FEM Prof Notes

8/22/2019 FEM Prof Notes

1/96

School of Civil, Urban & Geosystem Eng., SNU

Structural Analysis Lab.

Prof. Hae Sung Lee, http://strana.snu.ac.kr

Introduction to

Finite Element Method

Fall Semester, 2006

Hae Sung Lee

School of Civil, Urban and Geosystem Engineering

Seoul National University

8/22/2019 FEM Prof Notes

2/96

School of Civil, Urban & Geosystem Eng., SNU

Structural Analysis Lab.

Prof. Hae Sung Lee, http://strana.snu.ac.kr

Contents

1. Introduction

2. Approximation of Functions & Variational Calculus

3. Differential Equations in One Dimension

4. Multidimensional Problems-Elasticity

5. Discretization

6. Two Dimensional Elasticity Problems

7. Various Types of Elements

8. Numerical Integration

9. Convergence Criteria in Isoparameteric Element

10. Miscellaneous Topics

11. Problems with Higher Continuity Requirement - Beams

12. Mixed Formulation

8/22/2019 FEM Prof Notes

3/96

School of Civil, Urban & Geosystem Eng., SNU

Structural Analysis Lab.

Prof. Hae Sung Lee, http://strana.snu.ac.kr

1

Chapter 2A pproximation of F unctions and

V ariational Calculus

8/22/2019 FEM Prof Notes

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School of Civil, Urban & Geosystem Eng., SNU

Structural Analysis Lab.

Prof. Hae Sung Lee, http://strana.snu.ac.kr

2

z DiscretizationA function )(Xf can be expressed by linear combinations of basis functions of.

)()(1

XX =

=n

i

iigaf wheregi are the basis functions of.

Examples: Taylor series, Fourier series

z Approximations of a Function)()()()(

11

XXXX ==

==m

i

ii

hn

i

ii gafgaf where nm