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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
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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
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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
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8/22/2019 FEM Prof Notes
4/96
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
