Numerical Analysis(2.0 credits)
|Course Type||:||Specialized Courses|
|Course Name||:||Automotive Engineering||Automotive Engineering|
|Starts 1||:||3 Autumn Semester||3 Autumn Semester|
|Lecturer||:||Toshiro MATSUMOTO Professor||Tsuyoshi INOUE Professor|
|The purpose of this course is to acquire the fundamentals of numerical analysis through multibody dynamics simulation and numerical issues related to finite element methods. Through this course, students will develop an understanding of (1) the principles of multibody dynamics and some other methods frequently used in numerical analyses, and (2) various computation algorithms used in multibody dynamics simulation and the finite element method (students will also solve some simple practical examples).
The second part of the class is focused on the study of numerical method to analyze a partial differential equation. When mechanical structures are designed, their physical behaviors must be calculated in advance. Since the actual design objects have complicated structures, their analytical solutions in mathematical representation cannot be obtained. Therefore, some numerical analysis methods are needed for the simulation of the related physical behavior. The differential equation which is treated in the class is the simplest partial differential equation, Laplace’s equation, for two-dimensional problems. The students study this partial differential equation, and a numerical method called boundary element method (BEM). The class is given based on the handouts and the students cope with the assignments for formulating BEM and example numerical demonstrations.
By finishing this class, the students are targeted to have the capability of doing the following skills:
1. Understanding Laplace’s equation
2. Derivation of Green’s identity from Laplace’s equation
3. Formulation of the boundary element method
4. Developing a simple boundary element code
|Calculus, Linear Algebra, Physics, Computer Software, Kinematics, Mechanical Vibration, Mechanics of Materials, Solid Mechanics, Vector Analysis|
1. Numerical integration methods: General guideline
2. Numerical integration methods: Euler method, Backward Euler method
3. Numerical integration methods: Runge Kutta method
4. Numerical integration methods: Adams method
5. Numerical integration methods: Newmark beta method
6. Summary of part (1) and Programming with Matlab
7. Laplace’s equation as a partial differential equation and its boundary value problem
8. Formula of integration by parts
9. Fundamental solution and derivation of Green’s identity
10. Derivation of boundary integral equation
11. Discretization of the boundary integral equation
12. Applying boundary conditions and derivation of a system of linear algebraic equations
13. Numerical demonstration of the boundary element method through some examples
Students are required to solve the problems shown in the printed material, and report subjects given in each week.
|For first half part:
Printed material will be distributed, or download page will be prepared.
For second half part:
Printed handouts are used.
|For first half part:
Planar Multibody Dynamics: Formulation, Programming, and Applications, Parviz Nikravesh
For second half part:
John Katsikadelis: The Boundary Element Method for Engineers and Scientists, 2nd Edition, Theory and Applications, ISBN: 9780128044933, eBook ISBN: 9780128020104, Academic Press, (2016)
|Grades will be based on the evaluation of first and second half parts:
For first half:
class participations and homework (50%) and reports and/or examination(50%)
For second half:
The understanding of the theory and computation algorithm of BEM is evaluated through assignments. Students can pass when the basic formulation of the boundary integral equation, its discretization procedure, and corresponding computational algorithm are understood. The grade is evaluated accordingly when they can formulate the boundary element method for more complicated problem and can develop a boundary element computer code.
|- No extra requirements are imposed.
- The classes will be given in face-to-face way and remote way through Zoom.
|Students can ask questions at any time during classes.
Questions during off-class hours can be asked at the lecturers' rooms:
* Prof. Yasumasa Ito