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Differential Quadrature and Differential Quadrature Based Element Methods
Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications is a comprehensive guide to these methods and their various applications in recent years. Due to the attractive features of rapid convergence, high accuracy, and computational efficiency, the differential quadrature method and its based element methods are increasingly being used to study problems in the area of structural mechanics, such as static, buckling and vibration problems of composite structures and functional material structures. This book covers new developments and their applications in detail, with accompanying FORTRAN and MATLAB programs to help you overcome difficult programming challenges. It summarises the variety of different quadrature formulations that can be found by varying the degree of polynomials, the treatment of boundary conditions and employing regular or irregular grid points, to help you choose the correct method for solving practical problems.
Cover; Title Page; Copyright Page; Contents; Preface; Acknowledgments; Chapter 1 -- Differential quadrature method; 1.1 -- Introduction; 1.2 -- Integral quadrature; 1.3 -- Differential quadrature method; 1.4 -- Determination of weighting coefficients; 1.5 -- Explicit formulation of weighting coefficients; 1.6 -- Various grid points; 1.7 -- Error analysis ; 1.8 -- Local adaptive differential quadrature method; 1.9 -- Differential quadrature time integration scheme; 1.9.1 -- The method of the DQ-based time integration; 1.9.2 -- Application and discussion; 1.10 -- Summary; References.
3.3.5 -- Method of modification of weighting coefficient-23.3.6 -- Method of modification of weighting coefficient-3; 3.3.7 -- Method of modification of weighting coefficient-4; 3.3.8 -- Virtual boundary point method or La-DQM; 3.3.9 -- Method of modification of weighting coefficient-5; 3.4 -- Discussion; 3.5 -- Numerical examples; 3.6 -- Summary; References; Chapter 4 -- Quadrature element method; 4.1 -- Introduction; 4.2 -- Quadrature element method; 4.3 -- Quadrature bar element; 4.4 -- Quadrature Timoshenko beam element; 4.5 -- Quadrature plane stress (strain) element.
4.6 -- Quadrature thick plate element4.6.1 -- Displacement and strain fields; 4.6.2 -- Constitutive equation; 4.6.3 -- Quadrature rectangular thick plate element; 4.7 -- Quadrature thin beam element; 4.8 -- Quadrature thin rectangular plate element; 4.8.1 -- Quadrature rectangular plate element with Lagrange interpolation; 4.8.2 -- Quadrature rectangular plate element with Hermite interpolation; 4.8.3 -- Quadrature rectangular plate element with mixed interpolations; 4.9 -- Extension to quadrilateral plate element with curved edges; 4.10 -- Discussion; 4.10.1 -- Assemblage procedures.
4.10.2 -- Work equivalent load vector4.10.3 -- Quadrature plate elements with nodes other than GLL points; 4.10.4 -- Numerical examples; 4.11 -- Summary; References; Chapter 5 -- In-plane stress analysis; 5.1 -- Introduction; 5.2 -- Formulation-I; 5.3 -- Formulation-II; 5.4 -- Results and discussion; 5.5 -- Equivalent boundary conditions; 5.6 -- Summary; References; Chapter 6 -- Static analysis of thin plate; 6.1 -- Introduction; 6.2 -- Rectangular thin plate under general loading; 6.2.1 -- Basic equations; 6.2.2 -- Differential quadrature formulation; 6.2.3 -- Equivalent load; 6.3 -- Applications.
6.3.1 -- Rectangular plate under uniformly distributed load.
Includes bibliographical references and index.
Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications