## Course Title : Continuum Mechanics

Code 31170 3rd year 2 No Restriction Lecture Japanese Hosoda, T. and Higo, Y.,

### Course Description

Continuum Mechanics is a branch of the physical sciences concerned with the deformations and motions of continuous media under the influence of external effects.
The following basic items are explained with exercises: Fundamentals of tensor analysis, Mathematical formulation of srain, motion and stress, Conservation laws of continuous media (mass, momentum, angular momentum, energy consevation laws), Constitutive laws of elastic body and Newtonian fluids, Principle of vurtual work and minimum potential energy based on the calculus of variations, Finite Element Method, Applications in Elasticity and Fluid Dynamics.

### Grading

Mainly regular examination. Reports and attendance are also considered for grading.

### Course Goals

Based on the clear understanding of the mathematical formulation on deformation, stress and constitutive laws, students are requested to understand the derivation of the Equation of motion, Conservation laws of angular momentum and energy, certainly. Principle of vurtual work and minimum potential energy are attached inportance as the basis of Finit Element Method.

### Course Topics

Theme Class number of times Description
Elementary knowledge on tensor analysis 2 Definition of tensors, Integral theorem, Material derivative over a material volume, Transformation of components of tensors, etc.
Stress, strain and strain rate tensors 2 Definition of stress, strain and strain rate tensors, Transformation of components of these tensor variables, Invariants under coordinates transformation, Compatibility condition of strain, etc.
Mathematical formulation of conservation laws 2 Mathematical expression of conservation laws of continuous media (mass, momentum, angular momentum, energy)
Constitutive law of solids and fluids 2 Constitutive laws of elastic & visco elastic body and Newton fluids
Principles based on the calculus of variations and FEM 2 Principle of vurtual work and minimum potential energy based on the calculus of variations, Finite Element Method, etc.
Applications in elasticity and fluid dynamics 4 Applications in Elasticity and Fluid Dynamics. Wave propergation in elastic body, Thermal convection and Lorentz Chaos, etc.
Achievement confirmation 1 Achievement of learning is confirmed.

### Textbook

Printed materials on the contents of this subjetc are distributed in class.

### Prerequisite(s)

Basic understanding on differential and integral calculus and linear algebra

### Additional Information

Students can contact with Prof. Hosoda by sending e-mail to hosoda.takashi.4w@kyoto-u.ac.jp or visiting Hosoda's office (Katsura C1-3-265).