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.

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.

・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 the mathematical theory of elasticity and plasticity in three dimensions
- Understanding the constitutive equations of plasticity and its application to calculate the plasticity of metals.
- Understanding the 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 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) |
60minutes |

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) |
60minutes |

4. | Basics of Elastic Constitutive Equations ・Hook's law in three dimensions ・Plane Strain Problem ・Plane Stress Problem |
Review handouts (Elastic Constitutive Equations) |
60minutes |

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) |
60minutes |

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 ) |
60minutes |

7. | Deviatoric Stress and Stress Invariants ・Deviatoric Stress ・Stress Invariants ・Deviatoric Invariants |
Review handouts (Deviatoric Stress and Stress Invariants) |
60minutes |

8. | Yield Criterion for Isotropic Material ・Yielding ・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) |
60minutes |

9. | Basics of Constitutive Equations Simplification of Stress-Strain Curves ・Full plastic ・Ramberg-Osgood ・Bilinear hardening law Hook's law in three dimensions |
Review handouts (Constitutive Equations and Simplification of Stress-Strain Curves) |
60minutes |

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) |
60minutes |

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) |
60minutes |

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 ) |
60minutes |

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) |
60minutes |

14. | Final report | Review all handouts | 120minutes |

Total. | - | - | 900minutes |

Final report | Total. | |
---|---|---|

1. | 30% | 30% |

2. | 30% | 30% |

3. | 40% | 40% |

Total. | 100% | - |

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.

Understanding the case study on FEM and the case study on yield calculation is a guideline of 60 points.

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. |

Last modified : Sat Sep 09 08:46:16 JST 2023