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Differential Quadrature And Differential Quadrature Based Element Methods

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Differential Quadrature and Differential Quadrature Based Element Methods

Differential Quadrature and Differential Quadrature Based Element Methods Book
Author : Xinwei Wang
Publisher : Butterworth-Heinemann
Release : 2015-03-24
ISBN : 0128031077
Language : En, Es, Fr & De

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Book Description :

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

Mechanics of laminated Composite doubly curvel shell structures

Mechanics of laminated Composite doubly curvel shell structures Book
Author : Francesco Tornabene,Nicholas Fantuzzi
Publisher : Società Editrice Esculapio
Release : 2014-03-01
ISBN : 887488687X
Language : En, Es, Fr & De

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Book Description :

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.

An Adaptive Differential Quadrature Element Method for Large Deformation Contact Problems Involving Curved Beams with a Finite Number of Contact Points

An Adaptive Differential Quadrature Element Method for Large Deformation Contact Problems Involving Curved Beams with a Finite Number of Contact Points Book
Author : Anonim
Publisher : Unknown
Release : 2017
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Abstract: Contact problems involving large deformation of curved beams are difficult to analyze due to uncertainty of contact positions and strong nonlinearity. A nonlinear large-deformation model of curved beams is formulated in arc-length coordinates. A new adaptive differential quadrature element method (ADQEM) is proposed to predict contact positions of a curved beam with a finite number of contact points, where a dragging method and continuity conditions are combined to determine the contact positions. Simulation results show that the ADQEM greatly improves efficiency and accuracy of the large-deformation contact problem of the curved beam. The number of iterations in the present method does not greatly increase with the number of contact points.

A Differential Quadrature Hierarchical Finite Element Method

A Differential Quadrature Hierarchical Finite Element Method Book
Author : Bo Liu,Cuiyun Liu,Yang Wu
Publisher : Unknown
Release : 2021-06-28
ISBN : 9789811236754
Language : En, Es, Fr & De

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Book Description :

Download A Differential Quadrature Hierarchical Finite Element Method book written by Bo Liu,Cuiyun Liu,Yang Wu, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Application of the Differential Quadrature Finite Element Method to Free Vibration of Elastically Restrained Plate with Irregular Geometries

Application of the Differential Quadrature Finite Element Method to Free Vibration of Elastically Restrained Plate with Irregular Geometries Book
Author : Anonim
Publisher : Unknown
Release : 2018
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Abstract: The virtual spring technique is firstly introduced into the differential quadrature finite element method (DQFEM) to simulate the practical elastic restraints. The imposing procedures of the boundary conditions are simplified so that a certain kind of restraints can be easily achieved by merely setting different stiffness of the springs. The mapping technique is used to apply the DQFEM to irregular domain. The effects of different nodes collocation methods on the mapping results and vibration results are also discussed, through which one can conclude that the nodes distribution methods affect the accuracy of the mapping technique and the computing time. Especially, the uniformly distributed nodes are not the best selection for mapping process. The Guass Lobatto quadrature nodes are the good choice to obtain the better results in a relatively short time. Several numerical examples are carried out to demonstrate the validity and accuracy of the present solution by comparing with the results obtained by other researchers.

Progress in Intelligent Decision Science

Progress in Intelligent Decision Science Book
Author : Tofigh Allahviranloo
Publisher : Springer Nature
Release : 2021-04-10
ISBN : 3030665011
Language : En, Es, Fr & De

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Book Description :

Download Progress in Intelligent Decision Science book written by Tofigh Allahviranloo, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Laminated Composite Doubly Curved Shell Structures

Laminated Composite Doubly Curved Shell Structures Book
Author : Francesco Tornabene,Michele Bacciocchi,Nicholas Fantuzzi,Erasmo Viola
Publisher : Società Editrice Esculapio
Release : 2016-05-17
ISBN : 8874889585
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical Methods in Interdisciplinary Sciences

Mathematical Methods in Interdisciplinary Sciences Book
Author : Snehashish Chakraverty
Publisher : John Wiley & Sons
Release : 2020-06-02
ISBN : 1119585619
Language : En, Es, Fr & De

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Book Description :

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.

Discrete Element Analysis Methods of Generic Differential Quadratures

Discrete Element Analysis Methods of Generic Differential Quadratures Book
Author : Chang-New Chen
Publisher : Springer Science & Business Media
Release : 2008-09-12
ISBN : 3540311858
Language : En, Es, Fr & De

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Book Description :

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 and Its Application in Engineering

Differential Quadrature and Its Application in Engineering Book
Author : Chang Shu
Publisher : Springer Science & Business Media
Release : 2000-01-14
ISBN : 9781852332099
Language : En, Es, Fr & De

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Book Description :

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.

Computer Techniques Intelligent Systems Technologies Optimization Methods Computer Aided Design Computer Aided Manufacturing CAD CAM Manufacturinf Processes

Computer Techniques  Intelligent Systems Technologies  Optimization Methods  Computer Aided Design Computer Aided Manufacturing  CAD CAM   Manufacturinf Processes Book
Author : Cornelius T. Leondes
Publisher : World Scientific
Release : 2003
ISBN : 9789812383396
Language : En, Es, Fr & De

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Book Description :

This is an invaluable five-volume reference on the very broad and highly significant subject of computer aided and integrated manufacturing systems. It is a set of distinctly titled and well-harmonized volumes by leading experts on the international scene. The techniques and technologies used in computer aided and integrated manufacturing systems have produced, and will no doubt continue to produce, major annual improvements in productivity, which is defined as the goods and services produced from each hour of work. This publication deals particularly with more effective utilization of labor and capital, especially information technology systems. Together the five volumes treat comprehensively the major techniques and technologies that are involved.

DiQuMaSPAB

DiQuMaSPAB Book
Author : Francesco Tornabene,Nicholas Fantuzzi,Michele Bacciocchi
Publisher : Società Editrice Esculapio
Release : 2018-02-09
ISBN : 889385063X
Language : En, Es, Fr & De

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Book Description :

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.

Advanced Numerical and Semi Analytical Methods for Differential Equations

Advanced Numerical and Semi Analytical Methods for Differential Equations Book
Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : Wiley
Release : 2019-04-30
ISBN : 1119423422
Language : En, Es, Fr & De

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Book Description :

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 Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Computational Mechanics

Computational Mechanics Book
Author : B. H. V. Topping
Publisher : Unknown
Release : 2000
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Contains a selection of papers that were presented at The Fifth International Conference on Computational Structures Technology and The Second International Conference on Engineering Computational Technology, which were held in Leuven, Belgium from 6-8 September 2000.

Modeling and Simulation Based Engineering

Modeling and Simulation Based Engineering Book
Author : Satya N. Atluri,Padraic Eimear O'Donoghue
Publisher : Computational Mechanics
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Modeling and Simulation Based Engineering book written by Satya N. Atluri,Padraic Eimear O'Donoghue, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Computer Technology and Applications

Computer Technology and Applications Book
Author : Wolf Dietrich Reinhardt,John Martin
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Computer Technology and Applications book written by Wolf Dietrich Reinhardt,John Martin, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

BMT Abstracts

BMT Abstracts Book
Author : Anonim
Publisher : Unknown
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download BMT Abstracts book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Pressure Vessel and Piping Design and Analysis 2001

Pressure Vessel and Piping Design and Analysis  2001 Book
Author : Dennis H. Martens
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Pressure Vessel and Piping Design and Analysis 2001 book written by Dennis H. Martens, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Emerging Technologies

Emerging Technologies Book
Author : F. L. Cho
Publisher : Unknown
Release : 2000
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Emerging Technologies book written by F. L. Cho, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.