Nagoya University, School of Engineering Lecture information system (SYLLABUS)

### Numerical Analysis(2.0 credits)

Code:10261
Course Type:Specialized Courses
Class Format:Lecture
Course Name : Automotive Engineering Automotive Engineering
Starts 1 : 3 Autumn Semester 3 Autumn Semester
Elective/Compulsory : Elective Elective
Lecturer : Toshiro MATSUMOTO Professor  Tsuyoshi INOUE Professor

 •Course Purpose 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 •Prerequisite Subjects Calculus, Linear Algebra, Physics, Computer Software, Kinematics, Mechanical Vibration, Mechanics of Materials, Solid Mechanics, Vector Analysis •Course Topics (First part) 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 (Second part) 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. •Textbook For first half part: Printed material will be distributed, or download page will be prepared. For second half part: Printed handouts are used. •Additional Reading 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) •Grade Assessment 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. •Notes - No extra requirements are imposed. - The classes will be given in face-to-face way and remote way through Zoom. •Contacting Faculty Students can ask questions at any time during classes. Questions during off-class hours can be asked at the lecturers' rooms: * Prof. Yasumasa Ito E-mail: yito(at)nagoya-u.jp

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