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Fundamentals Of Enriched Finite Element Methods

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Extended Finite Element Method

Extended Finite Element Method Book
Author : Amir R. Khoei
Publisher : John Wiley & Sons
Release : 2015-02-23
ISBN : 1118457684
Language : En, Es, Fr & De

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Book Description :

Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Extended Finite Element Method: Theory and Applications introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. The XFEM approach is based on an extension of standard finite element method based on the partition of unity method. Extended Finite Element Method: Theory and Applications begins by introducing the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. It then covers the theory and application of XFEM in large deformations, plasticity and contact problems. The implementation of XFEM in fracture mechanics, including the linear, cohesive, and ductile crack propagation is also covered. The theory and applications of the XFEM in multiphase fluid flow, including the hydraulic fracturing in soil saturated media and crack propagation in thermo-hydro-mechanical porous media, is also discussed in detail. Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples

The Finite Element Method Its Basis and Fundamentals

The Finite Element Method  Its Basis and Fundamentals Book
Author : Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu
Publisher : Elsevier
Release : 2005-05-26
ISBN : 9780080472775
Language : En, Es, Fr & De

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Book Description :

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

Fundamentals and Applications of Rock Mechanics

Fundamentals and Applications of Rock Mechanics Book
Author : DEB DEBASIS,VERMA ABHIRAM KUMAR
Publisher : PHI Learning Pvt. Ltd.
Release : 2016-03-12
ISBN : 8120351827
Language : En, Es, Fr & De

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Book Description :

Rock mechanics is a first course in the field of mining and geotechnical engineering. Over the last decades, the concepts and applications of rock mechanics have evolved tremendously for understanding the stability and safety of structures made of/on the rock masses. This book elaborates the fundamental concepts of rock mechanics for designing and analysis of structures and excavations for a variety of applications. The text includes a fine blend of theory and worked-out examples and applications, and also emphasises the basics of stress and strain analysis, volume–weight relationship, rock mass classification systems, in situ stress measurements, stresses around underground opening, pillar and support design, subsidence, slope stability, rock failure criteria and behaviour of jointed rock mass. Numerical analysis procedures and interaction between rock bolts and rock masses are also introduced emphasising the mechanics and applications in rock engineering. Besides undergraduate and postgraduate students of civil (including geotechnical), mining and petroleum engineering, the book will also benefit the practicing engineers and researchers, who wish to acquaint themselves with state-of-the-art techniques of rock mechanics and its applications. Overall, this textbook is useful for both elementary as well as advanced learning.

Extended Finite Element Method

Extended Finite Element Method Book
Author : Zhuo Zhuang,Zhanli Liu,Binbin Cheng,Jianhui Liao
Publisher : Academic Press
Release : 2014-03-24
ISBN : 0124078567
Language : En, Es, Fr & De

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Book Description :

Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems. The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials. Authored by an expert team from one of China's leading academic and research institutions Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems

Geometrically Unfitted Finite Element Methods and Applications

Geometrically Unfitted Finite Element Methods and Applications Book
Author : Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Publisher : Springer
Release : 2018-03-13
ISBN : 3319714317
Language : En, Es, Fr & De

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Book Description :

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.

Fundamentals of the Finite Element Method for Heat and Mass Transfer

Fundamentals of the Finite Element Method for Heat and Mass Transfer Book
Author : Perumal Nithiarasu,Roland W. Lewis,Kankanhalli N. Seetharamu
Publisher : John Wiley & Sons
Release : 2016-01-21
ISBN : 1118535448
Language : En, Es, Fr & De

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Book Description :

Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition is a comprehensively updated new edition and is a unique book on the application of the finite element method to heat and mass transfer. • Addresses fundamentals, applications and computer implementation • Educational computer codes are freely available to download, modify and use • Includes a large number of worked examples and exercises • Fills the gap between learning and research

The Finite Element Method Set

The Finite Element Method Set Book
Author : Olek C Zienkiewicz,Robert L Taylor
Publisher : Elsevier
Release : 2005-11-25
ISBN : 9780080531670
Language : En, Es, Fr & De

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Book Description :

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

Least Squares Finite Element Methods

Least Squares Finite Element Methods Book
Author : Pavel B. Bochev,Max D. Gunzburger
Publisher : Springer Science & Business Media
Release : 2009-04-28
ISBN : 0387689222
Language : En, Es, Fr & De

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Book Description :

Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

The Finite Element Method

The Finite Element Method Book
Author : Bofang Zhu
Publisher : John Wiley & Sons
Release : 2018-06-13
ISBN : 1119107318
Language : En, Es, Fr & De

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Book Description :

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.

Advanced Finite Element Methods and Applications

Advanced Finite Element Methods and Applications Book
Author : Thomas Apel,Olaf Steinbach
Publisher : Springer Science & Business Media
Release : 2012-07-16
ISBN : 3642303161
Language : En, Es, Fr & De

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Book Description :

This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

Extended Finite Element Method

Extended Finite Element Method Book
Author : Soheil Mohammadi
Publisher : John Wiley & Sons
Release : 2008-04-30
ISBN : 0470697997
Language : En, Es, Fr & De

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Book Description :

This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications. One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been extended to nonlinear materials and other disciplines such as modelling contact and interface, simulation of inclusions and holes, moving and changing phase problems, and even to multiscale analyses. The book is self contained, with summaries of both classical and modern computational techniques. The main chapters include a comprehensive range of numerical examples describing various features of XFEM.

Extended Finite Element and Meshfree Methods

Extended Finite Element and Meshfree Methods Book
Author : Timon Rabczuk,Jeong-Hoon Song,Xiaoying Zhuang,Cosmin Anitescu
Publisher : Academic Press
Release : 2019-11-13
ISBN : 0128141077
Language : En, Es, Fr & De

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Book Description :

Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work

Rock Mechanics and Engineering Volume 1

Rock Mechanics and Engineering Volume 1 Book
Author : Xia-Ting Feng
Publisher : CRC Press
Release : 2017-03-16
ISBN : 131531908X
Language : En, Es, Fr & De

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Book Description :

Principles is the first volume of the five-volume set Rock Mechanics and Engineering and contains twenty-four chapters from key experts in the following fields: - Discontinuities; - Anisotropy; - Rock Stress; - Geophysics; - Strength Criteria; - Modeling Rock Deformation and Failure. The five-volume set “Comprehensive Rock Engineering”, which was published in 1993, has had an important influence on the development of rock mechanics and rock engineering. Significant and extensive advances and achievements in these fields over the last 20 years now justify the publishing of a comparable, new compilation. Rock Mechanics and Engineering represents a highly prestigious, multi-volume work edited by Professor Xia-Ting Feng, with the editorial advice of Professor John A. Hudson. This new compilation offers an extremely wideranging and comprehensive overview of the state-of-the-art in rock mechanics and rock engineering and is composed of peer-reviewed, dedicated contributions by all the key experts worldwide. Key features of this set are that it provides a systematic, global summary of new developments in rock mechanics and rock engineering practices as well as looking ahead to future developments in the fields. Contributors are worldrenowned experts in the fields of rock mechanics and rock engineering, though younger, talented researchers have also been included. The individual volumes cover an extremely wide array of topics grouped under five overarching themes: Principles (Vol. 1), Laboratory and Field Testing (Vol. 2), Analysis, Modelling and Design (Vol. 3), Excavation, Support and Monitoring (Vol. 4) and Surface and Underground Projects (Vol. 5). This multi-volume work sets a new standard for rock mechanics and engineering compendia and will be the go-to resource for all engineering professionals and academics involved in rock mechanics and engineering for years to come.

Meshfree Methods for Partial Differential Equations

Meshfree Methods for Partial Differential Equations Book
Author : Michael Griebel,Marc A. Schweitzer
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642561039
Language : En, Es, Fr & De

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Book Description :

Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

The Finite Element Method for Fluid Dynamics

The Finite Element Method for Fluid Dynamics Book
Author : Olek C Zienkiewicz,Robert L Taylor,P. Nithiarasu
Publisher : Elsevier
Release : 2005-12-08
ISBN : 008045559X
Language : En, Es, Fr & De

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Book Description :

Dealing with general problems in fluid mechanics, convection diffusion, compressible and incompressible laminar and turbulent flow, shallow water flows and waves, this is the leading text and reference for engineers working with fluid dynamics in fields including aerospace engineering, vehicle design, thermal engineering and many other engineering applications. The new edition is a complete fluids text and reference in its own right. Along with its companion volumes it forms part of the indispensable Finite Element Method series. New material in this edition includes sub-grid scale modelling; artificial compressibility; full new chapters on turbulent flows, free surface flows and porous medium flows; expanded shallow water flows plus long, medium and short waves; and advances in parallel computing. A complete, stand-alone reference on fluid mechanics applications of the FEM for mechanical, aeronautical, automotive, marine, chemical and civil engineers. Extensive new coverage of turbulent flow and free surface treatments

Encyclopedia Of Two phase Heat Transfer And Flow Iii Macro And Micro Flow Boiling And Numerical Modeling Fundamentals A 4 volume Set

Encyclopedia Of Two phase Heat Transfer And Flow Iii  Macro And Micro Flow Boiling And Numerical Modeling Fundamentals  A 4 volume Set  Book
Author : Thome John R
Publisher : World Scientific
Release : 2018-03-13
ISBN : 9813227427
Language : En, Es, Fr & De

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Book Description :

Set III of this encyclopedia is a new addition to the previous Sets I and II. It contains 26 invited chapters from international specialists on the topics of numerical modeling of two-phase flows and evaporation, fundamentals of evaporation and condensation in microchannels and macrochannels, development and testing of micro two-phase cooling systems for electronics, and various special topics (surface wetting effects, microfin tubes, two-phase flow vibration across tube bundles). The chapters are written both by renowned university researchers and by well-known engineers from leading corporate research laboratories. Numerous 'must read' chapters cover the fundamentals of research and engineering practice on boiling, condensation and two-phase flows, two-phase heat transfer equipment, electronics cooling systems, case studies and so forth. Set III constitutes a 'must have' reference together with Sets I and II for thermal engineering researchers and practitioners.

Damage and Fracture Mechanics

Damage and Fracture Mechanics Book
Author : Taoufik Boukharouba,Mimoun Elboujdaini,Guy Pluvinage
Publisher : Springer Science & Business Media
Release : 2009-08-09
ISBN : 904812669X
Language : En, Es, Fr & De

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Book Description :

The First African InterQuadrennial ICF Conference “AIQ-ICF2008” on Damage and Fracture Mechanics – Failure Analysis of Engineering Materials and Structures”, Algiers, Algeria, June 1–5, 2008 is the first in the series of InterQuadrennial Conferences on Fracture to be held in the continent of Africa. During the conference, African researchers have shown that they merit a strong reputation in international circles and continue to make substantial contributions to the field of fracture mechanics. As in most countries, the research effort in Africa is und- taken at the industrial, academic, private sector and governmental levels, and covers the whole spectrum of fracture and fatigue. The AIQ-ICF2008 has brought together researchers and engineers to review and discuss advances in the development of methods and approaches on Damage and Fracture Mechanics. By bringing together the leading international experts in the field, AIQ-ICF promotes technology transfer and provides a forum for industry and researchers of the host nation to present their accomplishments and to develop new ideas at the highest level. International Conferences have an important role to play in the technology transfer process, especially in terms of the relationships to be established between the participants and the informal exchange of ideas that this ICF offers.

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations Book
Author : A. K. Aziz
Publisher : Academic Press
Release : 2014-05-10
ISBN : 1483267989
Language : En, Es, Fr & De

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Book Description :

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.

The Discontinuous Enrichment Method DEM for Multi scale Transport Problems

The Discontinuous Enrichment Method  DEM  for Multi scale Transport Problems Book
Author : Anonim
Publisher : Stanford University
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

A discontinuous enrichment method (DEM) for the efficient finite element solution of advection-dominated transport problems in fluid mechanics whose solutions are known to possess multi-scale features is developed. Attention is focused specifically on the two-dimensional (2D) advection-diffusion equation, the usual scalar model for the Navier-Stokes equations. Following the basic DEM methodology [1], the usual Galerkin polynomial approximation is locally enriched by the free-space solutions to the governing homogeneous partial differential equation (PDE). For the constant-coefficient advection-diffusion equation, several families of free-space solutions are derived. These include a family of exponential functions that exhibit a steep gradient in some flow direction, and a family of discontinuous polynomials. A parametrization of the former class of functions with respect to an angle parameter is developed, so as to enable the systematic design and implementation of DEM elements of arbitrary orders. It is shown that the original constant-coefficient methodology has a natural extension to variable-coefficient advection-diffusion problems. For variable-coefficient transport problems, the approximation properties of DEM can be improved by augmenting locally the enrichment space with a "higher-order" enrichment function that solves the governing PDE with the advection field a(x) linearized to second order. A space of Lagrange multipliers, introduced at the element interfaces to enforce a weak continuity of the solution and related to the normal derivatives of the enrichment functions, is developed. The construction of several low and higher-order DEM elements fitting this paradigm is discussed in detail. Numerical results for several constant as well as variable-coefficient advection-diffusion benchmark problems reveal that these DEM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity by a large margin, especially when the flow is advection-dominated.