Numerical Analysis

Course Information

College	Toyama College	Year	2022
Course Title	Numerical Analysis
Course Code	0034	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 2
Department	ECOdesign Engineering Course	Student Grade	Adv. 2nd
Term	First Semester	Classes per Week	2
Textbook and/or Teaching Materials	計算力学　有限要素法の基礎，日本計算工学会，竹内則雄，樫山和男，寺田賢二郎
Instructor	Shirakawa Hidemi

Course Objectives

Through this course, understanding of the following will be facilitated
1. finite element method (FEM)
2. matrix structural analysis
3. solid mechanics
4. heat transfer
5. fluid mechanics
6. CAD&CAE

Rubric

	理想的な到達レベルの目安	標準的な到達レベルの目安	未到達レベルの目安
Finite element method (FEM)	Clearly understands finite element method (FEM), and has the ability to explain FEM in detail	Ability to explain FEM in general	Unable to explain FEM in general
Matrix structural analysis	Clearly understands matrix structural analysis and is able to explain this in detail. Has the ability to carry out collect caluculations on two-dimensional truss structure analysis.	Ability to explain matrix structural analysis in general. Can carry out calculations on two-dimensional truss structure analysis.	Unable to explain matrix structural analysis in general. Unable to carry out calculations on two-dimensional truss structure analysis.
FEM for elasticity	Clearly understands, and is able to carry out fundamental caluculations on elasity by FEM.	Ability to understand, and carry out fundamental caluculations on elasity by FEM.	Does not display understanding, and is unable to carry out fundamental caluculations on elasity by FEM.
FEM for heat conduction problem	Clearly understands, and has the ability to carry out fundamental caluculations on heat conduction by FEM.	Ability to understand, and carry out fundamental caluculations on heat conduction by FEM.	Unable to understand and carry out fundamental caluculations on elasity by FEM.
FEM for flow	Clearly understands, and able to carry out fundamental caluculations on flow by FEM.	Ability to understand, and carry out fundamental caluculations on flow by FEM.	Unable to understand and carry out fundamental caluculations on flow by FEM.
FEM for unsteady flow problem	Clearly understands, and has the ability to explain the basic caluculation methods on unstady flow problem by FEM in detail.	Ability to understand and explain the basic caluculation methods on unstady flow problem by FEM in general.	Unable to understand and explain the basic caluculation methods on unstady flow problem by FEM in general.
Numerical analysis using CAD & CAE	Clearly understands, and able to carry out numerical analysis using CAD/CAE system.	Ability to understands and carry out numerical analysis using CAD/CAE system.	Does not display understanding and in unable to carry out numerical analysis using CAD/CAE system.

Assigned Department Objectives

学習・教育到達度目標 A-5 （工学的な諸問題に対処する際に必要な数学，自然科学及び情報の基礎的知識を理解し，それらを適切に活用することができる。）

JABEE 1(2)(c) （数学及び自然科学に関する知識とそれらを応用する能力）

Teaching Method

Outline:

In this course, you will learn about principles of finite element method (FEM) and difference method and will also learn about physical and mathematical ideas, solution of space-time probrems, discretization procedutes, method of weight residual (MWR), governing equations such as weak formulation, strong formulation. This course will address the thermal conductivity analysis, the stress analysis for elastic body, the numerical analysis for steady and unsteady flow problems using CAD & CAE systems.

Style:

For the purpose of understanding the numerical calculation methods such as finite element method (FEM) and difference method, lectures and exercises facilitate the learning of principles and examples.

Notice:

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Introduction of Computational mechanics	Can explain the characteristics of numerical analysis method
		2nd	Matrix structural analysis	Can perform numerical analysis of structures
		3rd	Method of weight residual (MWR) & finite elemet method (FEM)	Can explain method of weight residual (MWR) and governing equation (weak form, strong form) using FEM
		4th	FEM for heat conduction problem	Can perform unmerical analysis of one-dimensional heat conduction problems
		5th	FEM for one-dimensional elasticity	Can perform unmerical analysis of one-dimensional elastictiy problems
		6th	FEM for potential flow	Can perform unmerical analysis of potential flow problems
		7th	Fundamental equations of elasticity	Can derive the equations of an elastic body
		8th	FEM for elasticity(1)	Can explain the equations used in FEM and the conditions of plane stress and plane strain
	2nd Quarter
		9th	FEM for elasticity(2)	Can explain how to discretize space, shape function and solve equations
		10th	FEM for elasticity(3)	Can explaine the properties of discretized equations and approximate solutions.
		11th	FEM for unsteady flow problem(1)	Can explain time discretization, explicit and implicit FEM and upwind-difference
		12th	FEM for unsteady flow problem(2)	Can explain numerical stability of numerical analysis
		13th	Numerical analysis using CAD & CAE system(1)	Can perform Numerical analysis of heat conduction problems
		14th	Numerical analysis using CAD & CAE system(2)	Can perform Numerical analysis of stress problems
		15th	Numerical analysis using CAD & CAE system(3)	Can perform Numerical analysis of flow problems
		16th	Summary

Evaluation Method and Weight (%)

	レポート	Total
Subtotal	100	100
理解度	100	100