Continuum Mechanics

Numbering Code G-ENG01 5F003 LJ73
G-ENG02 5F003 LJ73
Year/Term 2022 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Mon.2
Instructor name SUGIURA KUNITOMO (Graduate School of Engineering Professor)
YAGI TOMOMI (Graduate School of Engineering Professor)
Outline and Purpose of the Course 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.
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.
Schedule and Contents Introductions, 1time, Yagi
- Outline of Structural Analysis
- Mathematical Preliminaries (Vectors and Tensors)

Matrices and tensors, 1time, Yagi
- Summation Convention
- Eigenvalues and Eigenvectors

Differential and integral calculus of tensors, 1time, Yagi
- Quotient Laws
- Divergence Theorem

Kinematics, 1time, Yagi
- Material Description
- Spatial Description
- Material derivative

Deformation and strain, 1times, Yagi
- Strain tensors
- Compatibility conditions

Stress and equilibrium equation, 1time, Yagi
- Stress Tensors
- Equilbrium Equations

Conservation law and governing equation, 1time, Yagi
- Conservation of Mass
- Conservation of Linear Momentum
- Conservation of Energy

Constitutive equation of idealized material, 1time, Sugiura
- Perfect Fluid
- Linear Elastic Material(Isotropic)

Elastic-plastic behavior and constitutive equation of construction materials, 1time, Sugiura
- Yield Criteria
- Flow Rule
- Hardening Rule

Boundary value problem, 1time, Sugiura
- Governing Equations and Unknowns
- Navier-Stokes Equation
- Navier Equation

Variational principle, 2time, Sugiura
- Principle of Virtual Work
- Principle of Complementary Virtual Work

Various kinds of numerical analyses, 2times, Sugiura
- Weighted Residual Method
- Finite Element Method

Confirmation of the attainment level of learning, 1time, All
Feedback based on the Final Examination
Evaluation Methods and Policy Assessment will be based on exam, report and participation.
Course Requirements Basic knowledge for structural mechanics, soil mechanics and fluid mechanics are required.
Study outside of Class (preparation and review) As appropriate, the assignments are given based on the content of Lecture.
Textbooks Textbooks/References Handouts are given
References, etc. not specified
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