### 2020　Continuum Mechanics

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Undergraduate major in Systems and Control Engineering
Instructor(s)
Amaya Kenji  Miyazaki Yusuke
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Mon3-4(W611)  Thr3-4(W611)
Group
-
Course number
SCE.M301
Credits
2
2020
Offered quarter
1Q
Syllabus updated
2020/5/4
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

This course covers fundamentals of continuum mechanics. Continuum mechanics deals with the mechanics governing the deformation of both solid and fluid objects in nature. Topics of this course starts from mathematical preliminaries for analysis of continuum body such as configuration, vector and tensor analysis. Then, lectures cover fundamentals of strain, stress, constitutive equations, conservation of mass, momentum and energy to derive the governing equations of general continuous bodies. Next, lectures focuse on the analysis of the governing equation for both solid and fluid objects.

### Student learning outcomes

At the end of this course, students will be able to:
1) explain the fundamental concept of continuum mechanics applied to both solid and fluid objects in nature.
2) have an understanding of the concepts of finite deformation of bodies, stress, strain, and constitutive equations.

### Keywords

Continuum body, Solid mechanics, Fluid mechanics,Tensor analysis

### Competencies that will be developed

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

### Class flow

Towards the end of class, students are given exercise problems related to what is taught on that day to solve.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction of continuum mechanics Exercises to understand the mathematical preliminaries for analysis of continuum bodies
Class 2 Strain Exercises to understand the definitions of strain
Class 3 Stress Exercises to understand the definitions of stress
Class 4 Constitutive equations Exercises to understand the definitions of constitutive equations
Class 5 Mass conservation, continuum equations, Newton's laws of motion Exercises to understand laws of mass conservation, continuum equations, Newton's laws of motion
Class 6 The principal of virtual work, law of the conservation of energy Exercises to understand the principals of virtual work and law of the conservation of energy
Class 7 Analysis of various stress field in solids Exercises to analyze various stress field in solids
Class 8 Elastic wave propagation (1D,2D) Exercises to analyze 1D and 2D elastic wave propagation in solids
Class 9 Mathematical modeling of physical phenomena in the field and vector analysis Understanding of Mathematical modeling of physical phenomena in the field and vector analysis
Class 10 Equation of continuity and equation of conservation of momentum Understanding of Equation of continuity and equation of conservation of momentum
Class 11 Constitutive equations, basic equations of fluid dynamics Learn about constitutive equations and basic equations of fluid dynamics strain rates, perfect fluids, Newtonian fluids
Class 12 Navier-Stokes equations Exercise to understand Navier-Stokes equations
Class 13 Analysis of simple flow Learn about simple flows Poiseuille flow, Couette flow, Potential flow, and so on
Class 14 Final exam or explanation of the assignment Final exam or explanation of the assignment

### Textbook(s)

Text book specified by the instructor.

### Reference books, course materials, etc.

Course materials are provided during class.

### Assessment criteria and methods

Students will be assessed on their understanding of continuum mechanics, solid mechanics and fluid mechanics. Students course scores are based on exams(80%) and exercise problems.

### Related courses

• SCE.M304 ： Computational Mechanics
• SCE.A504 ： Advanced course of Computational Mechanics

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

No prerequisites. 