Search Results: an-analysis-of-the-finite-element-method

An Analysis of the Finite Element Method

Author: Gilbert Strang,George Fix

Publisher: Wellesley-Cambridge Press

ISBN: 9780980232783

Category: Mathematics

Page: 412

View: 3395

This second edition has two parts. The first part is the complete classic by Gilbert Strang and George Fix, first published in 1973. The original book demonstrates the solid mathematical foundation of the finite element idea, and the reasons for its success. The second part is a new textbook by Strang. It provides examples, codes, and exercises to connect the theory of the Finite Element Method directly to the applications. The reader will learn how to assemble the stiffness matrix K and solve the finite element equations KU=F. Discontinuous Galerkin methods with a numerical flux function are now included. Strang's approach is direct and focuses on learning finite elements by using them.

The Mathematical Theory of Finite Element Methods

Author: Susanne C Brenner,L. Ridgway Scott

Publisher: Springer Science & Business Media

ISBN: 1475736584

Category: Mathematics

Page: 363

View: 3886

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

The Finite Element Method

A Practical Course

Author: G.R. Liu,S. S. Quek

Publisher: Butterworth-Heinemann

ISBN: 0080994415

Category: Technology & Engineering

Page: 464

View: 7000

Written for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and techniques of the FEM in a concise and easy-to-understand format and applies the techniques to civil, mechanical, and aerospace problems. Updated throughout for current developments in FEM and FEM software, the book also includes case studies, diagrams, illustrations, and tables to help demonstrate the material. Plentiful diagrams, illustrations and tables demonstrate the material Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality Full set of PowerPoint presentation slides that illustrate and support the book, available on a companion website

The Finite Element Method in Engineering

Author: Singiresu S. Rao

Publisher: Butterworth-Heinemann

ISBN: 0128143649

Category: Technology & Engineering

Page: 782

View: 7158

The Finite Element Method in Engineering, Sixth Edition, provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique—an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how to set up finite element solutions in civil, mechanical and aerospace engineering applications. The new edition features updated real-world examples from MATLAB, Ansys and Abaqus, and a new chapter on additional FEM topics including extended FEM (X-FEM). Professional engineers will benefit from the introduction to the many useful applications of finite element analysis. Includes revised and updated chapters on MATLAB, Ansys and Abaqus Offers a new chapter, Additional Topics in Finite Element Method Includes discussion of practical considerations, errors and pitfalls in FEM singularity elements Features a brief presentation of recent developments in FEM including extended FEM (X-FEM), augmented FEM (A-FEM) and partition of unity FEM (POUFEM) Features improved pedagogy, including the addition of more design-oriented and practical examples and problems Covers real-life applications, sample review questions at the end of most chapters, and updated references

Essentials of the Finite Element Method

For Mechanical and Structural Engineers

Author: Dimitrios G Pavlou

Publisher: Academic Press

ISBN: 0128026065

Category: Technology & Engineering

Page: 500

View: 1690

Fundamental coverage, analytic mathematics, and up-to-date software applications are hard to find in a single text on the finite element method (FEM). Dimitrios Pavlou’s Essentials of the Finite Element Method: For Structural and Mechanical Engineers makes the search easier by providing a comprehensive but concise text for those new to FEM, or just in need of a refresher on the essentials. Essentials of the Finite Element Method explains the basics of FEM, then relates these basics to a number of practical engineering applications. Specific topics covered include linear spring elements, bar elements, trusses, beams and frames, heat transfer, and structural dynamics. Throughout the text, readers are shown step-by-step detailed analyses for finite element equations development. The text also demonstrates how FEM is programmed, with examples in MATLAB, CALFEM, and ANSYS allowing readers to learn how to develop their own computer code. Suitable for everyone from first-time BSc/MSc students to practicing mechanical/structural engineers, Essentials of the Finite Element Method presents a complete reference text for the modern engineer. Provides complete and unified coverage of the fundamentals of finite element analysis Covers stiffness matrices for widely used elements in mechanical and civil engineering practice Offers detailed and integrated solutions of engineering examples and computer algorithms in ANSYS, CALFEM, and MATLAB

Finite Elements for Analysis and Design

Computational Mathematics and Applications Series

Author: J. E. Akin

Publisher: Elsevier

ISBN: 008050647X

Category: Technology & Engineering

Page: 560

View: 5624

The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material. Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing Basic theory has been added in the book, including worked examples to enable students to understand the concepts Contains coverage of computational topics, including worked examples to enable students to understand concepts Improved coverage of sensitivity analysis and computational fluid dynamics Uses example applications to increase students' understanding Includes a disk with the FORTRAN source for the programs cided in the text

Fundamentals of the finite element method

Author: Hartley Grandin

Publisher: Waveland Pr Inc


Category: Mathematics

Page: 528

View: 2019

Fundamentals of Finite Element Analysis

Linear Finite Element Analysis

Author: Ioannis Koutromanos

Publisher: John Wiley & Sons

ISBN: 1119260086

Category: Technology & Engineering

Page: 712

View: 7731

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.

The Finite Element Analysis of Shells - Fundamentals


Author: Dominique Chapelle,Klaus-Jürgen Bathe

Publisher: Springer Science & Business Media

ISBN: 9783540413394

Category: Mathematics

Page: 330

View: 1332

Shell structures are found abundantly in engineering designs and are routinely analyzed with finite element methods. The objective of this book is to present, in a unified manner, modern finite element procedures for general shell analysis. The first chapters introduce the basic concepts for the analysis of shells, explain the mathematical preliminaries, and discuss the mathematical models of plates and shells including their asymptotic properties. The following chapters deal with finite element discretization methods for plates and shells. At the end of the book, applications of these methods in modern engineering practice are described and an overview of nonlinear shell analysis is given.

The Finite Element Method: Its Basis and Fundamentals

Author: Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu

Publisher: Butterworth-Heinemann

ISBN: 008095135X

Category: Technology & Engineering

Page: 756

View: 7372

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field problems Automatic mesh generation Plate bending and shells Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development. Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience. Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms.

Finite Element Procedures

Author: Klaus-Jürgen Bathe

Publisher: Klaus-Jurgen Bathe

ISBN: 9780979004902

Category: Engineering mathematics

Page: 1037

View: 3039

Application of the Finite Element Method in Implant Dentistry

Author: Jianping Geng,Weiqi Yan,Wei Xu

Publisher: Springer Science & Business Media

ISBN: 9783540737643

Category: Technology & Engineering

Page: 137

View: 9921

This book creates the theoretical foundation that novices need to perform the finite element method in implant dentistry. It shows how both the implant dentist and the designer can benefit from finite element analysis. The authors explain the theory and math of the finite element method. Then, you get practical applications alongside discussions of the critical issues in using finite element analysis for dental implant design.

The Finite Element Method: Theory, Implementation, and Applications

Author: Mats G. Larson,Fredrik Bengzon

Publisher: Springer Science & Business Media

ISBN: 3642332870

Category: Computers

Page: 395

View: 9281

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.​

An Introduction to the Mathematical Theory of Finite Elements

Author: J. T. Oden,J. N. Reddy

Publisher: Courier Corporation

ISBN: 0486142213

Category: Technology & Engineering

Page: 448

View: 1880

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.

Computational Techniques of Rotor Dynamics with the Finite Element Method

Author: Arne Vollan,Louis Komzsik

Publisher: CRC Press

ISBN: 1439847703

Category: Science

Page: 296

View: 1172

For more than a century, we have had a firm grasp on rotor dynamics involving rigid bodies with regular shapes, such as cylinders and shafts. However, to achieve an equally solid understanding of the rotational behavior of flexible bodies—especially those with irregular shapes, such as propeller and turbine blades—we require more modern tools and methods. Computational Techniques of Rotor Dynamics with the Finite Element Method explores the application of practical finite element method (FEM)-based computational techniques and state-of-the-art engineering software. These are used to simulate behavior of rotational structures that enable the function of various types of machinery—from generators and wind turbines to airplane engines and propellers. The book’s first section focuses on the theoretical foundation of rotor dynamics, and the second concentrates on the engineering analysis of rotating structures. The authors explain techniques used in the modeling and computation of the forces involved in the rotational phenomenon. They then demonstrate how to interpret and apply the results to improve fidelity and performance. Coverage includes: Use of FEM to achieve the most accurate computational simulation of all gyroscopic forces occurring in rotational structures Details of highly efficient and accurate computational and numerical techniques for dynamic simulations Interpretation of computational results, which is instrumental to developing stable rotating machinery Practical application examples of rotational structures’ dynamic response to external and internal excitations An FEM case study that illustrates the computational complexities associated with modeling and computation of forces of rotor dynamics Assessment of propellers and turbines that are critical to the transportation and energy industries Useful to practicing engineers and graduate-level students alike, this self-contained volume also serves as an invaluable reference for researchers and instructors in this field. CRC Press Authors Speak Louis Komzsik introduces you to two books that share a common mathematical foundation, the finite element analysis technique. Watch the video.

Programming the Finite Element Method

Author: I. M. Smith,D. V. Griffiths,L. Margetts

Publisher: John Wiley & Sons

ISBN: 1118535928

Category: Technology & Engineering

Page: 688

View: 560

Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary conditions, and interfaces to third party tools such as ParaView, METIS and ARPACK. As in the previous editions, a wide variety of problem solving capabilities are presented including structural analysis, elasticity and plasticity, construction processes in geomechanics, uncoupled and coupled steady and transient fluid flow and linear and nonlinear solid dynamics. Key features: • Updated to take into account advances in parallel computing as well as new material on thermal stress analysis • Programs use an updated version of Fortran 2003 • Includes exercises for students • Accompanied by website hosting software Programming the Finite Element Method, Fifth Edition is an ideal textbook for undergraduate and postgraduate students in civil and mechanical engineering, applied mathematics and numerical analysis, and is also a comprehensive reference for researchers and practitioners. Further information and source codes described in this text can be accessed at the following web sites: • /PFEM5 for the serial programs from Chapters 4-11 • for the parallel programs from Chapter 12

A Unified Approach to the Finite Element Method and Error Analysis Procedures

Author: Julian A. T. Dow

Publisher: Elsevier

ISBN: 9780080543420

Category: Technology & Engineering

Page: 533

View: 4193

A Unified Approach to the Finite Element Method and Error Analysis Procedures provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. New, simpler element formulation techniques, model-independent results, and error measures New polynomial-based methods for identifying critical points New procedures for evaluating sheer/strain accuracy Accessible to undergraduates, insightful to researchers, and useful to practitioners Taylor series (polynomial) based Intuitive elemental and point-wise error measures Essential background information provided in 12 appendices

The Finite Element Method for Fluid Dynamics

Author: Olek C Zienkiewicz,Robert L Taylor,P. Nithiarasu

Publisher: Butterworth-Heinemann

ISBN: 0080951376

Category: Technology & Engineering

Page: 584

View: 6236

The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on: Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems. Biofluid dynamics, covering flow throughout the human arterial system. Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics. Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz. Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation.

finite element methods

fifty years of the Courant element

Author: Michel Krizek,Pekka Neittaanmaki,Rolf Stenberg

Publisher: CRC Press

ISBN: 9780824792763

Category: Mathematics

Page: 536

View: 7831

These proceedings originated from a conference commemorating the 50th anniversary of the publication of Richard Courant's seminal paper, Variational Methods for Problems of Equilibrium and Vibration. These papers address fundamental questions in numerical analysis and the special problems that occur in applying the finite element method to various fields of science and engineering.

A Pragmatic Introduction to the Finite Element Method for Thermal and Stress Analysis

With the Matlab Toolkit SOFEA

Author: Petr Krysl

Publisher: World Scientific Publishing Company

ISBN: 9813101814

Category: Science

Page: 292

View: 2360

This textbook provides an accessible and self-contained description of the Galerkin finite element method for the two important models of continuum mechanics, transient heat conduction and elastodynamics, from formulation of the governing equations to implementation in Matlab. The coverage follows an intuitive approach: the salient features of each initial boundary value problem are reviewed, including a thorough description of the boundary conditions; the method of weighted residuals is applied to derive the discrete equations; and clear examples are introduced to illustrate the method.

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