The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas.Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world
An up-to-date, self-contained introduction to the theory and applications of the finite element method This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are important in bioengineering, fluid and thermal sciences, structural mechanics, and a host of applied sciences. Introduction to the Finite Element Method, Fourth Edition, covers:•Mathematical preliminaries and classical variational methods•1-D finite element models of second-order differential equations•Applications to 1-D heat transfer and fluid and solid mechanics problems•Finite element analysis of beams and circular plates•Plane trusses and frames•Eigenvalue and time-dependent problems in 1-D•Numerical integration and computer implementation in 1-D•Single-variable problems in two dimensions•2-D interpolation functions, numerical integration, and computer implementation in 2-D•Flows of viscous incompressible fluids•Plane elasticity•3-D finite element analysis
This lecture is written primarily for the non-expert engineer or the undergraduate or graduate student who wants to learn, for the first time, the finite element method with applications to electromagnetics. It is also designed for research engineers who have knowledge of other numerical techniques and want to familiarize themselves with the finite element method.Finite element method is a numerical method used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. Author Anastasis Polycarpou provides the reader with all information necessary to successfully apply the finite element method to one- and two-dimensional boundary-value problems in electromagnetics.The book is accompanied by a number of codes written by the author in Matlab. These are the finite element codes that were used to generate most of the graphs presented in this book. Specifically, there are three Matlab codes for the one-dimensional case (Chapter 1) and two Matlab codes for the two-dimensional case (Chapter 2). The reader may execute these codes, modify certain parameters such as mesh size or object dimensions, and visualize the results. The codes are available on the Morgan & Claypool Web site at http://www.morganclaypool.com.
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.
For final year graduate and postgraduate courses in the finite element method, this book introduces the method as applied to linear, non-linear and one- and two-dimensional problems of engineering and applied sciences. It includes a step-by-step systematic approach to the formulation and analysis of differential and integral equations in variational forms. The book adopts a differential equation approach, avoiding the need for knowledge of the variational principles of solid mechanics in the development of the finite element models. The need for the weighted-integral formulation of differential equations is explained clearly, providing the student with logical reasons for the recasting of differential equations into variational form.
A systematic introduction to the theories and formulations ofthe explicit finite element method As numerical technology continues to grow and evolve withindustrial applications, understanding the explicit finite elementmethod has become increasingly important, particularly in the areasof crashworthiness, metal forming, and impact engineering.Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is the first book to addressspecifically what is now accepted as the most successful numericaltool for nonlinear transient dynamics. The book aids readers inmastering the explicit finite element method and programming codewithout requiring extensive background knowledge of the generalfinite element. The authors present topics relating to the variationalprinciple, numerical procedure, mechanical formulation, andfundamental achievements of the convergence theory. In addition,key topics and techniques are provided in four clearly organizedsections: • Fundamentals explores a framework of the explicitfinite element method for nonlinear transient dynamics andhighlights achievements related to the convergence theory • Element Technology discusses four-node,three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity andother nonlinear materials as well as the mechanics model of ductiledamage • Contact and Constraint Conditions covers subjectsrelated to three-dimensional surface contact, with examples solvedanalytically, as well as discussions on kinematic constraintconditions Throughout the book, vivid figures illustrate the ideas and keyfeatures of the explicit finite element method. Examples clearlypresent results, featuring both theoretical assessments andindustrial applications. Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is an ideal book for bothengineers who require more theoretical discussions and fortheoreticians searching for interesting and challenging researchtopics. The book also serves as an excellent resource for courseson applied mathematics, applied mechanics, and numerical methods atthe graduate level.
Providing a systematic approach and simple introduction ot the finite element method, this self-contained book will enable the reader to obtain a clear understanding of the concepts involved in this traditionally complicated methodology.
Written for students with any engineering or applied science background, Erik Thompson\'s new text presents the theory, applications, and programming skills needed to understand the finite element method and use it to solve problems in engineering analysis and design. Offering concise, highly practical coverage, this introductory text provides complete finite element codes that can be run on the student version of MATLAB or easily converted to other languages. This text gives students the opportunity to:Master the basic theory: The text promotes an understanding and appreciation of the theoretical basis of finite element approximations by building on concepts that are intuitive to the students. Throughout, the text uses matrix notation to help students visualize the finite element matrices. Study problems reinforce basic theory.Experiment with the code: Numerical experiments show how to test programs for possible errors, experiment with boundary conditions, and study accuracy and stability. Code development exercises suggest ways to modify the codes to create additional capabilities. All codes are available on the book\'s web page along with sample data files for testing them. Each code can be run immediately using only the student version of MATLAB. Because each code is written using explicit programming, they also serve as pseudo-codes that can be used to develop programs in any computer language.Gain hands-on experience: Projects, representing a wide variety of engineering disciplines, enable students to conduct analyses of fairly complex problems. Many of these projects encourage investigations of new techniques for using the finite element method.
This updated, revised and extended edition gives a comprehensive introduction to the understanding and use of the finite element method as applied to structures. The text methodically covers all the important bridges in understanding up to and including the introduction of isoparametric elements.
This textbook presents finite element methods using exclusively one-dimensional elements. The aim is to present the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader easily understands the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. But although the description is easy it remains scientifically correct. The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics like plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics.