The Virtual Element Method And Its Applications

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The Virtual Element Method and its Applications

Author : Paola F. Antonietti
Publisher : Springer
ISBN 13 : 9783030953218
Total Pages : 0 pages
Book Rating : 4.9/5 (532 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. This book was released on 2023-10-10 with total page 0 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.

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.

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

The Finite Element Method: Its Basis and Fundamentals

Author : Olek C Zienkiewicz
Publisher : Elsevier
ISBN 13 : 008047277X
Total Pages : 753 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis The Finite Element Method: Its Basis and Fundamentals by : Olek C Zienkiewicz

Download or read book The Finite Element Method: Its Basis and Fundamentals written by Olek C Zienkiewicz and published by Elsevier. This book was released on 2005-05-26 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text

Finite Element Applications

Author : Michael Okereke
Publisher : Springer
ISBN 13 : 3319671251
Total Pages : 472 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 472 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.

The Finite Element Method

Author : Zhu
Publisher : John Wiley & Sons
ISBN 13 : 1119107334
Total Pages : 872 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis The Finite Element Method by : Zhu

Download or read book The Finite Element Method written by Zhu and published by John Wiley & Sons. This book was released on 2018-03-12 with total page 872 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.

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 Analysis in Geotechnical Engineering

Author : David M Potts
Publisher : Thomas Telford
ISBN 13 : 9780727727831
Total Pages : 456 pages
Book Rating : 4.7/5 (278 download)

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Book Synopsis Finite Element Analysis in Geotechnical Engineering by : David M Potts

Download or read book Finite Element Analysis in Geotechnical Engineering written by David M Potts and published by Thomas Telford. This book was released on 2001 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insight into the use of the finite method in geotechnical engineering. The first volume covers the theory and the second volume covers the applications of the subject. The work examines popular constitutive models, numerical techniques and case studies.

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 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:

Finite Element Method with Applications in Engineering

Author : Y. M. Desai
Publisher : Pearson Education India
ISBN 13 : 9788131724644
Total Pages : 492 pages
Book Rating : 4.7/5 (246 download)

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Book Synopsis Finite Element Method with Applications in Engineering by : Y. M. Desai

Download or read book Finite Element Method with Applications in Engineering written by Y. M. Desai and published by Pearson Education India. This book was released on 2011 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explains the finite element method with various engineering applications to help students, teachers, engineers and researchers. It explains mathematical modeling of engineering problems and approximate methods of analysis and different approaches.

Engineering Applications of Discrete Element Method

Author : Xuewen Wang
Publisher : Springer Nature
ISBN 13 : 9811579776
Total Pages : 186 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Engineering Applications of Discrete Element Method by : Xuewen Wang

Download or read book Engineering Applications of Discrete Element Method written by Xuewen Wang and published by Springer Nature. This book was released on 2020-09-10 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the engineering application of the discrete element method (DEM), especially the simulation analysis of the typical equipment (scraper conveyor, coal silos, subsoiler) in the coal and agricultural machinery. In this book, the DEM is applied to build rigid and loose coupling model, and the kinematic effect of the bulk materials, the mechanical effect of the interaction between the bulk materials, and the mechanical equipment in the operation process of the relevant equipment are studied. On this basis, the optimization design strategy of the relevant structure is proposed. This book effectively promotes the application of DEM in engineering, analyzes the operation state, failure mechanism, and operation effect of related equipment in operation, and provides theoretical basis for the optimal design of equipment. The book is intended for undergraduate and graduate students who are interested in mechanical engineering, researchers investigating coal and agricultural machinery, and engineers working on designing related equipments.

Automation of Finite Element Methods

Author : Jože Korelc
Publisher : Springer
ISBN 13 : 3319390058
Total Pages : 346 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 346 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.

A Rational Finite Element Basis

Author : Wachspress
Publisher : Academic Press
ISBN 13 : 0080956238
Total Pages : 330 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 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Rational Finite Element Basis

Galerkin Finite Element Methods for Parabolic Problems

Author : Vidar Thomee
Publisher : Springer Science & Business Media
ISBN 13 : 3662033593
Total Pages : 310 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomee

Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.

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.