2020 Finite Element Analysis

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Academic unit or major
Undergraduate major in Mechanical Engineering
Yoshino Masahiko  Nakano Yutaka  Okuma Masaaki 
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Course description and aims

This course consists of lectures on the fundamental theory of the finite element method and exercises in finite element analysis using computers.
The aim of this course is for students to acquire the ability to make practical use of the finite element method.

Student learning outcomes

Students learn basic theory and practical analysis techniques of 2D elasticity finite-element method. They understand analysis precision, how to construct FEM models, and evaluation methods of the analysis result.

Course taught by instructors with work experience

Applicable How instructors' work experience benefits the course
A lecturer who have experience working at a company will educate them so that they can learn a wide range of practical knowledge on the importance of the fundamentals of FEM simulation and its applications, including experience in the company.


Elasticity, potential field, two dimensions, triangle element, isoparametric element

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

At each class, students are given a lecture and exercise problems. Use your own laptop computer.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction Do you understand the necessity of finite-element method?
Class 2 approximate methods of solution of differential equations To understand numerical methods for Poisson's equation.
Class 3 Finite element method for potential field, 1D finite element method To understand approximation method using 1D finite element method.
Class 4 Finite element method for potential field, 2D finite element method To understand approximation method using 2D finite element method.
Class 5 theory of elasticity To review theory of elasticity.
Class 6 Fundamental theory of elastic FEM, principle of the virtual work To formulate with the principle of virtual work.
Class 7 Triangle element To understand characteristics of the triangle elements.
Class 8 2D finite element method for elastic analysis To understand principle of 2D elastic FEM analysis.
Class 9 isoparametric element To understand a isoparametric element.
Class 10 2D finite element method with isoparametric element To understand 2D finite element method with isoparametric element.
Class 11 axisymmetric element To understand the axisymmetric element.
Class 12 Finite element method with axisymmetric element To understand finite element method with axisymmetric element.
Class 13 Expertise of finite element method To understand expertise of finite element method.
Class 14 Exercise in finite element analysis To solve exercise problems.


Lecture materials will be uploaded to OCW.

Reference books, course materials, etc.

Books specified by the instructor.

Assessment criteria and methods

To be evaluated based on reports and evaluation test.

Related courses

  • MEC.B213 : Partial Differential Equations
  • MEC.C201 : Mechanics of Materials
  • MEC.A201 : Engineering Mechanics
  • MEC.B214 : Vector Analysis
  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is required to have knowledge on "Linear Algebra I,II (LAS.M102,LAS.M106)","Mechanics of Materials A(MEC.C201)","Engineering Mechanics(MEC.A201)", Partial Differential Equations, Tensor, and Vector Analysis.


It is required to bring a note PC in which the software Excel is installed.

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