcomes |Course Activity |Material to be Collected |

|Outcome | | | |

| |They will have the ability to apply knowledge of |Use of calculus, linear algebra, statics, basic heat |Homework and exams |

|● |mathematics, science and engineering in their |transfer, stress analysis. | |

| |chosen fields. | | |

| |They will have the ability to design and conduct |None | |

| |engineering experiments, and to analyze and | | |

| |interpret experimental results. | | |

|○ |They will have the ability to design systems, |Students work on assigned projects in groups of 3. The |Project reports |

| |components, or processes to meet specified |projects are chosen from different fields of engineering | |

| |objectives in their chosen fields. | | |

| |They will have the ability to work as members of |Three students from different fields of engineering are |Project reports |

|○ |multidisciplinary project and/or research teams, |selected randomly to form design teams. Team members | |

| |and have an understanding of leadership in teams |work on assigned design projects from different | |

| |and organizations. |disciplines of engineering | |

| |They will have the ability to identify, |The student completes several homework assignments that |Homework, exams and project |

|● |formulate, and solve engineering problems. |require them to formulate and solve several simple design|reports |

| | |problems. Four team projects require them to work on | |

| | |some what more involved design problems | |

|○ |They will have an understanding of professional |Since the design team members are from different fields, |Project reports |

| |and ethical responsibility and the value of |and the assigned projects may be from another fields, tem| |

| |mentorship and peer support. |members learn from each other about different fields | |

| |They will have the ability to communicate |The student writes four design project reports containing|Project reports. |

| |effectively in written form. |their problem formulation, solution procedure, results | |

|● | |and conclusions. | |

| |They will have the ability to communicate |None | |

| |effectively in oral form. | | |

| |They will have the ability to communicate |Written reports include graphical representation of data |Project reports. |

|○ |effectively in graphical form. |and graphical optimization where appropriate. | |

| |They will have an education that is supportive of|None | |

| |a broad awareness of the diversity of the world | | |

| |and its cultures, and that provides an | | |

| |understanding of the impact of engineering | | |

| |practice in the global community. | | |

| |They will understand the importance of updating |None | |

| |and maintaining their technical skills and | | |

| |continuing their education throughout their | | |

| |professional careers. | | |

| |They will have a knowledge of contemporary |Contemporary examples of system designs are presented in | |

| |issues. |lecture. | |

| |They will have the ability to use the principles,|Word processor, MATHEMATICA, LINDO, and IDESIGN programs |Home work and project reports. |

|○ |techniques, skills and modern engineering tools |are used in projects and home work. | |

| |necessary for successful engineering practice | | |

| |and/or research in their chosen fields. | | |

○ denotes moderate contribution to the outcome ● denotes substantial contribution to the outcome

Prepared by: Jasbir S. Arora Date: 13 October 2000

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