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Author : Jeffrey David Meese
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (129 download)
Download or read book Mixed Element Formulation for the Finite Element-boundary Integral Method written by Jeffrey David Meese and published by . This book was released on 2003 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : O. C. Zienkiewicz
Publisher : Elsevier
ISBN 13 : 0080531679
Total Pages : 1863 pages
Book Rating : 4.0/5 (85 download)
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
Author : John P. Wolf
Publisher : John Wiley & Sons
ISBN 13 : 9780471486824
Total Pages : 398 pages
Book Rating : 4.4/5 (868 download)
Download or read book The Scaled Boundary Finite Element Method written by John P. Wolf and published by John Wiley & Sons. This book was released on 2003-03-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
Author : Luigi Morino
Publisher : Springer Science & Business Media
ISBN 13 : 9401157065
Total Pages : 243 pages
Book Rating : 4.4/5 (11 download)
Download or read book IABEM Symposium on Boundary Integral Methods for Nonlinear Problems written by Luigi Morino and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the IABEM Symposium held in Pontignano, Italy, May 28-June 3, 1995
Author : Claes Johnson
Publisher : Courier Corporation
ISBN 13 : 0486131599
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)
Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Author : Ioannis Koutromanos
Publisher : John Wiley & Sons
ISBN 13 : 1119260086
Total Pages : 724 pages
Book Rating : 4.1/5 (192 download)
Download or read book Fundamentals of Finite Element Analysis written by Ioannis Koutromanos and published by John Wiley & Sons. This book was released on 2018-02-12 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis.
Author : J. T. Oden
Publisher : Courier Corporation
ISBN 13 : 0486142213
Total Pages : 450 pages
Book Rating : 4.4/5 (861 download)
Download or read book An Introduction to the Mathematical Theory of Finite Elements written by J. T. Oden and published by Courier Corporation. This book was released on 2012-05-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
Author : O. C. Zienkiewicz
Publisher : Butterworth-Heinemann
ISBN 13 : 9780750650557
Total Pages : 482 pages
Book Rating : 4.6/5 (55 download)
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:
Author : Vladimir Kompiš
Publisher : Springer
ISBN 13 : 3709125480
Total Pages : 231 pages
Book Rating : 4.7/5 (91 download)
Download or read book Selected Topics in Boundary Integral Formulations for Solids and Fluids written by Vladimir Kompiš and published by Springer. This book was released on 2014-05-04 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book outlines special approaches using singular and non-singular, multi-domain and meshless BEM formulations, hybrid- and reciprocity-based FEM for the solution of linear and non-linear problems of solid and fluid mechanics and for the acoustic fluid-structure interaction. Use of Trefftz functions and other regularization approaches to boundary integral equations (BIE), boundary contour and boundary node solution of BIE, sensitivity analysis, shape optimization, error analysis and adaptivity, stress and displacement derivatives in non-linear problems smoothing using Trefftz polynomials and other special numerical approaches are included. Applications to problems such as noise radiation from rolling bodies, acoustic radiation in closed and infinite domains, 3D dynamic piezoelectricity, Stefan problems and coupled problems are included.
Author : Vivette Girault
Publisher : Springer Science & Business Media
ISBN 13 : 3642616232
Total Pages : 386 pages
Book Rating : 4.6/5 (426 download)
Download or read book Finite Element Methods for Navier-Stokes Equations written by Vivette Girault and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
Author : Anders Logg
Publisher : Springer Science & Business Media
ISBN 13 : 3642230997
Total Pages : 723 pages
Book Rating : 4.6/5 (422 download)
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Author : Tania G.B. DeFigueiredo
Publisher : Springer Science & Business Media
ISBN 13 : 3642845045
Total Pages : 210 pages
Book Rating : 4.6/5 (428 download)
Download or read book A New Boundary Element Formulation in Engineering written by Tania G.B. DeFigueiredo and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1 The Hybrid Displacement Boundary Element Model This work is concerned with the derivation of a numerical model for the solution of boundary-value problems in potential theory and linear elasticity. It is considered a boundary element model because the final integral equation involves some boundary integrals, whose evaluation requires a boundary discretization. Furthermore, all the unknowns are boundary vari ables. The model is completely new; it differs from the classical boundary element formulation ·in the way it is generated and consequently in the fi nal equations. A generalized variational principle is used as a basis for its derivation, whereas the conventional boundary element formulation is based on Green's formula (potential problems) and on Somigliana's identity (elas ticity), or alternatively through the weighted residual technique. 2 The multi-field variational principle which generates the formulation in volves three independent variables. For potential problems, these are the potential in the domain and the potential and its normal derivative on the boundary. In the case of elasticity, these variables are displacements in the domain and displacements and tractions on the boundary. For this reason, by analogy with the assumed displacement hybrid finite element model, ini tially proposed by Tong [1] in 1970, it can be called a hybrid displacement model. The final system of equations to be solved is similar to that found in a stiffness formulation. The stiffness matrix for this model is symmetric and can be evaluated by only performing integrations along the boundary.
Author : Mats G. Larson
Publisher : Springer Science & Business Media
ISBN 13 : 3642332870
Total Pages : 403 pages
Book Rating : 4.6/5 (423 download)
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.
Author : J. T. Oden
Publisher : Courier Corporation
ISBN 13 : 0486317900
Total Pages : 517 pages
Book Rating : 4.4/5 (863 download)
Download or read book Finite Elements of Nonlinear Continua written by J. T. Oden and published by Courier Corporation. This book was released on 2013-04-15 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view. The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical solution of the equations governing the discrete model. Though the theory and methods are sufficiently general to be applied to any nonlinear problem, emphasis has been placed on problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. Problems in rarefied gas dynamics and nonlinear partial differential equations are also examined. Other topics include topological properties of finite element models, applications to linear and nonlinear boundary value problems, and discrete models of nonlinear thermomechanical behavior of dissipative media. This comprehensive text is valuable not only to students of structural analysis and continuum mechanics but also to professionals researching the numerical analysis of continua
Author : Apostol Poceski
Publisher : Springer Science & Business Media
ISBN 13 : 3642846769
Total Pages : 357 pages
Book Rating : 4.6/5 (428 download)
Download or read book Mixed Finite Element Method written by Apostol Poceski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, based on 16 years of work on the finite element method, the author presents the essence of a new, direct approach to the FEM. The work is focused on the mixed method and shows how reliable results may be obtained with fewer equations than usual. The basic principles, the fundamentals and the essence of the FEM are presented, then the method is applied to the analysis of one, two, and three-dimensional problems. It is shown that mixed elements offer superior accuracy compared with stiffness elements. Finally, some new achievements and perspectives for further development are presented. The book is intended for undergraduate and graduate students, mathematicians, research engineers and practicing engineers. To understand the book, a familiarity with classical mechanics is sufficient.
Author : Aslak Tveito
Publisher : Springer Nature
ISBN 13 : 3030611574
Total Pages : 116 pages
Book Rating : 4.0/5 (36 download)
Download or read book Modeling Excitable Tissue written by Aslak Tveito and published by Springer Nature. This book was released on 2020-10-30 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.
Author : Stephen Kirkup
Publisher : Stephen Kirkup
ISBN 13 : 9780953403103
Total Pages : 136 pages
Book Rating : 4.4/5 (31 download)
Download or read book The Boundary Element Method in Acoustics written by Stephen Kirkup and published by Stephen Kirkup. This book was released on 1998 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
