## Course Title : Fundamental Theory of Elasticity and Stress Analysis

Code 32000 3rd year 4 No Restriction Lecture Japanese Assoc. Prof. Tsukada & Assoc. Prof. Murata,

### Course Description

Stress, strain, displacement and basic equations in linear elasticity are first lectured, and then Airy's stress function and its application to solve two dimensional problems in linear elasticity are explained. Moreover, energy theorems and their application to a numerical stress analysis method are explained.

### Grading

Several Exercises are presented in the term. Midterm exam and final exam are also presented. Grade is evaluated by the sum of the exercises and the exams with the weight of 30% and 70% respectively.

### Course Goals

One objective of this course is to master the basis to solve the boundary value problems in linear elasticity analytically or numerically. Another one is to obtain the basic knowledge of numerical stress analysis methods such as FEM and BEM.

### Course Topics

Theme Class number of times Description
Stress, strain and displacement 2 Introduction of linear elasticity containing its history is first presented, and then stress, strain, displacement, equations between them, principal stress and strain, Mohr's circle of stress and strain, and etc. are lectured.
Basic equations of linear elasticity and boundary condition 2 Basic equations of linear elasticity in Cartesian coordinate system and polar coordinate system are presented, and then the methods to solve the equations are lectured.
Airy's stress function and solution of 2D problem of elasticity 5 Airy's stress function that is a biharmonic function is presented for Cartesian coordinate system and polar coordinate system, and a method to obtain the stress and displacement in a two dimensional elastic body using Airy's stress function is lecured.
Energy theorems in elasticity and solution of boundary value problem 4 Strain energy function, principle of virtual work, and principle of minimum potential energy are lectured, and then the relation between basic equations in linear elasticity and these energy princile is lectured. Moreover the method to solve a boundary value problem in linear elasticity based on the energy theorems is explained.
Basis of numerical stress analysis methods 1 Overview of FEM, FDM and BEM is presented, and then formulation of FEM using the energy theorems is explained. Moreover some examples of stress analysis using FEM and BEM are shown.
Learning achievement check and summary 1 Students are asked to solve several problems. The solution of them are shown. Student can check their achievement to the course goals and summarize this course.

Not specified.

### Textbook(supplemental)

Shigeo Takezono et al., Introduction of Mechanics of elasticity-from basic theory to numerical analysis-, Morikita Publishing Co., ISBN:978-4-627-66641-2 ### Prerequisite(s)

Differential calculus, integral calculus, and linear algebra are necessary for taking this course.

It is strongly recommended to solve again the example problems explained in the lecture by yourself.

### Web Sites

This course does not have a web site. But some lecture documents may be deribered by the net. The URL to download the lecture documents will be announced in the class.

### Additional Information

Additional information is presented in the first class of each teacher.