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Author: B. Backstrom
Publisher: Gb Pub
ISBN: 9789197555302
Category : Science
Languages : en
Pages : 324
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Book Description
Have you ever solved a partial differential equation ? The laws of physics may be transformed mathematically into second-order partial differential equations (PDEs). The simplest one of this type is known as the Laplace equation. This governs the distribution of gravitation in free space. Other PDEs, for the electric and magnetic fields etc., are somewhat similar but more complicated. Few of these equations have exact solutions, which explains why they do not receive the attention they deserve in the academic curriculum. Only in recent years has it become possible to solve PDEs numerically on an ordinary PC by finite element analysis (FEA). The present book is unique in its approach. It is not another volume on conceivable algorithms of FEA. Its main purpose is to exploit a free web program for dealing with PDEs occurring in physics. This program solves a typical example in seconds and promptly presents the results graphically by a variety of plots. The main topics treated are the following. Plotting Functions, Laplace and Poisson PDEs, Electricity, Magnetism, Heat, Problems in 3D Space, Electromagnetic Waves, Wave Mechanics, Fluid Dynamics. More information is available on the author's web site.
Author: B. Backstrom
Publisher: Gb Pub
ISBN: 9789197555302
Category : Science
Languages : en
Pages : 324
Get Book Here
Book Description
Have you ever solved a partial differential equation ? The laws of physics may be transformed mathematically into second-order partial differential equations (PDEs). The simplest one of this type is known as the Laplace equation. This governs the distribution of gravitation in free space. Other PDEs, for the electric and magnetic fields etc., are somewhat similar but more complicated. Few of these equations have exact solutions, which explains why they do not receive the attention they deserve in the academic curriculum. Only in recent years has it become possible to solve PDEs numerically on an ordinary PC by finite element analysis (FEA). The present book is unique in its approach. It is not another volume on conceivable algorithms of FEA. Its main purpose is to exploit a free web program for dealing with PDEs occurring in physics. This program solves a typical example in seconds and promptly presents the results graphically by a variety of plots. The main topics treated are the following. Plotting Functions, Laplace and Poisson PDEs, Electricity, Magnetism, Heat, Problems in 3D Space, Electromagnetic Waves, Wave Mechanics, Fluid Dynamics. More information is available on the author's web site.
Author: Gunnar Backstrom
Publisher:
ISBN: 9789197955263
Category : Science
Languages : en
Pages : 322
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Book Description
The laws of physics may be transformed mathematically into second-order partial differential equations (PDEs). The simplest one of this type is known as the Laplace equation. This governs the distribution of gravitation in free space. Other PDEs, for the electric and magnetic fields etc., are somewhat similar but more complicated. Few of these equations have exact solutions, which explains why they do not receive the attention they deserve in the academic curriculum. Only in recent years has it become possible to solve PDEs numerically on an ordinary PC by finite element analysis (FEA). The present book is unique in its approach. It is not another volume on conceivable algorithms of FEA. Its main purpose is to exploit a free web program for dealing with PDEs occurring in physics. This program solves a typical example in seconds and promptly presents the results graphically by a variety of plots.
Author: Gunnar Backstrom
Publisher:
ISBN: 9789144486710
Category : Finite element method
Languages : en
Pages : 312
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Book Description
Author: Gunnar Backstrom
Publisher: Gb Pub
ISBN: 9789197555326
Category : Education
Languages : en
Pages : 240
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Book Description
Simple Fields of Physics by FEA Understanding Elasticity the Easy Way Elastic deformation is of enormous importance in mechanical engineering and has long been a prominent item in technical education. The theory profits from major developments during the 1800s. Stress and strain do not transform as directly as vectors, and the subject is somewhat counter-intuitive. A century ago one had to resort to graphical devices, such as the Mohr circle, to handle elasticity concepts. Most textbooks still use this antiquated technique. With the advent of the PC it became possible to transform stress and strain analytically and to plot results in informative ways. In addition, elastic deformation could then be studied by means of finite element analysis, which dramatically extended the range of applications. The present volume contains other enhancements with respect to ordinary textbooks. Problems of torsion and warping are solved by PDEs, even for hollow shafts. There is also a treatise on thermoelastic defor-mation. Many examples are in three dimensions. Finally, wave motion is studied by a slight extension of the PDE formalism. The latter is sufficient for solving problems of forced as well as free vibration. Eigenstates can thus be illustrated for objects in 2D and 3D. This book assumes no previous knowledge of FEA. In the first chapters it introduces the graphics facilities of FlexPDE and then demonstrates how Laplace and Poisson equations may be solved. The free student version of this program is sufficient throughout.
Author: Zhangxin Chen
Publisher: Springer Science & Business Media
ISBN: 3540240780
Category : Science
Languages : en
Pages : 415
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Book Description
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.
Author: Douglas H. Norrie
Publisher: Academic Press
ISBN: 1483218910
Category : Technology & Engineering
Languages : en
Pages : 337
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Book Description
The Finite Element Method: Fundamentals and Applications demonstrates the generality of the finite element method by providing a unified treatment of fundamentals and a broad coverage of applications. Topics covered include field problems and their approximate solutions; the variational method based on the Hilbert space; and the Ritz finite element method. Finite element applications in solid and structural mechanics are also discussed. Comprised of 16 chapters, this book begins with an introduction to the formulation and classification of physical problems, followed by a review of field or continuum problems and their approximate solutions by the method of trial functions. It is shown that the finite element method is a subclass of the method of trial functions and that a finite element formulation can, in principle, be developed for most trial function procedures. Variational and residual trial function methods are considered in some detail and their convergence is examined. After discussing the calculus of variations, both in classical and Hilbert space form, the fundamentals of the finite element method are analyzed. The variational approach is illustrated by outlining the Ritz finite element method. The application of the finite element method to solid and structural mechanics is also considered. This monograph will appeal to undergraduate and graduate students, engineers, scientists, and applied mathematicians.
Author: Sinan Muftu
Publisher: Academic Press
ISBN: 0128232005
Category : Technology & Engineering
Languages : en
Pages : 542
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Book Description
Finite Element Method: Physics and Solution Methods aims to provide the reader a sound understanding of the physical systems and solution methods to enable effective use of the finite element method. This book focuses on one- and two-dimensional elasticity and heat transfer problems with detailed derivations of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. Following the chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing partial differential equation is defined over a subsegment (element) of the solution domain. As well as being a guide to thorough and effective use of the finite element method, this book also functions as a reference on theory of elasticity, heat transfer, and mechanics of beams. - Covers the detailed physics governing the physical systems and the computational methods that provide engineering solutions in one place, encouraging the reader to conduct fully informed finite element analysis - Addresses the methodology for modeling heat transfer, elasticity, and structural mechanics problems - Extensive worked examples are provided to help the reader to understand how to apply these methods in practice
Author: P. SESHU
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120323157
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.
Author: Nitin S. Gokhale
Publisher: FINITE TO INFINITE
ISBN: 8190619500
Category : Engineering
Languages : en
Pages : 27
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Book Description
Highlights of the book: Discussion about all the fields of Computer Aided Engineering, Finite Element Analysis Sharing of worldwide experience by more than 10 working professionals Emphasis on Practical usuage and minimum mathematics Simple language, more than 1000 colour images International quality printing on specially imported paper Why this book has been written ... FEA is gaining popularity day by day & is a sought after dream career for mechanical engineers. Enthusiastic engineers and managers who want to refresh or update the knowledge on FEA are encountered with volume of published books. Often professionals realize that they are not in touch with theoretical concepts as being pre-requisite and find it too mathematical and Hi-Fi. Many a times these books just end up being decoration in their book shelves ... All the authors of this book are from IIT€™s & IISc and after joining the industry realized gap between university education and the practical FEA. Over the years they learned it via interaction with experts from international community, sharing experience with each other and hard route of trial & error method. The basic aim of this book is to share the knowledge & practices used in the industry with experienced and in particular beginners so as to reduce the learning curve & avoid reinvention of the cycle. Emphasis is on simple language, practical usage, minimum mathematics & no pre-requisites. All basic concepts of engineering are included as & where it is required. It is hoped that this book would be helpful to beginners, experienced users, managers, group leaders and as additional reading material for university courses.
Author: Y. M. Desai
Publisher: Pearson Education India
ISBN: 9788131724644
Category : Electronic books
Languages : en
Pages : 492
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Book Description
The book explains the finite element method with various engineering applications to help students, teachers, engineers and researchers. It explains mathematical modeling of engineering problems and approximate methods of analysis and different approaches.
