1994 Catalog Data: 14:650:231 Mechanical Engineering Computational Analysis and Design(3 credits)

Computational methods used in modeling mechanical engineering systems. Design project using computer to judge engineering alternatives.

Prerequisite: 14:440:127 (Freshman computing course) Engineering majors only

Textbook: Gerald & Wheatley, Applied Numerical Analysis, 5th Ed., Addison-Wesley, Reading, MA, 1993.

Coordinator: R. Pelz, Associate Professor of Mechanical and Aerospace Engineering

Goals:

This course is designed to introduce to sophomores applied numerical analysis and computational problems found in mechanical engineering. The use of computers in engineering design and analysis is the main theme. Computer projects demonstrate the use of the computer as an engineering tool.

Conduct of course:

The course consists of two lectures of 80 minutes each per week. There are 5 quizzes throughout the semester. There are 4 application-based computer projects in which the students must write their own code and solvers. There is an expanded design project in which the computer is used to analyze/solve the problem and perform a certain optimizations of design. The projects and course lectures are closely integrated.

Topics:

1. Introduction to computers and programming.(1 class)
2. Solving nonlinear equations (3 classes)
3. Solving sets of equations (3 classes)
4. Interpolating polynomials (2 classes)
5. Numerical differentiation & integration (4 classes)
6. Design Project (2 classes)
7. Numerical solution to Ordinary Differential Equations (4 classes)
8. Boundary-Value Problems (2 classes)
9. Curve-fitting (1 class)
10. Quizzes (5 classes)
11. Review before Final (1 class)

Computer Projects:

1. This introductory project brings all students to an even level on the computer system, the graphics and programming. The project involves finding the roots and extrema of a high degree polynomial.
2. The project concerns finding the static loads in the members of a simple truss. The truss has 16 pin joints and 32 forces. A number of different applied loads were given to simulate a load moving across the lower part of the truss/bridge. Students had to derive and enter the 32x32 matrix of the structure, write their own linear system solver, and analyze the load distribution as the external loads change.
3. Using the actual (x,y) coordinates of a supercritical wing section, the students had to construct a cubic spline interpolating polynomial through the points and describe the section at another sequence of points.
4. The project concerns the integration and differentiation of tabular data. An example is to find the buoyancy force and center of buoyancy for a discretized ship hull.
5. The design project comes from dynamics, in which the students have to solve a system of nonlinear ordinary differential equations numerically for the trajectory of the body. The design aspect enter through an optimization with the design parameters being initial conditions and specific coefficients of the equations. The parameters are related to the physical systems. Multiple designs are requested.

ABET catagory content:

Engineering Science: 2 credits

Engineering Design: 1 credit

Prepared by Dr. R. Pelz March 1994