授業の目的 【日本語】
Goals of the Course(JPN) | | The finite element method (FEM) is widely used in various engineering problems, and the students study the advanced physical modelling of the phenomena, constructing the corresponding mathematical models, advanced computational algorithms of FEM, and how to develop the computer code.
The lecture is based on the handouts and the students are going to cope with the assignments for formulating FEM and example numerical demonstrations. |
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授業の目的 【英語】
Goals of the Course | | The finite element method (FEM) is widely used in various engineering problems, and the students study the advanced physical modelling of the phenomena, constructing the corresponding mathematical models, advanced computational algorithms of FEM, and how to develop the computer code.
The lecture is based on the handouts and the students are going to cope with the assignments for formulating FEM and example numerical demonstrations. |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | By finishing this class, the students are targeted to have the capability of doing the following skills:
1. Developing the advanced physical model
2. Developing the advanced mathematical model corresponding to the above derived physical model
3. Formulation of the multi-dimensional finite element method
4. Developing and using a finite element code |
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到達目標 【英語】
Objectives of the Course | | By finishing this class, the students are targeted to have the capability of doing the following skills:
1. Developing the advanced physical model
2. Developing the advanced mathematical model corresponding to the above derived physical model
3. Formulation of the multi-dimensional finite element method
4. Developing and using a finite element code |
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バックグラウンドとなる科目【日本語】
Prerequisite Subjects | | | Mathematics I, II (Calculus, Linear Algebra), Vector Analysis, Elasticity |
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バックグラウンドとなる科目【英語】
Prerequisite Subjects | | | Mathematics I, II (Calculus, Linear Algebra), Vector Analysis, Elasticity |
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授業の内容【日本語】
Course Content | | 1. Vector, tensor, index notation
2. Formula of integration by parts
3. Cauchy’s formula and stress tensor
4. Balance of force and moment, derivation of equilibrium equation and symmetry of stress tensor
5. Strain tensor
6. Generalized Hooke’s law
7. Navier’s equation
8. Virtual work principle
9. Weighted-residual form and weak form
10. Discretization of weak form and introduction of shape functions
11. Expression of weight-function (virtual displacement) with shape function
12. Derivation of stiffness matrix and equivalent nodal force vector by means of element integration
13. Computation algorithm of finite element method
14. Numerical examples through actual finite element code
Assignments are given regarding the lecture topics. |
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授業の内容【英語】
Course Content | | 1. Vector, tensor, index notation
2. Formula of integration by parts
3. Cauchy’s formula and stress tensor
4. Balance of force and moment, derivation of equilibrium equation and symmetry of stress tensor
5. Strain tensor
6. Generalized Hooke’s law
7. Navier’s equation
8. Virtual work principle
9. Weighted-residual form and weak form
10. Discretization of weak form and introduction of shape functions
11. Expression of weight-function (virtual displacement) with shape function
12. Derivation of stiffness matrix and equivalent nodal force vector by means of element integration
13. Computation algorithm of finite element method
14. Numerical examples through actual finite element code
Assignments are given regarding the lecture topics. |
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成績評価の方法と基準【日本語】
Course Evaluation Method and Criteria | | | The understanding of the theory and computation algorithm of FEM is evaluated through assignments and achievement test. Students can pass when the basic formulation of the weak-form of finite element method and its corresponding computational algorithm are understood. The grade is evaluated accordingly when they can formulate the finite element method for more complicated problem and can develop a finite element computer code. |
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成績評価の方法と基準【英語】
Course Evaluation Method and Criteria | | | The understanding of the theory and computation algorithm of FEM is evaluated through assignments and achievement test. Students can pass when the basic formulation of the weak-form of finite element method and its corresponding computational algorithm are understood. The grade is evaluated accordingly when they can formulate the finite element method for more complicated problem and can develop a finite element computer code. |
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履修条件・注意事項【日本語】
Course Prerequisites / Notes | | - No extra requirements are imposed.
- The classes will be given in face-to-face way. |
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履修条件・注意事項【英語】
Course Prerequisites / Notes | | - No extra requirements are imposed.
- The classes will be given in face-to-face way. |
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教科書【日本語】
Textbook | | | Handouts are delivered and other documents are put on Web and downloaded. |
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教科書【英語】
Textbook | | | Handouts are delivered and other documents are put on Web and downloaded. |
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参考書【日本語】
Reference Book | | Introduction to Approximate Solution Techniques, Numerical Modeling, and
Finite Element Methods, Marcel Dekker Inc |
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参考書【英語】
Reference Book | | Introduction to Approximate Solution Techniques, Numerical Modeling, and
Finite Element Methods, Marcel Dekker Inc |
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授業時間外学習の指示【日本語】
Self-directed Learning Outside Course Hours | | | Try to derive the presented formulas by yourself. |
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授業時間外学習の指示【英語】
Self-directed Learning Outside Course Hours | | | Try to derive the presented formulas by yourself. |
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使用言語【英語】
Language used | | |
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使用言語【日本語】
Language used | | |
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授業開講形態等【日本語】
Lecture format, etc. | | | Lectures are given in face-to-face way in the classroom. |
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授業開講形態等【英語】
Lecture format, etc. | | | Lectures are given in face-to-face way in the classroom. |
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遠隔授業（オンデマンド型）で行う場合の追加措置【日本語】
Additional measures for remote class (on-demand class) | | |
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遠隔授業（オンデマンド型）で行う場合の追加措置【英語】
Additional measures for remote class (on-demand class) | | |
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