Download or read book Application and Implementation of Finite Element Methods written by J. E. Akin and published by . This book was released on 1984 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book The Finite Element Method Theory Implementation and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Download or read book Understanding and Implementing the Finite Element Method written by Mark S. Gockenbach and published by SIAM. This book was released on 2006-01-01 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding and Implementing the Finite Element Method Mark S. Gockenbach "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." --Anthony Kearsley, research mathematician, National Institute of Standards and Technology The infinite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the finite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics.
Download or read book Implementation of Finite Element Methods for Navier Stokes Equations written by F. Thomasset and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
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
Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-10-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.
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.
Download or read book Finite Element Method written by Pin Tong and published by Dover Books on Engineering. This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces mathematical foundations, developing them coherently and rigorously to reveal the method's broad applications. It emphasizes use of the variational approach, providing appendixes on variational calculus and matrix algebra for a self-contained treatment. Detailed examples employ Poisson's equations and the general Sturm-Liouville problem. 1977 edition.
Download or read book Introduction to the Finite Element Method and Implementation with MATLAB written by Gang Li and published by Cambridge University Press. This book was released on 2020-07-30 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connecting theory with numerical techniques using MATLAB®, this practical textbook equips students with the tools required to solve finite element problems. This hands-on guide covers a wide range of engineering problems through nine well-structured chapters including solid mechanics, heat transfer and fluid dynamics; equilibrium, steady state and transient; and 1-D, 2-D and 3-D problems. Engineering problems are discussed using case study examples, which are solved using a systematic approach, both by examining the steps manually and by implementing a complete MATLAB®code. This topical coverage is supplemented by discourse on meshing with a detailed explanation and implementation of 2-D meshing algorithms. Introducing theory and numerical techniques alongside comprehensive examples this text increases engagement and provides students with the confidence needed to implement their own computer codes to solve given problems.
Download or read book Finite Element Methods Concepts and Applications in Geomechanics written by Debasis Deb and published by PHI Learning Pvt. Ltd.. This book was released on 2010 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Method for Solids and Structures written by Sung W. Lee and published by Cambridge University Press. This book was released on 2021-06-17 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the basic mathematics needed for a balanced understanding of finite element method theory and its implementation.
Download or read book Finite Elements for Engineers with ANSYS Applications written by Mohamed Gadala and published by Cambridge University Press. This book was released on 2020-07-09 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering theory and practical industry usage of the finite element method, this highly-illustrated step-by-step approach thoroughly introduces methods using ANSYS.
Download or read book Geometrically Unfitted Finite Element Methods and Applications written by Stéphane P. A. Bordas and published by Springer. This book was released on 2018-03-13 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
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.
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.
Download or read book Finite Element Methods written by Jonathan Whiteley and published by Springer. This book was released on 2017-01-26 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
