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# Topic: Finite element method

###### In the News (Tue 20 Aug 19)

 Finite element method - Wikipedia, the free encyclopedia The method was provided with a rigorous mathematical foundation in 1973 with the publication of Strang and Fix's An Analysis of The Finite Element Method, and has since been generalized into a branch of applied mathematics for numerical modeling of physical systems in a wide variety of engineering disciplines, e.g., electromagnetics and fluid dynamics. The development of the finite element method in structural mechanics is often based on an energy principle, e.g., the virtual work principle or the minimum total potential energy principle, which provides a general, intuitive and physical basis that has a great appeal to structural engineers. Methods that use higher degree piecewise polynomial basis functions are often called spectral element methods, especially if the degree of the polynomials increases as the triangulation size h goes to zero. en.wikipedia.org /wiki/Finite_Element_Method   (2200 words)

 Finite Element Method The main advantage of the serendipity elements is that since the internal nodes of the higher-order Lagrange elements do not contribute to the inter-element connectivity, the elimination of internal nodes results in reductions in the size of the element matrices. The nodes of element 1 are numbered as 1, 2, and 3, and the nodes of element 2 are 1, 3, and 4. While the displacement at the same nodal points of different elements are the same, the forces are not necessarily the same due to the fact that the equilibrium of the forces at a node is enforced. documents.wolfram.com /applications/structural/FiniteElementMethod.html   (5776 words)

 Finite Element Method   (Site not responding. Last check: 2007-11-06) The finite element method is a method for solving partial differential equations (PDEs). The purpose of the method is to determine an approximation to the function u(x). The method is applicable to a wide range of physical and engineering problems, provided it can be expressed as a PDE. Reference books on the finite element method are listed on www.science-books.net. www.finite-element-method.info /intro.htm   (135 words)

 Finite-element method The behaviour of a particular type of element is analysed in terms of the loads and responses at discrete nodes. The result of the analysis of a typical element type is a small matrix relating a vector of nodal displacements to a vector of applied nodal forces. The natural-coördinate method (Desai and Abel, 1972, pp. audilab.bmed.mcgill.ca /~funnell/AudiLab/teach/fem/fem.html   (1816 words)

 THE MESHLESS FINITE ELEMENT METHOD A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. The same point distribution in FEM may have different shape functions (the triangulation is not unique) and the evaluation of nodal connectivity does not necessarily have to be bounded in time to yield accurate results (for instance, the Delaunay tessellation is of order n, but it does not necessarily yield accuracy shape functions). Generate all the polyhedral elements using the nodes belonging to each sphere and the nodes of all the coincident and nearby spheres (the criterion to choose these spheres is given in Appendix I). meshlessfem.tripod.com /THEORY/MFEM_FILES/mfem_index.html   (4676 words)

 eBay - finite element method, Nonfiction Books, Textbooks, Education items on eBay.com   (Site not responding. Last check: 2007-11-06) Introduction To The Finite Element Method by J.N. Re... The Finite Element Method by J. Zhu, O.C. Zienkie... The Finite Element Method in Electromagnetics by Jia... search-desc.ebay.com /search/search.dll?query=finite+element+method&...   (462 words)

 3 Finite Element Method They realised that if say a loaded plate was divided into small triangles or quadrilaterals (`elements') and the displacement within an element was assumed to be linear in space variables, then the stress could be calculated throughout the element and the sum of all the stresses would have to agree with the loading. It was quickly realised that this very practical method could be put in a sound mathematical framework, and once that framework was developed, the method could be applied to problems other than structural analysis. It is important to distinguish our understanding of how finite element analysis approximates the solution of a differential system from the details of how the method is implemented. info.sjc.ox.ac.uk /scr/sobey/iblt/chapter1/notes/node6.html   (1311 words)

 Mathematics of the Finite Element Method Finite element method provides a greater flexibility to model complex geometries than finite difference and finite volume methods do. This is the basis of the finite element analysis method. The integrations over each element are approximated by a single value in a linear element or by the average over the Gauss points in a quadratic element. math.nist.gov /mcsd/savg/tutorial/ansys/FEM   (643 words)

 Butterworth-Heinemann Engineering: Finite Element Method - tutor resource material FEAPpv is a general purpose finite element analysis program which is designed for research and educational use. The program is described in The Finite Element Method 3 Volume set or individually in Volume One and Volume Two. Professor Taylor has written several computer programs for the finite element analysis of structural and non-structural systems, one of which, FEAP, is now used worldwide in education and research environments. www.bh.com /companions/fem   (1241 words)

 Amazon.com: Programming the Finite Element Method: Books: Ian M. Smith,Vaughan Griffiths   (Site not responding. Last check: 2007-11-06) Many textbooks exist which describe the principles of the finite element method of analysis and the wide scope of its applications to the solution of practical engineering problems. Non-Linear Finite Element Analysis of Solids and Structures by M. All other finite element books have code which is somewhat outdated in that they use Fortran77 and only cover direct equation solvers, and do not cover iterative solvers. www.amazon.com /exec/obidos/tg/detail/-/0470849703?v=glance   (1629 words)

 GuideMe.com Finite Element Method Bookstore   (Site not responding. Last check: 2007-11-06) Finite Element Approximation of the Navier-Stokes Equations Vol 749 ~ Finite elements in nonlinear mechanics : papers presented at the International conference on finite elements in nonlinear solid and structural mechanics, held at Geilo, Norway in August 1977 ; editors, Pêal G. Bergan... Mathematical aspects of finite element methods : proceedings of the conference held in Rome, 10-12 December 1975 ~ www.guideme.com /Bookstores/FEM.HTM   (3670 words)

 Zienkiewicz: The Finite Element Method In the years since the fourth edition of this seminal work was published, active research has further developed the Finite Element Method into the pre-eminent tool for the modelling of physical systems. Written by the pre-eminent professors in their fields, this new edition of the Finite Element Method maintains the comprehensive style of the earlier editions and authoritatively incorporates the latest developments of this dynamic field. In the years since the fourth edition of this seminal work was published, active research has developed the Finite Element Method into the pre-eminent tool for the modelling of physical systems. www.science-books.net /featured/zienkiewicz.htm   (607 words)

 A finite element method example   (Site not responding. Last check: 2007-11-06) However, element stiffness matrices for elements that touch the Dirichlet boundary have a slightly different form. Similarly elements 6,7,8 have matrices of size 1,2 and 1 respectively. However, since this type of numbering is not uncommon for finite element solvers DOUG has been developed with this in mind. www.maths.bath.ac.uk /~parsoft/doug/userguide/node10.html   (439 words)

 2. The Finite Element Method   (Site not responding. Last check: 2007-11-06) For the calculation of the demagnetizing field a hybrid finite element/ boundary element method is used as explained in Sec. This method requires the solution of a Poisson and a Laplace equation. Therefore the former is used in this chapter as an example for a short introduction to the finite element method [ magnet.atp.tuwien.ac.at /scholz/projects/diss/html/node6.html   (53 words)

 Amazon.com: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis: Books: Thomas J. R. Hughes   (Site not responding. Last check: 2007-11-06) Nonlinear Finite Elements for Continua and Structures by Ted Belytschko The Finite Element Methodology though conceptually simple (eat the elephant by chopping it up into mouthfuls), becomes somewhat involved when applied, because the of tricks used to get solutions, after all you still may have to solve 100,000 PDEs to get your approximate solution to an otherwise intractable problem. If you are looking to gain some backgrounding in how to construct finite element models using a program to solve problems, this book is probably much more than you need. www.amazon.com /exec/obidos/tg/detail/-/0486411818?v=glance   (1335 words)

 FEM Books-Structural mechanics Finite Elements- An Introduction, Becker, E. B., Carey, G. and Oden, J. Finite Elements- An Introduction for Engineers, Livesley, R. Finite Elements and Solution Procedures for Structural Analysis, Vol. Fundamentals of the Finite Element Method, Grandin, H., 1986, 1991 Theory and Practice of Finite Elements, Ern, A. and Guermond, J. Using Finite Elements in Mechanical Design,Mottram, J. and Shaw, C. There are also other books where one or more chapters dealing with the finite element technique are included on the subject Structural and Solid Mechanics in general. www.solid.ikp.liu.se /fe/str.html   (1385 words)

 Working With ProE For our solid model, the rotation constraints are irrelevant (since nodes of solid elements do not have this degree of freedom anyway). For example, in the analysis of a pressurized tank on a support system with a number of nozzle connections to other pipes, one load set might contain only the internal pressure, another might contain the support forces, another a temperature load, and more might contain the forces applied at each nozzle location. This is at the expense of more than double the number of elements. www.mece.ualberta.ca /tutorials/ansys/AU/ProE/ProE.html   (1432 words)

 Finite Element Method (5th Edition) Volume 1 - The Basis Description: Written by the pre-eminent professors in their fields, this new edition maintains the comprehensive style of the earlier editions and authoritatively incorporates the latest developments of this dynamic field. Expanded to three volumes the book now covers the basis of the method and its application to advanced solid mechanics and also advanced fluid dynamics. Volume 1: The Basis is intended as a broad overview of the Finite Element Method. www.knovel.com /knovel2/Toc.jsp?BookID=509   (786 words)

 [No title] Introduction to Finite Element Method I and II. Aladin is a computational toolkit for the interactive matrix and finite element analysis... Finite elements programm Z88 by Dr. Frank Rieg for Windows NT/95/98, Windows 2000, Linux and UNIX. staff.ttu.ee /~alahe/alem.html   (223 words)

 [No title]   (Site not responding. Last check: 2007-11-06) Stationary principles, principle of stationary potential energy, potential energy of an elastic boty, the Raleigh-Ritz method, variational principles and governing equations. Formulation of element matrices, equilibrium and compatibility in the solution, stress calculations, temperature effects. Axisymmetric elements, finite elements for axial symmetry, loads without axial symmetry. www.angelfire.com /pop/richi/MENG0628.html   (105 words)

 Finite Element Method - MHA021   (Site not responding. Last check: 2007-11-06) CALFEM - A Finite Element Toolbox to MATLAB V3.3 (disc+manual), Byggnadsmekanik och Hållfasthetslära, Lunds Universitet, 1999. Introduction to element approximations in 2D; properties of the stiffness matrix. uses the Finite Element Method with linear triangular elements to approximate the solution of some partial differential equations in 2D. www.am.chalmers.se /~moller/index_fem_m3_gk.html   (788 words)

 FINITE ELEMENT ANALYSIS/METHODS National Agency for Finite Element Methods and Standards (NAFEMS) Application of Combined Finite Element Method and Finite Difference Method Welcome to the World of Finite Element Analysis www.steelynx.net /fea.html   (98 words)

 Finite Element method   (Site not responding. Last check: 2007-11-06) This assures that some of the most important integral relations satisfied by the differential equations are preserved by the finite element discretization. This includes conservation of energy and magnetic flux in the absence of dissipation. The matrices are sparse, having nonzero elements only between those vertices connected by the side of a triangle. www.math.nyu.edu /mfdd/strauss/fem7pl/node4.html   (241 words)

 Structural Dynamics - Finite Element Method Eigenvalues of the generalized eigen problem where the mass and stiffness matrices are symmetric with real coefficients. The eigenvalues are determined by the Jacobi method. Eigenvalues of the generalized eigen problem via the slicing method, which is essentially the Sturm Sequence method. www.vibrationdata.com /StructuralFE.htm   (648 words)

 FEM Books-Desai   (Site not responding. Last check: 2007-11-06) An introduction and application of the finite element method to several fields of engineering activity is presented. This book is directed to the senior undergraduate and first year graduate students. Partial contents: history and concept of the finite element method; mechanics of finite element analysis; 1D problems in solid mechanics, potential flow, time-dependent flow, beam bending and beam columns, mass transport, overland flow, stress wave propagation and soil consolidation; 2D problems; 2D potential flow, thermal flow and seepage; 2D elasticity; 3D analysis of frame structures. ohio.ikp.liu.se /fe/desa.html   (94 words)

 Homepage of Scaled Boundary Finite-Element Method After the boundary is discretized with surface finite elements, the governing partial differential equations are transformed to ordinary differential equations which are solved analytically. The resulting semi-analytical solutions represent singularites and unbounded domains accurately and efficiently in contrast to the standard finite-element method. No fundamental solution as required in the boundary-element method is necessary. lchwww.epfl.ch /wolfweb   (141 words)

 IFER - Internet Finite Element Resources This document describes and provides access to finite element analysis software via the Internet. We list all public domain and shareware programs which have come to our notice, and a selection of pointers to commercial packages. The use of any of these programs and the interpretation of any results obtained remains the responsibility of the user. homepage.usask.ca /~ijm451/finite/fe_resources/fe_resources.html   (136 words)

 The Finite Element Method Site It is totally free and can be run directly from the Internet. The main purpose of the software is to explain basic concepts and demonstrate the capabilities of Finite Element Method. The book makes FEM extremely simple to understand. dattaraj_rao.tripod.com /FEM   (115 words)

 Introduction to Finite Element Method I & II   (Site not responding. Last check: 2007-11-06) Introduction to Finite Element Method I and II Introduction to Finite Element Method - I and II Course Numbers: 20-MECH-525 and 526; Winter and Spring Quarters Click here to see some examples of the final projects from this course and other FEA applications in engineering Distributed Load; Transformation of Coordinate Systems; Element Stress urbana.mie.uc.edu /yliu/FEM-525/FEM-525.htm   (94 words)

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