Engineering
Finite Element Method : Theory, Software and Practice
Description
This book deals with basic theory, concepts and applications of finite element method in the areas of structural analysis, heat transfer and metal working processes. The finite element formulations are developed through easy to understand derivations for the analyses (static, transient dynamic and geometrical nonlinear) of bars, beams, plane stress/plane strain and axisymmetric solids, plates, shells and three-dimensional structures, made of both isotropic as well as composite materials. Chapters on heat transfer and metal working analyses have also been added to increase the scope of application. A significant feature of this book is the presentation of a user-friendly computer code "SB-FEM" (available on an accompanying disk) which can be used to solve several real world problems included in the text. The computer code covers the gap between theory and application and thus enables the reader to use the finite element method to solve practical problems with minimum effort and within a very short time. Written in a simple straightforward manner with broad coverage and consistent style in the presentation, this book may be an indispensable text for students (senior undergraduate or graduate students) as well as practicing engineers in the relevant fields.
Table of Contents
Preface; Introduction to Finite Element Method: Introduction; Purpose of Using FEM; Applications of FEM; Brief History of FEM; Basic Steps in FEA; Stages in Finite Element Programming; Ingredients of Finite Element Method: Introduction; Discretization of the Domain; Interpolation Models; Derivation of Element Matrices and Vectors; Assembly of Element Matrices; Incorporation of Boundary Conditions; Solution of Finite Element Equations; Computation of Resultant Variables; Software for Finite Element Analysis: Introduction; Features of the Computer Code; Preprocessing (Building the Model); Processing (Applying Loads and Obtaining the Solution); Postprocessing (Reviewing the Results); SB-FEM Commands and Command Interpreter; Installation of SB-FEM; Using SB-FEM Code; Analysis of Trusses/Bars: Introduction; Bar Element (Local Coordinates); Bar (Truss) Element (Oriented Arbitrarily in Two-Dimensional Plane); Bar (Truss) Element (Oriented Arbitrarily in Three-Dimensional Space); Assembly of Multiple Element Contributions; Example Problems; Analysis of Beams: Introduction; Euler-Bernoulli Beam; Shear Deformation in Beams; The 3-Noded Timoshenko Beam Element; Example Problems; Two-dimensional Stress Analysis: Introduction; Triangular Elements; Quadrilateral Elements; Example Problems; Analysis of Plates: Introduction; Forces and Moments Acting on the Plate; Thin Plate Theory; Shear Deformation in Plates; Finite Element Formulation; Example Problems; Three-dimensional Stress Analysis: Introduction; Tetrahedral Elements; Eight Noded Brick Element; Twenty Noded Brick Element; Layered Brick Elements; Example Problems; Transient Dynamic Analysis: Introduction; General Derivation of Finite Element Dynamic Equilibrium Equations; Numerical Solution of Finite Element Equations; Consistent and Lumped Mass Matrices; Example Problems; Geometrical Non-Linearity: Introduction; Non-Linear Strain-Displacement Relations; Large Displacement Finite Element Formulation; Example Problems; Non-linear Analysis of Shells: Introduction; Basic Equations; Finite Element Formulation; Example Problems; Heat Transfer Analysis: Introduction; Heat Balance Equation; Finite Element Formulation; Two-dimensional Axisymmetric Case; Example Problems; Metal Working Analysis: Introduction; FEM Formulation in Metal Forming; Rigid-Plastic Finite Element Formulation; Friction Modeling; Thermal Formulation; Combined Mechanical and Thermal Analysis; Example Problems; Bibliography; Appendices: Some Mathematical Theorems; Basic Equations of Structural Mechanics; Constitutive Relations for Composites; Variational Principle; Numerical Integration; SB-FEM Elements; SB-FEM Commands; Some SB-FEM Input Files; Subject Index