Discrete Element Analysis Methods of Generic Differential Quadratures

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.

Generalization of DQ — Extended Differential Quadrature.- DQEM Analysis of One-Dimensional Elasticity Problems.- DQEM Analysis of Euler-Bernoulli Beam Structures.- DQEM Analysis of Static Deflection of Three-Dimensional Trusses.- DQEM Analysis of Static Deflection of Three-Dimensional Frames.- DQEM Analysis of Vibration of Frames Considering Warping Torsion.- DQEM Analysis of Timoshenko Beam Structures.- DQEM Analysis of Curved Beam Structures.- Development of DQEM Irregular Elements.- DQEM Analysis of Two-Dimensional Steady-State Field Problems.- DQEM Analysis of Two-Dimensional Elasticity Problems.- DQEM Analysis of Kirchhoff-Love Plate Problems.- DQFDM Analysis.- Generalized Coordinate Differential Quadrature Element Method.- EDQ Based Direct Time Integration Methods.