Analysis techniques (mathematical theory) to safety design of the structure will be learned. Especially, mathematical theory
of elasticity and plasticity in three dimensions will be studied in this lecture.

Understanding of stress analysis techniques (mathematical theory) to 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.

・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.

- Understanding of mathematical theory of elasticity and plasticity
- Understanding of the constitutive equations of plasticity and its application to reliability analysis.
- Understanding of basis of reliability analysis using the finite element method analysis and its application.

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1. | Guidance and Stochastic basis of reliability engineering | Review handouts | 190minutes |

2. | Stress Components in 3 dimensions （Tensor representation of stress） |
Review handouts (Stress Components in 3 dimensions) |
190minutes |

3. | Stress in a given plane · Coordinate transformation of stress and strain |
Review handouts (Stress in a given plane) |
190minutes |

4. | Principal Stresses in Three Dimensions ・What is principal stresses. ・How to calculate the principal stresses. |
Review handouts (Principal Stress) |
190minutes |

5. | Principal Stresses in Two Dimensions (Calculation of principal stress using Mole's circle) |
Review handouts (Principal Stress) |
190minutes |

6. | Deviator Stress and Stress Invariant ・Deviator Stress and plastic deformation ・Stress Invariant |
Review handouts (Stress Invariant) |
190minutes |

7. | Yield Criterion for Isotropic Material ・Yielding ・How to calculate Yielding in multi axial condition ・Yielding curves |
Review handouts (Yield Criterion ) |
190minutes |

8. | Equivalent Stress ・Scalar representation of stress in multi axial condition |
Review handouts (Equivalent Stress) |
190minutes |

9. | Basics of Elastic Constitutive Equations ・Hook's law in three dimensions |
Review handouts (Elastic Constitutive Equations) |
190minutes |

10. | Simplification of Stress-Strain Curves ・Full plastic ・Ramberg-Osgood ・Bilinear hardening law |
Review handouts (Stress-Strain Curves) |
190minutes |

11. | Incremental Strain Theory and Prandtl-Reuss Reuss Constitutive Equation ・Incremental Strain Theory ・Reuss Constitutive Equation ・Equivalent plastic strain increment and Equivalent plastic strain |
Review handouts (Constitutive Equation for plasticity) |
190minutes |

12. | 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 (Equivalent plastic strain) |
190minutes |

13. | Basic of finite element analysis ・Stress analysis by matrix calculation ・Case study: Stress analysis of truss using rod elements |
Review handouts (Basic of finite element analysis) |
190minutes |

14. | Final exam and Commentary | Review all handouts | 180minutes |

Total. | - | - | 2650minutes |

Practice problem | Final exercise | Total. | |
---|---|---|---|

1. | 10% | 20% | 30% |

2. | 15% | 20% | 35% |

3. | 15% | 20% | 35% |

Total. | 40% | 60% | - |

Practice problem 40 points and final exercise 60 points, Passes over 60 points

The Mathematical Theory of Plasticity

Materials phisics1 and Materials phisics2

Materials phisics1 and Materials phisics2

- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge

Work experience | Work experience and relevance to the course content if applicatable |
---|---|

Applicatable | Lecture of Strength of Materials is given Based on the practical experience of reliability calculation for design and manufacture of ships and bridges. |

Last modified : Wed Jun 26 04:04:09 JST 2019