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Numerical Applications

ME 493. Numerical Applications in Mechanical Analysis and Design - in this course, various solution techniques to numerically solve mechanical engineering problems are studied. Problem topics are generated from mechanical design, mechanism and thermal analysis, and special subjects such as dynamics of satellites and interplanetary spacecraft. Both user generated codes and standard software libraries are employed. Excel, MathCAD, and Visual Basic were extensively used in this course.

The main topics of study in this course are solving differential equations, non-linear equations, and non-linear interpolation.

Solving Differential Equations - I created a spreadsheet to use Euler's Method and Modified Euler's Method for solving a differential equation. The results of both methods are plotted against the exact solution to visually see the accuracy of each method.

Solving a non-linear equation using Visual Basic - One typical problem in engineering is the study of heat transfer through a wall. The coefficient of conduction, convection, and width of the wall are used to define what's called the Biot number. This number is used to solve several roots of a trigonometric equation which will then be used to solve the amount of heat transfer through the wall. I created a program the calculates the first four roots of the trigonometric equation. These results are usually included in a table in heat transfer textbooks, but this program provides more accurate results. In addition, I used a variable damping coefficient that helps reduce the number of required iterations.

Calculating a derivative from an unknown function using data points - Another program I developed takes data from a function of time, and calculates the derivative. The program will then save the data to a file with the x values (time), y values (temperature), and the derivative (rate of change of temperature). It also outputs the temperature at any point within the interval, even if that point is not one of the data points. I used an accurate, non-linear method for interpolation for precise results.