Differential Quadrature And Differential Quadrature Based Element Methods
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Differential Quadrature And Differential Quadrature Based Element Methods
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Author : Xinwei Wang
language : en
Publisher: Butterworth-Heinemann
Release Date : 2015-03-24
Differential Quadrature And Differential Quadrature Based Element Methods written by Xinwei Wang and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Computers categories.
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
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Author : Chang Shu
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-14
Differential Quadrature And Its Application In Engineering written by Chang Shu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-14 with Mathematics categories.
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.
Discrete Element Analysis Methods Of Generic Differential Quadratures
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Author : Chang-New Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-12
Discrete Element Analysis Methods Of Generic Differential Quadratures written by Chang-New Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-12 with Mathematics categories.
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.
Anisotropic Doubly Curved Shells
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Author : Francesco Tornabene
language : en
Publisher: Società Editrice Esculapio
Release Date : 2019-11-01
Anisotropic Doubly Curved Shells written by Francesco Tornabene and has been published by Società Editrice Esculapio this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-01 with Technology & Engineering categories.
This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.
Mathematics Applied To Engineering And Management
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Author : Mangey Ram
language : en
Publisher: CRC Press
Release Date : 2019-08-08
Mathematics Applied To Engineering And Management written by Mangey Ram and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-08 with Mathematics categories.
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
Mechanical Engineering And Materials
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Author : Jinyang Xu
language : en
Publisher: Springer Nature
Release Date : 2021-03-24
Mechanical Engineering And Materials written by Jinyang Xu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-24 with Technology & Engineering categories.
This book gathers the latest advances, innovations, and applications in the field of mechanical engineering, as presented by leading international researchers and engineers at the 2020 International Conference on Mechanical Engineering and Materials (ICMEM), held in Beijing, China on October 16-17, 2020. ICMEM covers all aspects of mechanical engineering and material sciences, such as computer-aided design, virtual design and design visualization, intelligent design, usability design, automobile structure, human-machine interface design, manufacturing engineering, aerospace engineering, automation and robotics, micro-machining, MEMS/ NEMS, composite materials, biomaterials, smart materials, superconducting materials, materials properties and applications, materials manufacturing, nanotechnology, nano-materials and nano-composites, etc. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations.
Mathematical Methods In Interdisciplinary Sciences
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Author : Snehashish Chakraverty
language : en
Publisher: John Wiley & Sons
Release Date : 2020-07-15
Mathematical Methods In Interdisciplinary Sciences written by Snehashish Chakraverty and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-15 with Mathematics categories.
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.
Sinc Methods For Quadrature And Differential Equations
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Author : John Lund
language : en
Publisher: SIAM
Release Date : 1992-01-01
Sinc Methods For Quadrature And Differential Equations written by John Lund and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
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.
Hygro Thermo Magneto Electro Elastic Theory Of Anisotropic Doubly Curved Shells
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Author : Francesco Tornabene
language : en
Publisher: Società Editrice Esculapio
Release Date : 2023-10-13
Hygro Thermo Magneto Electro Elastic Theory Of Anisotropic Doubly Curved Shells written by Francesco Tornabene and has been published by Società Editrice Esculapio this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-13 with Technology & Engineering categories.
This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the physical behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.
Automated Solution Of Differential Equations By The Finite Element Method
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Author : Anders Logg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-24
Automated Solution Of Differential Equations By The Finite Element Method written by Anders Logg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-24 with Computers categories.
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.