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FEM Prof Notes

Aug 08, 2018

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Tahir Bashir
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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

  • 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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    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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    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