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Author : Wachspress
Publisher : Academic Press
Page : 330 pages
File Size : 51,8 Mb
Release : 1975-09-26
Category : Computers
ISBN : 9780080956237
A Rational Finite Element Basis
Author : Anonim
Publisher : Unknown
Page : 331 pages
File Size : 44,8 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 128229010X
A rational finite element basis.
Author : Eugene Wachspress
Publisher : Springer
Page : 292 pages
File Size : 55,9 Mb
Release : 2015-10-13
Category : Technology & Engineering
ISBN : 9783319216140
This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation. Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book “A Rational Finite Element Basis” (with minor updates and corrections) written by Dr. Wachspress. Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously. Part three consists of annotated MATLAB programs implementing theory presented in Parts one and two.
Author : Olgierd Cecil Zienkiewicz
Publisher : Unknown
Page : 726 pages
File Size : 45,5 Mb
Release : 2000
Category : Continuum mechanics
ISBN : 0750650494
Author : J. P. Moitinho de Almeida,Edward A. Maunder
Publisher : John Wiley & Sons
Page : 315 pages
File Size : 42,9 Mb
Release : 2017-03-20
Category : Technology & Engineering
ISBN : 9781118424155
A comprehensive treatment of the theory and practice of equilibrium finite element analysis in the context of solid and structural mechanics Equilibrium Finite Element Formulations is an up to date exposition on hybrid equilibrium finite elements, which are based on the direct approximation of the stress fields. The focus is on their derivation and on the advantages that strong forms of equilibrium can have, either when used independently or together with the more conventional displacement based elements. These elements solve two important problems of concern to computational structural mechanics: a rational basis for error estimation, which leads to bounds on quantities of interest that are vital for verification of the output and provision of outputs immediately useful to the engineer for structural design and assessment. Key features: Unique in its coverage of equilibrium – an essential reference work for those seeking solutions that are strongly equilibrated. The approach is not widely known, and should be of benefit to structural design and assessment. Thorough explanations of the formulations for: 2D and 3D continua, thick and thin bending of plates and potential problems; covering mainly linear aspects of behaviour, but also with some excursions into non-linearity. Highly relevant to the verification of numerical solutions, the basis for obtaining bounds of the errors is explained in detail. Simple illustrative examples are given, together with their physical interpretations. The most relevant issues regarding the computational implementation of this approach are presented. When strong equilibrium and finite elements are to be combined, the book is a must-have reference for postgraduate students, researchers in software development or numerical analysis, and industrial practitioners who want to keep up to date with progress in simulation tools.
Author : Philippe G. Ciarlet
Publisher : SIAM
Page : 552 pages
File Size : 48,6 Mb
Release : 2002-04-01
Category : Mathematics
ISBN : 9780898715149
This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.
Author : P.G. Ciarlet
Publisher : Elsevier
Page : 551 pages
File Size : 45,9 Mb
Release : 1978-01-01
Category : Mathematics
ISBN : 9780080875255
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments should provide many suggestions for conducting seminars.
Author : J. T. Oden,J. N. Reddy
Publisher : Courier Corporation
Page : 450 pages
File Size : 55,9 Mb
Release : 2012-05-23
Category : Technology & Engineering
ISBN : 9780486142210
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,Robert Leroy Taylor,J. Z. Zhu
Publisher : Unknown
Page : 733 pages
File Size : 40,5 Mb
Release : 2005
Category : Engineering mathematics
ISBN : 7506292548
Author : Gautam Dasgupta
Publisher : Springer
Page : 333 pages
File Size : 45,6 Mb
Release : 2017-12-05
Category : Technology & Engineering
ISBN : 9781493974238
This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids. The book is divided into two distinct parts of nine chapters and seven appendices. The first chapter reviews the energy concepts in structural mechanics with bar problems, which is continued in the next chapter for truss analysis using Mathematica programs. The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed by four-node elements. Chapters five and six describe Taig’s isoparametric interpolants and Iron’s patch test. Rayleigh vector modes, which satisfy point-wise equilibrium, are elaborated on in chapter seven along with successful patch tests in the physical (x,y) Cartesian frame. Chapter eight explains point-wise incompressibility and employs (Moore-Penrose) inversion of rectangular matrices. The final chapter analyzes patch-tests in all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed in closed algebraic form. Appendices give a short introduction to Mathematica, followed by truss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. All Mathematica codes for theoretical formulations and graphics are included with extensive numerical examples.
Author : Olgierd Cecil Zienkiewicz
Publisher : Unknown
Page : 689 pages
File Size : 45,9 Mb
Release : 2000
Category : Continuum mechanics
ISBN : 0750650494
Author : Steffen Weißer
Publisher : Springer
Page : 246 pages
File Size : 49,7 Mb
Release : 2019-07-18
Category : Computers
ISBN : 9783030209612
This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.
Author : Barna Szabó,Ivo Babuška
Publisher : John Wiley & Sons
Page : 408 pages
File Size : 49,7 Mb
Release : 1991-09-03
Category : Technology & Engineering
ISBN : 0471502731
Covers the fundamentals of linear theory of finite elements, from both mathematical and physical points of view. Major focus is on error estimation and adaptive methods used to increase the reliability of results. Incorporates recent advances not covered by other books.
Author : Pavel Solin,Karel Segeth,Ivo Dolezel
Publisher : CRC Press
Page : 404 pages
File Size : 45,6 Mb
Release : 2003-07-28
Category : Mathematics
ISBN : 9780203488041
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
Author : Susanne Brenner,L. Ridgway Scott
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 45,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475736588
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
