Course title
Finite Element Method

YOSHIHARA Shouichirou
Course description
With the development of computers, the accuracy of structural analysis has improved dramatically, and this method has become indispensable for evaluating stress and strain in structures. However, the finite element method in structural analysis is an application and development of Newton's laws and material mechanics, and it goes without saying that the accumulation of the basics has led to the development of today's simulation analysis. In this lecture, we will learn the analytical methods of the finite element method, understand them through exercises, and deepen our physical understanding by conducting our own analyses and comparing the results with reference solutions obtained by analytical methods.
Purpose of class
The objectives of this class are as follows:.
1. To demonstrate the mechanics of materials (understanding by simplified models) by 3D analysis and to recognize the agreement and disagreement between them. 2.
2. To understand the significance and limitations of mechanics of materials models, and to acquire 2D and 3D CAE analysis methods.
Goals and objectives
  1. To learn CAE methods based on the finite element method and to understand deformation and stress.
  2. To be able to explain the analysis method of finite element analysis.
  3. To be able to perform stress analysis and coupled behavior analysis using commercially available software and to quantitatively evaluate deformation phenomena using CAE.
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Overview of the finite element method
Structural analysis
Components and types
Engineering simulation
Matrix structural analysis
Contents of Chapter 1 190minutes
2. Matrix structural analysis
Matrix structure analysis of a spring
Chapter 2, Section 2.1. 190minutes
3. Matrix structural analysis
Matrix analysis of a truss
Chapter 2, Section 2.2. 190minutes
4. Finite element method for one-dimensional elastic bodies
Dynamics of 1D elastic bodies
Chapter 3, Section 3.1. 190minutes
5. 3.1次元弾性体の有限要素法
第3章3.2節の内容 190minutes
6. Midterm exam and explanation Review of lessons 1 through 5 and midterm exam 190minutes
7. Finite element method for two-dimensional elastic bodies
Concept and notation of tensor
Dynamics of two-dimensional elastic bodies
Chapter 4, Sections 4.1 - 4.2. 190minutes
8. Finite element method for two-dimensional elastic bodies
Finite element method for two-dimensional elastic bodies
Chapter 4, Section 4.3. 190minutes
9. Two-dimensional isoparametric elements
Four-node isoparametric quadrilateral elements
8-node isoparametric quadrilateral elements
Chapter 5, Sections 5.1-5.2. 190minutes
10. Two-dimensional isoparametric elements
Triangular first-order elements using area coordinates
Six-node isoparametric triangular quadratic element with area coordinates
Numerical examples of the approximate performance of quadrilateral and triangular elements
Chapter 5, Sections 5.3 to 5.5. 190minutes
11. 3-D isoparametric elements Contents of Chapter 6 190minutes
12. Simulation analysis of commercially available software
Finite element method for beams
Refer to handouts, write reports 190minutes
13. Simulation analysis of commercially available software
Consideration of the analysis results of the finite element method for beams
Refer to handouts, write reports 190minutes
14. Final exam and explanation Review of lectures 7 to 13 and final exam 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Report midterm examination final exam Total.
1. 0% 20% 20% 40%
2. 0% 20% 20% 40%
3. 20% 0% 0% 20%
Total. 20% 40% 40% -
Evaluation method and criteria
There will be a report (20 points), a mid-term exam (40 points), and a final exam (40 points), for a total of 100 points. The report will be divided into two parts.
Of the 100 points, 60 points will be considered a passing grade. The criterion for passing this course is to be able to understand the analysis methods of the finite element method. In addition, the student should be able to calculate stress and strain using the finite element method.
Textbooks and reference materials
The following is a list of planned textbooks.
Nonlinear CAE Association (ed.), Finite Element Method Learning by Example, Morikita Publishing Co. in Japanese
Students should take Strength of Materials.
Office hours and How to contact professors for questions
  • Available on Thursdays from 12:30 to 1:00 p.m.
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic problem-solving skills
Active-learning course
Most classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
Last modified : Fri Mar 18 22:05:07 JST 2022