Course Title : Continuum Mechanics

Code 10F003 Master and Doctor Course 1st term Mon 2nd C1-192 2 No Restriction Lecture Japanese Kunitomo Sugiura, Tomomi Yagi,

Course Description

Continuum mechanics is a unified basis for solid mechanics and fluid mechanics. The aims of this course are to introduce the continuum mechanics from their basics to the some forms of constitutive law and also to provide students with mathematical way of understanding the continuum mechanics. This course contains the fundamentals of vector and tensor calculus, the basic equations of continuum mechanics, the tensor expressions of elastic problems and further applications.

Assessment will be based on exam, report and participation.

Course Goals

Fundamental theorems on structural mechanics and design will be learned, and ability to judge the proprieties of each computational structural analysis will be acquired.

Course Topics

Theme Class number of times Description
Introductions 1 - Outline of Structural Analysis
- Mathematical Preliminaries(Vectors and Tensors)
Matrices and tensors 1 - Summation Convention
- Eigenvalues and Eigenvectors
differential and integral calculus of tensors 1 - Quotient Laws
- Divergence Theorem
Kinematics 1 - Material Description
- Spatial Description
- Material derivative
Deformation and strain 2 - Strain tensors
- Compatibility conditions
Stress and equilibrium equation 1 - Stress Tensors
- Equilbrium Equations
Conservation law and governing equation 1 - Conservation of Mass
- Conservation of Linear Momentum
- Conservation of Energy
Constitutive equation of idealized material 1 - Perfect Fluid
- Linear Elastic Material(Isotropic)
Elastic-plastic behavior and constitutive equation of construction materials 1 - Yield Criteria
- Flow Rule
- Hardening Rule
Boundary value problem 1 - Governing Equations and Unknowns
- Navier-Stokes Equation
- Navier Equation
Variational principle 1 - Principle of Virtual Work
- Principle of Complementary Virtual Work
Various kinds of numerical analyses 2 - Weighted Residual Method
- Finite Element Method
Confirmation of the attainment level of learning 1 Feedback based on the Final Examination

Prerequisite(s)

Basic knowledge for structural mechanics, soil mechanics and fluid mechanics are required.

Independent Study Outside of Class

As appropriate, the assignments are given based on the content of Lecture.