Differential quadrature and differential quadrature based element methods. Theory and applications (Q2825505)

The book explores the applications of the differential quadrature method (DQM) to problems of structural mechanics, including static stress analysis, buckling analysis and vibration and dynamic analysis. Linear, geometrically nonlinear, and material nonlinear problems are involved. The book contains two parts. One part treats the theory, and another part the applications. FORTRAN computer code and Matlab files are included in the appendices.NEWLINENEWLINE Chapter 1 presents the basic principle of the DQM. Various grid distributions are summarized, and the error analysis of the DQM is briefly discussed. A local adaptive DQM is given, too. Examples are given to demonstrate its superiority over the existing time integration schemes. Chapter~2 presents the basic principles of the differential quadrature method. Two different approaches are described to formulate the weighting coefficients of the DQ beam element. One approach uses Hermite interpolation, and the other employs Lagrange interpolation. Chapter~3 shows how to apply various boundary conditions. Chapter~4 presents the basic principles of the weak-form quadrature element method. Chapters 5--11 present applications of the DQM and the DQ-based element methods.