Enhanced Introduction To Finite Elements For Engineers
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Enhanced Introduction to Finite Elements for Engineers
The book presents the fundamentals of the Galerkin Finite Element Method for linear boundary value problems from an engineering perspective. Emphasis is given to the theoretical foundation of the method rooted in Functional Analysis using a language accessible to engineers. The book discusses standard procedures for applying the method to time-dependent and nonlinear problems and addresses essential aspects of applying the method to non-linear dynamics and multi-physics problems. It also provides several hand-calculation exercises as well as specific computer exercises with didactic character. About one fourth of the exercises reveals common pitfalls and sources of errors when applying the method. Carefully selected literature recommendations for further studies are provided at the end of each chapter. The reader is expected to have prior knowledge in engineering mathematics, in particular real analysis and linear algebra. The elements of algebra and analysis required in the main part of the book are presented in corresponding sections of the appendix. Students should already have an education in strength of materials or another engineering field, such as heat or mass transport, which discusses boundary value problems for simple geometries and boundary conditions.
Introduction to Finite Elements in Engineering
Author: Tirupathi R. Chandrupatla
language: en
Publisher: Pearson College Division
Release Date: 2002-01
This book provides an integrated approach to finite element methodologies. The development of finite element theory is combined with examples and exercises involving engineering applications. The steps used in the development of the theory are implemented in complete, self-contained computer programs. While the strategy and philosophy of the previous editions has been retained, the Third Edition has been updated and improved to include new material on additional topics. Chapter topics cover fundamental concepts, matrix algebra and gaussian elimination, one-dimensional problems, trusses, two-dimensional problems using constant strain triangles, axisymmetric solids subjected to axisymmetric loading, two-dimensional isoparametric elements and numerical integration, beams and frames, three-dimensional problems in stress analysis, scalar field problems, dynamic considerations, and preprocessing and postprocessing. For practicing engineers as a valuable learning resource.
An Introduction to the Mathematical Theory of Finite Elements
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.