Recently, computer simulation has been widely used for functional and strength design for electronic equipment and large structures.
In this computer simulation, the finite element method has succeeded in practical application of actual product design. In
order to utilize this finite element method, the understanding of the mathematical basis is indispensable, and the utilization
in the actual product design does not advance so much, since the theory is very difficult. The utilization of the computer
simulation is required for future industries, and it is necessary to learn the basis of the simulation in the university.
In this course, students learn the basic mathematical theory of the finite element method, which is most frequently used in
strength calculation of structures using recent computers, and the basis of the finite element method in product design by
solving some case studies using general-purpose FEM code.
Learn what the finite element method is. Especially, the mathematical theory used for the finite element method is studied.
In addition, the purpose of this lecture is to deepen the understanding of the basic theory of the finite element method,
and to enable to assemble a simple code. The purpose of this lecture is to deepen the understanding of the basic theory by
solving some case studies using the recent general-purpose finite element method code, and to image the application of the
finite element method to the design.
- Understand the basic mathematical theory of mechanical properties of materials.
- Understand the basic theory of the finite element method. Then, acquire the ability of strength calculation of a simple structure using the method.
- Acquire the ability to calculate the strength of a relatively simple structure using a general-purpose code of the finite element method.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | The outline of the finite element method is explained. In addition, how the method is used in industry will be introduced, and the necessity of the finite element method will be learned. | Prepara handouts | 190minutes |
| 2． | To understand the finite element method, it is essential to understand the mathematical theory of stress and strain of materials.
Here, we first learn in detail the mathematical description method for stress and strain in three-dimensional space. ・ Stress component notation ・ Stress invariant (principal stress) |
Prepara handouts | 190minutes |
| 3． | Stress and strain physically form separate spaces. To describe the deformation behavior of an actual material, it is necessary
to think of a constitutive equation that connects these two separate spaces. Here, we will learn about the constitutive equations
in the range where the material behaves elastically. ・ Hooke's law in 3D space ・ Various quantities of elastic properties in three-dimensional space ・ Hooke's law using a two-dimensional approximation method |
Prepara handouts | 190minutes |
| 4． | As a continuation of the lecture on constitutive equations, we will learn how to determine when a material reaches its elastic
limit and its mathematical description. ・ Introduction of deviation stress and concept of invariants ・ Mises yielding judgment ・ Understanding of material behavior by yield surface |
Prepara handouts | 190minutes |
| 5． | The constitutive equation of plastic deformation is examined as a mathematical description of the deformation behavior when
the material exceeds the yield. ・ Equivalent stress ・ Prandtl-Reuss's constitutive equation ・ Path-dependent strain concept based on incremental theory ・ Equivalent strain increment and equivalent strain |
Prepara handouts | 190minutes |
| 6． | In order to understand and utilize the constitutive equations that we have learned so far, we will solve a case study on plastic
working in an exercise format. ・ Example of block compression deformation analysis ・ Example of plastic bending analysis of thin plate |
Prepara handouts | 190minutes |
| 7． | From this lecture, we will start studying the basic theory of the finite element method. First, we will learn the idea of
the stiffness equation using a simple strength of materials problem. ・ Elements and discretization problems ・ Stiffness equation (elemental stiffness equation, total stiffness equation) ・ Examples of statically indeterminate problems |
Prepara handouts | 190minutes |
| 8． | The mechanical calculation using the stiffness equation is examined using the analysis of the cantilever. ・ Creation of material matrix ・ Creation of displacement-strain matrix ・ Stiffness matrix and energy conservation law ・ Inverse matrix solving and displacement calculation |
Prepara handouts | 190minutes |
| 9． | Phase transformation and microstructural formation *Kinetics od solid-state reaction *Multipahse trasformation *Isothremal transformation *Continuous transformation diagram |
Prepara handouts | 190minutes |
| 10． | Learn about the discretization and numerical integration methods required for the finite element method. ・ Discretization and elements ・ Numerical integration method |
Prepara handouts | 190minutes |
| 11． | Learn how to use general-purpose FEM code using an actual program. ・ Types and features of general-purpose FEM codes ・ How to use general-purpose FEM code |
Prepara handouts | 190minutes |
| 12． | Learn how to use a general-purpose FEM code using an example of elastic deformation. ・ Calculation of stress, strain and deflection of cantilever beams ・ Calculation of stress, strain and displacement in truss structure |
Prepara handouts | 190minutes |
| 13． | Learn how to use a general-purpose FEM code using an example of deformation that exceeds the elastic limit of a material. ・ Yield judgment in simple tension and bending deformation of plate ・ Yield judgment in multiaxial stress state |
Prepara handouts | 190minutes |
| 14． | Summary | Review all handouts | 180minutes |
| Total. | - | - | 2650minutes |
| Practice | Final Report | Total. | |
|---|---|---|---|
| 1. | 40% | 60% | 100% |
| 2. | 0% | ||
| Total. | 40% | 60% | - |
A report regarding the lecture contents(50%）
Practice regarding lecture contents(50%）
Understanding the mathematical description of mechanical properties and how to solve basic mechanical problems using the finite element method is the basis of evaluation.
Practice regarding lecture contents(50%）
Understanding the mathematical description of mechanical properties and how to solve basic mechanical problems using the finite element method is the basis of evaluation.
- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| Applicable | This lecture given based on the practical experience of reliability calculation for design and manufacture of ships and bridges. |
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
- 12.RESPONSIBLE CONSUMPTION & PRODUCTION
Last modified : Fri Mar 18 21:59:23 JST 2022