Course title
Strength of Materials

KANDA Yoshihiko
Course description
Analysis techniques (mathematical theory) to calculate the strength of the structure will be learned. Especially mathematical theory of elasticity and plasticity in three dimensions to apply to the finite element method will be studied in this lecture.
Purpose of class
Understanding of stress analysis techniques (mathematical theory) to the safety design of the structure in three dimensions.
・Learn how to express stress and strain in the three-dimensional state of the structure.
・Learn the calculation method of yielding and stress and strain in multiaxial stress state in three-dimensional space.
・Understand the fundamentals of finite element method analysis and learn the ability to calculate stress calculation with simple structure by finite element method.
Goals and objectives
  1. Understanding of the mathematical theory of elasticity and plasticity in three dimensions
  2. Understanding the constitutive equations of plasticity and its application to calculate the plasticity of metals.
  3. Understanding the basis of reliability analysis using the finite element method analysis and its application.
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Guidance for lectures on the strength of materials Review syllabus 60minutes
2. Stress Components in three dimensions
・Tensor representation of stress
・Stress in a given plane
・Coordinate transformation of stress and strain
Review handouts
(Stress Components in three dimensions)
3. Principal Stresses in Three Dimensions
・The principal stresses
・How to calculate the principal stresses.
・Principal Stresses in Two Dimensions
(Calculation of principal stress using Mole's circle)
Review handouts
(Principal Stresses)
4. Basics of Elastic Constitutive Equations
・Hook's law in three dimensions
・Plane Strain Problem
・Plane Stress Problem
Review handouts
(Elastic Constitutive Equations)
5. Finite Element Method (FEM) Analysis 1
・Stress analysis by matrix calculation
・Case study: Stress analysis of truss using rod elements
Review handouts
(Finite Element Method (FEM) Analysis 1)
6. Finite Element Method (FEM) Analysis 2
An example of elastic beam calculation using matrices B and D
・D Matrix (Material Property)
・B Matrix (Strain-Displacement Matrix)
・Energy Conservation Law of Finite Elements Method
・An Example of Deflection Calculation of A Cantilever Beam
Review handouts
(Finite Element Method (FEM) Analysis 2 )
7. Deviatoric Stress and Stress Invariants
・Deviatoric Stress
・Stress Invariants
・Deviatoric Invariants
Review handouts
(Deviatoric Stress and Stress Invariants)
8. Yield Criterion for Isotropic Material
・How to calculate Yielding in multi axial condition
Equivalent Stress
・Scalar representation of stress in multi-axial condition
・Yielding curves
Review handouts
(Yield Criterion and Equivalent Stress)
9. Basics of Constitutive Equations
Simplification of Stress-Strain Curves
・Full plastic
・Bilinear hardening law
Hook's law in three dimensions
Review handouts
(Constitutive Equations and Simplification of Stress-Strain Curves)
10. Incremental Strain Theory and Prandtl-Reuss Reuss Constitutive Equation
・Incremental Strain Theory
・Reuss Constitutive Equation
・Equivalent plastic strain increment and Equivalent plastic strain
Expression of plastic behavior by equivalent stress and equivalent plastic strain
・How to determine the undetermined multiplier
・Constitutive equations of plane strain and plane stress state
Review handouts
(Incremental Strain Theory and Prandtl-Reuss Reuss Constitutive Equation)
11. Case study of plane strain compression of block
・Equation of equilibrium of forces acting on the infinitesimal element
・Equation of yield criterion
・Pressure distribution
・Load and average pressure
Review handouts
(plane strain compression of the block)
12. Case study of axisymmetric compression of the cylinder
・Equation of equilibrium of forces acting on the infinitesimal element
・Yield criterion
・Load and average pressure
Review handouts
(axisymmetric compression of the cylinder )
13. Elastoplastic analysis of the truss using FEM
・Analysis of elastic deformation of truss
・Analysis of the secondary deformation (Plastic deformation)
・Relationship between external force and displacement
Review handouts
(Elastoplastic analysis of the truss)
14. Final report Review all handouts 120minutes
Total. - - 900minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Final report Total.
1. 30% 30%
2. 30% 30%
3. 40% 40%
Total. 100% -
Evaluation method and criteria
The final report is 100 points, Passes over 60 points of total points.
Understanding the case study on FEM and the case study on yield calculation is a guideline of 60 points.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Textbooks and reference materials
Understand the lecture contents of material mechanics.
Office hours and How to contact professors for questions
  • Wednesday, 10:00 to 12:00
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic self-management skills
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
Applicable Lectures will be given based on experience in design, reliability evaluation, and molding processes for automotive components.
Education related SDGs:the Sustainable Development Goals
    Last modified : Fri Feb 02 04:17:12 JST 2024