Differential Quadrature and Differential Quadrature Based Element Methods Book

Differential Quadrature and Differential Quadrature Based Element Methods


  • Author : Xinwei Wang
  • Publisher : Butterworth-Heinemann
  • Release Date : 2015-03-24
  • Genre: Technology & Engineering
  • Pages : 408
  • ISBN 10 : 9780128031070

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Differential Quadrature and Differential Quadrature Based Element Methods Excerpt :

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. Offers a clear explanation of both the theory and many applications of DQM to structural analyses Discusses and illustrates reliable ways to apply multiple boundary conditions and develop reliable grid distributions Supported by FORTRAN and MATLAB programs, including subroutines to compute grid distributions and weighting coefficients

Differential Quadrature and Its Application in Engineering Book

Differential Quadrature and Its Application in Engineering


  • Author : Chang Shu
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Technology & Engineering
  • Pages : 340
  • ISBN 10 : 9781447104070

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Differential Quadrature and Its Application in Engineering Excerpt :

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.

A Differential Quadrature Hierarchical Finite Element Method Book

A Differential Quadrature Hierarchical Finite Element Method


  • Author : Bo Liu
  • Publisher : World Scientific
  • Release Date : 2021-08-03
  • Genre: Technology & Engineering
  • Pages : 652
  • ISBN 10 : 9789811236778

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A Differential Quadrature Hierarchical Finite Element Method Excerpt :

The differential quadrature hierarchical finite element method (DQHFEM) was proposed by Bo Liu. This method incorporated the advantages and the latest research achievements of the hierarchical finite element method (HFEM), the differential quadrature method (DQM) and the isogeometric analysis (IGA). The DQHFEM also overcame many limitations or difficulties of the three methods.This unique compendium systemically introduces the construction of various DQHFEM elements of commonly used geometric shapes like triangle, tetrahedrons, pyramids, etc. Abundant examples are also included such as statics and dynamics, isotropic materials and composites, linear and nonlinear problems, plates as well as shells and solid structures.This useful reference text focuses largely on numerical algorithms, but also introduces some latest advances on high order mesh generation, which often has been regarded as the major bottle neck for the wide application of high order FEM.

Advanced Numerical and Semi Analytical Methods for Differential Equations Book

Advanced Numerical and Semi Analytical Methods for Differential Equations


  • Author : Snehashish Chakraverty
  • Publisher : John Wiley & Sons
  • Release Date : 2019-03-20
  • Genre: Mathematics
  • Pages : 256
  • ISBN 10 : 9781119423447

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Advanced Numerical and Semi Analytical Methods for Differential Equations Excerpt :

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment

Discrete Element Analysis Methods of Generic Differential Quadratures Book

Discrete Element Analysis Methods of Generic Differential Quadratures


  • Author : Chang-New Chen
  • Publisher : Springer Science & Business Media
  • Release Date : 2008-09-12
  • Genre: Mathematics
  • Pages : 282
  • ISBN 10 : 9783540311850

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Discrete Element Analysis Methods of Generic Differential Quadratures Excerpt :

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.

Mathematical Methods in Interdisciplinary Sciences Book

Mathematical Methods in Interdisciplinary Sciences


  • Author : Snehashish Chakraverty
  • Publisher : John Wiley & Sons
  • Release Date : 2020-06-02
  • Genre: Mathematics
  • Pages : 464
  • ISBN 10 : 9781119585619

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Mathematical Methods in Interdisciplinary Sciences Excerpt :

Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problems Heat conduction and diffusion problems Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

Progress in Intelligent Decision Science Book

Progress in Intelligent Decision Science


  • Author : Tofigh Allahviranloo
  • Publisher : Springer Nature
  • Release Date : 2021-01-29
  • Genre: Technology & Engineering
  • Pages : 989
  • ISBN 10 : 9783030665012

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Progress in Intelligent Decision Science Excerpt :

This book contains the topics of artificial intelligence and deep learning that do have much application in real-life problems. The concept of uncertainty has long been used in applied science, especially decision making and a logical decision must be made in the field of uncertainty or in the real-life environment that is formed and combined with vague concepts and data. The chapters of this book are connected to the new concepts and aspects of decision making with uncertainty. Besides, other chapters are involved with the concept of data mining and decision making under uncertain computations.

Laminated Composite Doubly Curved Shell Structures Book

Laminated Composite Doubly Curved Shell Structures


  • Author : Francesco Tornabene
  • Publisher : Società Editrice Esculapio
  • Release Date : 2016-05-17
  • Genre: Technology & Engineering
  • Pages : 872
  • ISBN 10 : 9788874889587

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Laminated Composite Doubly Curved Shell Structures Excerpt :

The title, “Laminated Composite Doubly-Curved Shell Structures. Differential and Integral Quadrature. Strong Form Finite Elements” illustrates the theme treated and the prospective followed during the composition of the present work. The aim of this manuscript is to analyze the static and dynamic behavior of thick and moderately thick composite shells through the application of the Differential Quadrature (DQ) method. The book is divided into two volumes wherein the principal higher order structural theories are illustrated in detail and the mechanical behavior of doubly-curved structures are presented by several static and dynamic numerical applications. In particular, the first volume is mainly theoretical, whereas the second one is mainly related to the numerical DQ technique and its applications in the structural field. The numerical results reported in the present volume are compared to the one available in the literature, but also to the ones obtained through several codes based on the Finite Element Method (FEM). Furthermore, an advanced version of the DQ method, termed Strong Formulation Finite Element Method (SFEM), is presented. The SFEM solves the differential equations inside each element in the strong form and implements the mapping technique typical of the FEM.

Mathematics Applied to Engineering and Management Book

Mathematics Applied to Engineering and Management


  • Author : Mangey Ram
  • Publisher : CRC Press
  • Release Date : 2019-08-08
  • Genre: Mathematics
  • Pages : 302
  • ISBN 10 : 9781351123280

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Mathematics Applied to Engineering and Management Excerpt :

This book offers the latest research advances in the field of mathematics applications in engineering sciences and provides a reference with a theoretical and sound background, along with case studies. In recent years, mathematics has had an amazing growth in engineering sciences. It forms the common foundation of all engineering disciplines. This new book provides a comprehensive range of mathematics applied to various fields of engineering for different tasks in fields such as civil engineering, structural engineering, computer science, electrical engineering, among others. It offers articles that develop the applications of mathematics in engineering sciences, conveys the innovative research ideas, offers real-world utility of mathematics, and plays a significant role in the life of academics, practitioners, researchers, and industry leaders. Focuses on the latest research in the field of engineering applications Includes recent findings from various institutions Identifies the gaps in the knowledge of the field and provides the latest approaches Presents international studies and findings in modelling and simulation Offers various mathematical tools, techniques, strategies, and methods across different engineering fields

Mechanics of Laminated Composite Doubly Curved Shell Structures Book

Mechanics of Laminated Composite Doubly Curved Shell Structures


  • Author : Francesco Tornabene
  • Publisher : Società Editrice Esculapio
  • Release Date : 2021-12-01
  • Genre: Technology & Engineering
  • Pages : 824
  • ISBN 10 : 9791220879620

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Mechanics of Laminated Composite Doubly Curved Shell Structures Excerpt :

This manuscript comes from the experience gained over ten years of study and research on shell structures and on the Generalized Differential Quadrature method. The title, Mechanics of Laminated Composite Doubly-Curved Shell Structures, illustrates the theme followed in the present volume. The present study aims to analyze the static and dynamic behavior of moderately thick shells made of composite materials through the application of the Differential Quadrature (DQ) technique. A particular attention is paid, other than fibrous and laminated composites, also to “Functionally Graded Materials” (FGMs). They are non-homogeneous materials, characterized by a continuous variation of the mechanical properties through a particular direction. The GDQ numerical solution is compared, not only with literature results, but also with the ones supplied and obtained through the use of different structural codes based on the Finite Element Method (FEM). Furthermore, an advanced version of GDQ method is also presented. This methodology is termed Strong Formulation Finite Element Method (SFEM) because it employs the strong form of the differential system of equations at the master element level and the mapping technique, proper of FEM. The connectivity between two elements is enforced through compatibility conditions.

Advanced Differential Quadrature Methods Book

Advanced Differential Quadrature Methods


  • Author : Zhi Zong
  • Publisher : CRC Press
  • Release Date : 2009-01-20
  • Genre: Science
  • Pages : 362
  • ISBN 10 : 1420082493

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Advanced Differential Quadrature Methods Excerpt :

Modern Tools to Perform Numerical Differentiation The original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and engineering have developed a range of innovative DQ-based methods to overcome these shortcomings. Advanced Differential Quadrature Methods explores new DQ methods and uses these methods to solve problems beyond the capabilities of the direct DQ method. After a basic introduction to the direct DQ method, the book presents a number of DQ methods, including complex DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain DQ, and localized DQ. It also provides a mathematical compendium that summarizes Gauss elimination, the Runge–Kutta method, complex analysis, and more. The final chapter contains three codes written in the FORTRAN language, enabling readers to quickly acquire hands-on experience with DQ methods. Focusing on leading-edge DQ methods, this book helps readers understand the majority of journal papers on the subject. In addition to gaining insight into the dynamic changes that have recently occurred in the field, readers will quickly master the use of DQ methods to solve complex problems.

DiQuMaSPAB Book

DiQuMaSPAB


  • Author : Francesco Tornabene
  • Publisher : Società Editrice Esculapio
  • Release Date : 2018-02-09
  • Genre: Technology & Engineering
  • Pages : 112
  • ISBN 10 : 9788893850636

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DiQuMaSPAB Excerpt :

The main aim of this book is to show the features of DiQuMASPAB so ware through the description of its graphical interface, by giving special emphasis to all those aspects implemented in the code. DiQuMASPAB, acronym of “Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams”, is a computational code, which can be used for the numerical analysis of doubly curved shells made of innovative materials, using the Generalized Differential Quadrature (GDQ) and the Generalized Integral Quadrature (GIQ) methods. The software can investigate the mechanical behavior of these structures through different approaches and structural theories. In particular, this code allows considering a kinematic expansion characterized by different degrees of freedom for the Equivalent Single Layer (ESL) theories and for each layer when the Layer-Wise (LW) approach is taken into account. As far as the materials are concerned, it is possible to consider different lamination schemes, as well as various distributions of the volume fraction of the constituents for those layers that vary their mechanical properties along the thickness. In addition, the software analyzes structures with variable thickness and characterized by variable mechanical properties that can change point by point. A finite element formulation is also available to investigate the mechanical behavior of plane structures characterized by irregular domains and mechanical discontinuities.

Differential Quadrature and Its Application in Engineering Book
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Differential Quadrature and Its Application in Engineering


  • Author : Chang Shu
  • Publisher : Springer Science & Business Media
  • Release Date : 2000-01-14
  • Genre: Mathematics
  • Pages : 340
  • ISBN 10 : 1852332093

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Differential Quadrature and Its Application in Engineering Excerpt :

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.

Sinc Methods for Quadrature and Differential Equations Book

Sinc Methods for Quadrature and Differential Equations


  • Author : John Lund
  • Publisher : SIAM
  • Release Date : 1992-01-01
  • Genre: Mathematics
  • Pages : 304
  • ISBN 10 : 9780898712988

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Sinc Methods for Quadrature and Differential Equations Excerpt :

Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for treating differential equations. These methods are an alternative to finite difference and finite element schemes, and are especially adaptable to problems with singular solutions. The text is written to facilitate easy implementation of the theory into operating numerical code. The authors' use of differential equations as a backdrop for the presentation of the material allows them to present a number of the applications of the sinc method. Many of these applications are useful in numerical processes of interest quite independent of differential equations. Specifically, numerical interpolation and quadrature, while fundamental to the Galerkin development, are useful in their own right.