弾性力学 / (IMAC-U) Theory of Elasticity

単位数／Credit(s): 2.00単位. 担当教員／Instructor: 山本 剛. 年度: 2025. 科目ナンバリング／Course Numbering: TMA-MEE329E. 開講言語／Language of Instruction: English.

開講年度／Year

2025年度前期

授業の目的・概要及び達成 方法等／Course Objectives and Summary/ Learning Goals (J)

The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)

When an elastic body is subjected to a load, it deforms and stresses are caused. The basis of continuum mechanics called elasticity which treats these phenomena mathematically is explained, where deformation is assumed to be infinitesimal. This lecture gives the basis of solid mechanics.

他の授業科目との関連及び 履修上の注意（E）／Relevance to Other Subjects/Considerations for Taking the Class

It is assumed that the students in the course will have fundamental knowledge in "Mechanics of Materials" and "Mathematics".

授業計画（E）／Course Description

1. Introduction of Mechanics of Elasticity
2. Inner and cross products
3. Strain-displacement relations in the rectangular coordinate system
4. Coordinate transformation equation
5. Compatibility equations for strain
6. Equations of Equilibrium in the rectangular coordinate system
7. Equations of Equilibrium in the cylindrical coordinate system
8. Cauchy's stress theorem and Principal stress
9. Constitutive equations
10. Navier equation
11. Plane theory of elasticity
12. Airy Stress Function1
13. Airy Stress Function2
14. Anisotropic elasticity
15. Summary
16. Examination

授業時間外学修／Preparation and Review(J)

The session time is limited and therefore self-directed learning is important. Students are required to prepare and review for each class.

授業時間外学修（E）／Preparation and Review

The students are requested to study the fundamental items described in the textbook before and after each class, and to elaborate the part(s) designated by the lecturer in the class. Several assignments will be provided in the course, and the students are asked to solve them and hand in their solutions as a report.

成績評価方法及び基準（E）／Evaluation methods and criteria

1. Assignments: 30%
2. Examination: 70%

教科書および参考書／Textbook and References

• Theory of Elasticity, Stephen P. Timoshenko, McGraw Hill Higher Education
• Statistical Mechanics of Elasticity, J.H. Weiner, Dover Publications

オフィスアワー／Office Hours(J)

The students are welcome to contact the lecturer in order to arrange an meeting for questions.
Contact details: gyamamoto@tohoku.ac.jp

連絡先（メールアドレス等）※Emailは＠の置き換え注意/Contact,etc)／Contact： Please insert '@' in the email address.

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