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.
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Table of Contents
1. Introduction 2. Mathematical modeling of physical systems 3. Integral formulations and variational methods 4. Finite element formulation of one-dimensional boundary value problems 5. Finite element method for planar bars and trusses 6. Euler-Bernoulli beam element 7. Isoparametric elements for two-dimensional elastic solids 8. Rectangular and triangular elements for two-dimensional elastic solids 9. Finite element solution of one-dimensional heat transfer problems 10. Heat transfer problems in two dimensions 11. Transient thermal analysis 12. Transient analysis of solids and structures
