Download or read book A Finite Element Method for the Two dimensional Helmholtz Equation in Unbounded Regions written by Michael J. Scheidler and published by . This book was released on 1979 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Finite Element Method for Problems Involving the Helmholtz Equation in Two Dimensional Exterior Regions written by Samuel Paul Marin and published by . This book was released on 1978 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Elements for Wave Electromagnetics written by IEEE Antennas and Propagation Society and published by Institute of Electrical & Electronics Engineers(IEEE). This book was released on 1994 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Finite Elements and Approximation written by O. C. Zienkiewicz and published by Courier Corporation. This book was released on 2006-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.
Download or read book A Finite Element Method for Problems Involving the Heimholtz Equation in Two Dimensional Exterior Regions written by Samuel Paul Marin and published by . This book was released on 1978 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid Structure Interaction Problem written by Siamak Amini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers the problem of the dynamic fluid-structure interaction between a finite elastic structure and the acoustic field in an unbounded fluid-filled exterior domain. The exterior acoustic field is modelled through a boundary integral equation over the structure surface. However, the classical boundary integral equation formulations of this problem either have no solutions or do not have unique solutions at certain characteristic frequencies (which depend on the surface geometry) and it is necessary to employ modified boundary integral equation formulations which are valid for all frequencies. The particular approach adopted here involves an arbitrary coupling parameter and the effect that this parameter has on the stability and accuracy of the numerical method used to solve the integral equation is examined. The boundary integral analysis of the exterior acoustic problem is coupled with a finite element analysis of the elastic structure in order to investigate the interaction between the dynamic behaviour of the structure and the associated acoustic field. Recently there has been some controversy over whether or not the coupled problem also suffers from the non-uniqueness problems associated with the classical integral equation formulations of the exterior acoustic problem. This question is resolved by demonstrating that .the solution to the coupled problem is not unique at the characteristic frequencies and that it is necessary to employ an integral equation formulation valid for all frequencies.
Download or read book The Finite Element Method in Engineering written by S. S. Rao and published by Elsevier. This book was released on 2013-10-22 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method in Engineering introduces the various aspects of finite element method as applied to engineering problems in a systematic manner. It details the development of each of the techniques and ideas from basic principles. New concepts are illustrated with simple examples wherever possible. Several Fortran computer programs are given with example applications to serve the following purposes: to enable the reader to understand the computer implementation of the theory developed; to solve specific problems; and to indicate procedure for the development of computer programs for solving any other problem in the same area. The book begins with an overview of the finite element method. This is followed by separate chapters on numerical solution of various types of finite element equations; the general procedure of finite element analysis; the development higher order and isoparametric elements; and the application of finite element method for static and dynamic solid and structural mechanics problems like frames, plates, and solid bodies. Subsequent chapters deal with the solution of one-, two-, and three-dimensional steady state and transient heat transfer problems; the finite element solution of fluid mechanics problems; and additional applications and generalization of the finite element method.
Download or read book Finite Element Solutions of the Two Dimensional Helmholtz Equation written by P. Silvester and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Finite Element Method written by D. H. Norrie and published by New York : Academic Press. This book was released on 1973 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method.
Download or read book Finite Element Method written by Sinan Muftu and published by Elsevier. This book was released on 2022-07-19 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Method: Physics and Solution Methods enables the reader to develop a sound understanding of physical systems so that they can get the most out of their use of the finite element method. Nearly all physical systems in the FEM realm are represented by partial differential equations. This book focuses on 1D and 2D elasticity, and 1D and 2D heat transfer problems, with a detailed derivation of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. After a chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing PDE is defined over a sub-segment (element) of the solution domain. As well as being an invaluable guide to thorough and effective use of the finite element method, this book also functions as an authoritative reference on theory of elasticity, heat transfer and mechanics of beams and plates.
Download or read book The finite element method in the 1990 s written by Eugenio Onate and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited on the occasion of Prof. Olgierd C. Zienkiewicz' 70th birthday, this book contains original contributions from eminent scientists dealing with a wide range of theoretical aspects of the Finite Element Method and its application to a variety of engineering problems. The book provides an overview of the state-of-the-art of finite element technology in the last decade of the 20th century.
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 2005-06-23 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 Solution of Boundary Value Problems written by O. Axelsson and published by Academic Press. This book was released on 2014-05-10 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.
Download or read book The Finite Element Method in Partial Differential Equations written by Andrew R. Mitchell and published by John Wiley & Sons. This book was released on 1977 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Trefftz Finite and Boundary Element Method written by Qing-Hua Qin and published by Computational Mechanics. This book was released on 2000 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an accessible and up-to-date introduction to the Trefftz finite element method. The author's main emphasis is on fundamental concepts and the development of different Trefftz element formulations for stress analysis of various elastic problems. The book is a reference for postgraduate students, researchers, scientists and professional engineers in computational mechanics, structural design, and applied mathematics.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1984 with total page 1278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
