### 2016　Continuum Mechanics

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Undergraduate major in Materials Science and Engineering
Instructor(s)
Yasuda Kouichi
Course component(s)
Lecture
Day/Period(Room No.)
Tue7-8(S7-202)  Fri7-8(S7-202)
Group
-
Course number
MAT.C308
Credits
2
2016
Offered quarter
2Q
Syllabus updated
2016/4/27
Lecture notes updated
2016/7/26
Language used
Japanese
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### Course description and aims

This course gives an overview of mechanics, from Newtonian, Lagrangian, Hamiltonian formulation, and via Mechanics of Materials, to Continuum Mechanics. Students should acquire accomplishments to intuitively grasp force balance of multi-body systems and internal stress and strain states in materials although they are usually not visible. By solving each assignment one by one, the students can understand the general principles in mechanics, which is the fundamentals for modern scientists and engineers, and also brings the students touch of learning in their life.

### Student learning outcomes

By the end of this course, students will be able to
1) intuitively grasp force balance of multi-body systems
2) intuitively understand internal stress and strain states in materials
3) propose mechanical model to express phenomena in our real world
4) treat mathematical formulation in vector and tensor

### Keywords

Newtonian Mechanics, D'Alembert Principle, Free Body Diagram, Lagrangian, Hamiltonian, Stress Vector, Mohr's Circle, Tension, Compression, Shear, Beam, Stress Tensor, Strain Tensor, Displacement, Constitutive Equation, 2-dimensional Elastic Theory

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills ✔ Communication skills ✔ Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

The students are required to download teaching materials in every class and read it before coming to class.
The instructor explains the essential points of each class and gives assignment to the students.
The students should solve the assignments during the class.
The instructor designates one of the students who should explain the solution by using chalk and blackboard.
The instructor comments on it, or makes a correction when the solution is not perfect.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Review on Newtonian Mechanics, Equation of Motion, Principle of Virtual Work Explain Principle of Virtual Work
Class 2 Review on Newtonian Mechanics, D'Alembert Princple, Derive Lagrange Equation by using D'Alembert's Princple,
Class 3 Analytical Mechanics, Lagrangue Equation, Application to Coupled System between Mechanical and Electrical Systems Explain how to make Lagrangian and to solve Lagrange Equation
Class 4 Analytical Mechanics, Hamilton Equation, Hamiltonian in Quantum Mechanics Derive Hamilton Equation
Class 5 Mechanics of Materials, Stress Vector, Review on Vector, Free body Diagram Define Stress Vector
Class 6 Mechanics of Materials, Stress tensor, Introduction to Tensor, Mohr's Circle Derive Stress Tensor
Class 7 Mechanics of Materials, Strain, Hooke's Law, Young's modulus, Modulus of Rigidity, Poisson's Ratio, Bulk Modulus Define Strain Tensor and 4 Elastic Modulus
Class 8 Mechanics of Materials, Tension and compression of rod, Thermal Stress Soleve Problems on Tension and Compression in Rod and Thermal Sress
Class 9 Mechanics of Materials, Torsion, Bending of Beam, Shear Force Diagram, Bending Moment Diagram Solve Problems on Torsion and Bending Beam
Class 10 Mechanics of Materials, Displacement of Beam Solve Problem on Displacemnet of Bending Beam
Class 11 Continuum Mechanics, Stress Tensor, Equlibrium Equation Define Stress Tensor in general
Class 12 Continuum Mechanics, Strain Tensor, Compatibility Equation Define Strain Tensor in general
Class 13 Continuum Mechanics, Constitutive Equation, Generalized Hooke's Law Expalin Generalized Hooke's Law
Class 14 Continuum Mechanics, Fundamentals of 2-dimensional Elastic Theory, Stress Function Define Stress Functiona
Class 15 Continuum Mechanics, Application of 2-dimensional Elastic Thoery Show some exaples of 2 Dimentional Elastic theory

### Textbook(s)

Teaching materials are distributed in OCW-i

### Reference books, course materials, etc.

Landau and Lifshits: Mechanics in theoretical physics series, S.P.Timoshenko, and J.N.Goodier, Theory of Elasticity,

### Assessment criteria and methods

Students will be assessed on their understanding of Lagrange Equation, Free Body Diagram, Stress Tensor, Strain Tensor, and their ability to apply them to solve problems.
Students’ course scores are based on mid-term(50%) and final exams (50%)

### Related courses

• LAS.P101 ： Fundamentals of Mechanics 1
• LAS.P102 ： Fundamentals of Mechanics 2
• MAT.A202 ： Fundamentals of Mechanics of Materials F

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Taking the related classes is recommended, not mandatory.

### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

kyasuda[at]ceram.titech.ac.jp

### Office hours

Contact by e-mail in advance to schedule an appointment

### Other

The classes are served for students to use their brains and polish their intelligence.