Discrete Element Analysis Methods of Generic Differential Quadratures

1. Front Matter

   Pages I-XI

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2. Introduction

   Pages 1-5

3. Generalization of DQ — Extended Differential Quadrature

   Pages 7-37

4. DQEM Analysis of One-Dimensional Elasticity Problems

   Pages 39-51

5. DQEM Analysis of Euler-Bernoulli Beam Structures

   Pages 53-72

6. DQEM Analysis of Static Deflection of Three-Dimensional Trusses

   Pages 73-83

7. DQEM Analysis of Static Deflection of Three-Dimensional Frames

   Pages 85-102

8. DQEM Analysis of Vibration of Frames Considering Warping Torsion

   Pages 103-121

9. DQEM Analysis of Timoshenko Beam Structures

   Pages 123-135

10. DQEM Analysis of Curved Beam Structures

    Pages 137-158

11. Development of DQEM Irregular Elements

    Pages 159-174

12. DQEM Analysis of Two-Dimensional Steady-State Field Problems

    Pages 175-196

13. DQEM Analysis of Two-Dimensional Elasticity Problems

    Pages 197-209

14. DQEM Analysis of Kirchhoff-Love Plate Problems

    Pages 211-221

15. DQFDM Analysis

    Pages 223-242

16. Generalized Coordinate Differential Quadrature Element Method

    Pages 243-255

17. EDQ Based Direct Time Integration Methods

    Pages 257-268

18. Back Matter

    Pages 269-282

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Following the advance in computer technology, the numerical technique has made signi?cant progress in the past decades. Among the major techniques available for numerically analyzing continuum mechanics problems, ?nite d- ference method is most early developed. It is di?cult to deal with cont- uum mechanics problems showing complex curvilinear geometries by using this method. The other method that can consistently discretize continuum mechanics problems showing arbitrarily complex geometries is ?nite element method. In addition, boundary element method is also a useful numerical method. In the past decade, the di?erential quadrature and generic di?erential quadraturesbaseddiscreteelementanalysismethodshavebeendevelopedand usedto solve various continuum mechanics problems. These methods have the same advantage as ?nite element method of consistently discretizing cont- uum mechanics problems having arbitrarily complex geometries. This book includes my research results obtained in developing the related novel discrete element analysis methods using both of the extended di?erential quadrature based spacial and temporal elements. It is attempted to introduce the dev- oped numerical techniques as applied to the solution of various continuum mechanics problems, systematically.

• Differential Quadrature
• Discrete Element Analysis
• Elasticity
• General Field Problems
• Generic Differential Quadrature
• Vibration
• algorithm
• algorithms
• calculus
• geometry
• mechanics

• Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China

  Chang-New Chen

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