## Course Title : Continuum Mechanics

Code 35150 3rd year 1st term Tuesday・5 kyotsu4 2 This class is intended mainly for students of the International Course. Lecture English Hosoda, T., Higo, Y. and Pipatpongsa, T.

### 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 such as fundamentals of tensor analysis, Mathematical formulation of stress, strain, motion and displacement, Conservation laws of continuous media (mass, momentum, angular momentum, energy conservation laws), constitutive laws of solids and fluids, principle of virtual work and minimum potential energy based on the calculus of variations and applications in elasticity, stress distribution, wave propagation and fluid dynamics.

Mainly regular examination. Assignments are also considered to some extent.

### Course Goals

Based on the clear understanding of the mathematical formulation on deformation, stress and constitutive laws, students are required to understand the derivation of the equation of motion, conservation laws of angular momentum and energy. Principle of energy, variational method and initial-boundary-value problems are appended for enhancing understanding through theoretical applications

### 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
Principle of energy, variational method and initial-boundary-value problems 2 Principle of virtual work and minimum potential energy based on the calculus of variations as well as initial-boundary-value problems
Applications in elasticity and fluid dynamics 4 Applications in Elasticity and Fluid Dynamics. Stress distribution and Wave propagation in elastic body, Thermal convection and Lorentz Chaos, etc.
Class feedback 1 Achievement confirmation

### Textbook

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

### Textbook(supplemental)

P. Chadwick, "Continuum Mechanics: Concise Theory and Problems", Dover Publications
A.J.M. Spencer, "Continuum Mchanics", Dover Publications
G.E. Mase, "Schaum's Outline of Continuum Mechanics", McGraw-Hill

### Prerequisite(s)

Basic understanding on differential and integral calculus and linear algebra