The Virtual Element Method And Its Applications

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The Virtual Element Method and its Applications

Author : Paola F. Antonietti
Publisher : Springer Nature
ISBN 13 : 303095319X
Total Pages : 621 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis The Virtual Element Method and its Applications by : Paola F. Antonietti

Download or read book The Virtual Element Method and its Applications written by Paola F. Antonietti and published by Springer Nature. This book was released on 2022-10-08 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications. The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics. The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.

Virtual Element Methods in Engineering Sciences

Author : Peter Wriggers
Publisher : Springer Nature
ISBN 13 : 3031392558
Total Pages : 457 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Virtual Element Methods in Engineering Sciences by : Peter Wriggers

Download or read book Virtual Element Methods in Engineering Sciences written by Peter Wriggers and published by Springer Nature. This book was released on 2023-11-29 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive treatment of the virtual element method (VEM) for engineering applications, focusing on its application in solid mechanics. Starting with a continuum mechanics background, the book establishes the necessary foundation for understanding the subsequent chapters. It then delves into the VEM's Ansatz functions and projection techniques, both for solids and the Poisson equation, which are fundamental to the method. The book explores the virtual element formulation for elasticity problems, offering insights into its advantages and capabilities. Moving beyond elasticity, the VEM is extended to problems in dynamics, enabling the analysis of dynamic systems with accuracy and efficiency. The book also covers the virtual element formulation for finite plasticity, providing a framework for simulating the behavior of materials undergoing plastic deformation. Furthermore, the VEM is applied to thermo-mechanical problems, where it allows for the investigation of coupled thermal and mechanical effects. The book dedicates a significant portion to the virtual elements for fracture processes, presenting techniques to model and analyze fractures in engineering structures. It also addresses contact problems, showcasing the VEM's effectiveness in dealing with contact phenomena. The virtual element method's versatility is further demonstrated through its application in homogenization, offering a means to understand the effective behavior of composite materials and heterogeneous structures. Finally, the book concludes with the virtual elements for beams and plates, exploring their application in these specific structural elements. Throughout the book, the authors emphasize the advantages of the virtual element method over traditional finite element discretization schemes, highlighting its accuracy, flexibility, and computational efficiency in various engineering contexts.

Automation of Finite Element Methods

Author : Jože Korelc
Publisher : Springer
ISBN 13 : 3319390058
Total Pages : 367 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Automation of Finite Element Methods by : Jože Korelc

Download or read book Automation of Finite Element Methods written by Jože Korelc and published by Springer. This book was released on 2016-06-08 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.

Finite Element Method

Author : Michael R. Gosz
Publisher : CRC Press
ISBN 13 : 1351992031
Total Pages : 430 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Finite Element Method by : Michael R. Gosz

Download or read book Finite Element Method written by Michael R. Gosz and published by CRC Press. This book was released on 2017-03-27 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) is the dominant tool for numerical analysis in engineering, yet many engineers apply it without fully understanding all the principles. Learning the method can be challenging, but Mike Gosz has condensed the basic mathematics, concepts, and applications into a simple and easy-to-understand reference. Finite Element Method: Applications in Solids, Structures, and Heat Transfer navigates through linear, linear dynamic, and nonlinear finite elements with an emphasis on building confidence and familiarity with the method, not just the procedures. This book demystifies the assumptions made, the boundary conditions chosen, and whether or not proper failure criteria are used. It reviews the basic math underlying FEM, including matrix algebra, the Taylor series expansion and divergence theorem, vectors, tensors, and mechanics of continuous media. The author discusses applications to problems in solid mechanics, the steady-state heat equation, continuum and structural finite elements, linear transient analysis, small-strain plasticity, and geometrically nonlinear problems. He illustrates the material with 10 case studies, which define the problem, consider appropriate solution strategies, and warn against common pitfalls. Additionally, 35 interactive virtual reality modeling language files are available for download from the CRC Web site. For anyone first studying FEM or for those who simply wish to deepen their understanding, Finite Element Method: Applications in Solids, Structures, and Heat Transfer is the perfect resource.

The Mimetic Finite Difference Method for Elliptic Problems

Author : Lourenco Beirao da Veiga
Publisher : Springer
ISBN 13 : 3319026631
Total Pages : 399 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Mimetic Finite Difference Method for Elliptic Problems by : Lourenco Beirao da Veiga

Download or read book The Mimetic Finite Difference Method for Elliptic Problems written by Lourenco Beirao da Veiga and published by Springer. This book was released on 2014-05-22 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

The Finite Element Method for Boundary Value Problems

Author : Karan S. Surana
Publisher : CRC Press
ISBN 13 : 1498780512
Total Pages : 824 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Finite Element Method for Boundary Value Problems by : Karan S. Surana

Download or read book The Finite Element Method for Boundary Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2016-11-17 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.

Finite Element Applications

Author : Michael Okereke
Publisher : Springer
ISBN 13 : 3319671251
Total Pages : 488 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Finite Element Applications by : Michael Okereke

Download or read book Finite Element Applications written by Michael Okereke and published by Springer. This book was released on 2018-01-23 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook demonstrates the application of the finite element philosophy to the solution of real-world problems and is aimed at graduate level students, but is also suitable for advanced undergraduate students. An essential part of an engineer’s training is the development of the skills necessary to analyse and predict the behaviour of engineering systems under a wide range of potentially complex loading conditions. Only a small proportion of real-life problems can be solved analytically, and consequently, there arises the need to be able to use numerical methods capable of simulating real phenomena accurately. The finite element (FE) method is one such widely used numerical method. Finite Element Applications begins with demystifying the ‘black box’ of finite element solvers and progresses to addressing the different pillars that make up a robust finite element solution framework. These pillars include: domain creation, mesh generation and element formulations, boundary conditions, and material response considerations. Readers of this book will be equipped with the ability to develop models of real-world problems using industry-standard finite element packages.

Sources of Quantum Mechanics

Author : B. L. Van Der Waerden
Publisher : Courier Corporation
ISBN 13 : 048645892X
Total Pages : 450 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Sources of Quantum Mechanics by : B. L. Van Der Waerden

Download or read book Sources of Quantum Mechanics written by B. L. Van Der Waerden and published by Courier Corporation. This book was released on 2007-01-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Amsterdam: North-Holland Pub. Co., 1967.

TEXTBOOK OF FINITE ELEMENT ANALYSIS

Author : P. SESHU
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 8120323157
Total Pages : 340 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis TEXTBOOK OF FINITE ELEMENT ANALYSIS by : P. SESHU

Download or read book TEXTBOOK OF FINITE ELEMENT ANALYSIS written by P. SESHU and published by PHI Learning Pvt. Ltd.. This book was released on 2003-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.

The Boundary Element Method, Volume 1

Author : L. C. Wrobel
Publisher : John Wiley & Sons
ISBN 13 : 9780471720393
Total Pages : 480 pages
Book Rating : 4.7/5 (23 download)

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Book Synopsis The Boundary Element Method, Volume 1 by : L. C. Wrobel

Download or read book The Boundary Element Method, Volume 1 written by L. C. Wrobel and published by John Wiley & Sons. This book was released on 2002-04-22 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary element method (BEM) is a modern numerical techniquewhich has enjoyed increasing popularity over the last two decades,and is now an established alternative to traditional computationalmethods of engineering analysis. The main advantage of the BEM isits unique ability to provide a complete solution in terms ofboundary values only, with substantial savings in modelling effort. This two-volume book set is designed to provide the readers with acomprehensive and up-to-date account of the boundary element methodand its application to solving engineering problems. Each volume isa self-contained book including a substantial amount of materialnot previously covered by other text books on the subject. Volume 1covers applications to heat transfer, acoustics, electrochemistryand fluid mechanics problems, while volume 2 concentrates on solidsand structures, describing applications to elasticity, plasticity,elastodynamics, fracture mechanics and contact analysis. The earlychapters are designed as a teaching text for final yearundergraduate courses. Both volumes reflect the experience of theauthors over a period of more than twenty years of boundary element research. This volume, Applications in Thermo-Fluids and Acoustics, provides acomprehensive presentation of the BEM from fundamentals to advancedengineering applications and encompasses: Steady and transient heat transfer Potential and viscous fluid flows Frequency and time-domain acoustics Corrosion and other electrochemical problems. A unique feature of this book is an in-depth presentation of BEMformulations in all the above fields, including detaileddiscussions of the basic theory, numerical algorithms and practicalengineering applications of the method. Written by an internationally recognised authority in the field,this is essential reading for postgraduates, researchers andpractitioners in civil, mechanical and chemical engineering andapplied mathematics.

The Finite Element Method: Solid mechanics

Author : O. C. Zienkiewicz
Publisher : Butterworth-Heinemann
ISBN 13 : 9780750650557
Total Pages : 482 pages
Book Rating : 4.6/5 (55 download)

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Book Synopsis The Finite Element Method: Solid mechanics by : O. C. Zienkiewicz

Download or read book The Finite Element Method: Solid mechanics written by O. C. Zienkiewicz and published by Butterworth-Heinemann. This book was released on 2000 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mathematical Theory of Finite Element Methods

Author : Susanne Brenner
Publisher : Springer Science & Business Media
ISBN 13 : 1475736584
Total Pages : 369 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Mathematical Theory of Finite Element Methods by : Susanne Brenner

Download or read book The Mathematical Theory of Finite Element Methods written by Susanne Brenner and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

An Introduction to the Finite Element Method

Author : Junuthula Narasimha Reddy
Publisher :
ISBN 13 : 9780071244732
Total Pages : 766 pages
Book Rating : 4.2/5 (447 download)

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Book Synopsis An Introduction to the Finite Element Method by : Junuthula Narasimha Reddy

Download or read book An Introduction to the Finite Element Method written by Junuthula Narasimha Reddy and published by . This book was released on 2006 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas.Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world

A Rational Finite Element Basis

Author : Wachspress
Publisher : Academic Press
ISBN 13 : 0080956238
Total Pages : 347 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis A Rational Finite Element Basis by : Wachspress

Download or read book A Rational Finite Element Basis written by Wachspress and published by Academic Press. This book was released on 1975-09-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Rational Finite Element Basis

The Finite Element Method Set

Author : O. C. Zienkiewicz
Publisher : Elsevier
ISBN 13 : 0080531679
Total Pages : 1863 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis The Finite Element Method Set by : O. C. Zienkiewicz

Download or read book The Finite Element Method Set written by O. C. Zienkiewicz and published by Elsevier. This book was released on 2005-11-25 with total page 1863 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics. * This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference

The Finite Element Method

Author : Bofang Zhu
Publisher : John Wiley & Sons
ISBN 13 : 1119107334
Total Pages : 873 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis The Finite Element Method by : Bofang Zhu

Download or read book The Finite Element Method written by Bofang Zhu and published by John Wiley & Sons. This book was released on 2018-03-12 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.

Isogeometric Analysis

Author : J. Austin Cottrell
Publisher : John Wiley & Sons
ISBN 13 : 0470749091
Total Pages : 352 pages
Book Rating : 4.4/5 (77 download)

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Book Synopsis Isogeometric Analysis by : J. Austin Cottrell

Download or read book Isogeometric Analysis written by J. Austin Cottrell and published by John Wiley & Sons. This book was released on 2009-08-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: “The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It is very original. There is no other book on this topic.” —René de Borst, Eindhoven University of Technology Written by leading experts in the field and featuring fully integrated colour throughout, Isogeometric Analysis provides a groundbreaking solution for the integration of CAD and FEA technologies. Tom Hughes and his researchers, Austin Cottrell and Yuri Bazilevs, present their pioneering isogeometric approach, which aims to integrate the two techniques of CAD and FEA using precise NURBS geometry in the FEA application. This technology offers the potential to revolutionise automobile, ship and airplane design and analysis by allowing models to be designed, tested and adjusted in one integrative stage. Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique. The authors offer a clear explanation as to how to add isogeometric capabilities to existing finite element computer programs, demonstrating how to implement and use the technology. Detailed programming examples and datasets are included to impart a thorough knowledge and understanding of the material. Provides examples of different applications, showing the reader how to implement isogeometric models Addresses readers on both sides of the CAD/FEA divide Describes Non-Uniform Rational B-Splines (NURBS) basis functions