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Introduction to Finite Elements in Engineering

ISBN-10: 0132162741
ISBN-13: 9780132162746
Edition: 4th 2012 (Revised)
List price: $256.20 Buy it from $22.04 Rent it from $67.43
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Book details

List price: $256.20
Edition: 4th
Copyright year: 2012
Publisher: Prentice Hall PTR
Publication date: 10/19/2011
Binding: Hardcover
Pages: 448
Size: 7.25" wide x 9.25" long x 0.75" tall
Weight: 2.068
Language: English

Tirupathi R. Chandrupatla has been a Professor and Founding Chair of Mechanical Engineering at Rowan University, Glassboro, New Jersey since 1995. He received his M.S. degree in design and manufacturing from the Indian Institute of Technology, Bombay, and his Ph.D. from the University of Texas at Austin. He began his career as a design engineer with Hindustan Machine Tools (HMT), Bangalore. His first teaching post was at I.I.T., Bombay. He has also taught at the University of Kentucky, and GMI Engineering and Management Institute (Kettering University), before joining Rowan. Chandrupatla is author of Introduction to Finite Elements in Engineering, Optimization Concepts and Applications in Engineering, and Finite Element Analysis for Engineering and Technology. The first book has been translated into Spanish, Korean, Greek, and Chinese languages. Chandrupatla's research interests include design, optimization, manufacturing engineering, finite element analysis, and quality and reliability. He published widely in these areas and serves as a consultant to industry. Chandrupatla is a registered Professional Engineer and also a Certified Manufacturing Engineer. He is a member of ASEE, ASME, SAE, and SME.

Ashok D. Belegundu has been a Professor of Mechanical Engineering at Pennsylvania State University, University Park, since 1986. Prior to this, he taught at GMI, now Kettering University, in Michigan. He received his B. Tech. degree from I.I.T. Madras and his Ph.D. from the University of Iowa. He has been a principal investigator on research projects involving optimization for several agencies including the National Science Foundation, Army Research Office, NASA, SERC (UK), MacNeal-Schwendler Corporation, Gentex Corporation, and Ingersoll-Rand. He has organized two international conferences on optimization in industry and has authored or edited four books and written a chapter in a book. A detailed list of his publications and projects can be found at http: //www.mne.psu.edu/Directories/Faculty/Belegundu-A.html. He has advised more than fifty graduate students. He has given short courses on finite elements and optimization to the Forging Industry Association, Hazleton Pumps, Infosys (India). He has served as an associate editor for AIAA Journal and for Mechanics Based Design of Structures and Machines. He teaches a distance education course on optimal design through Penn State.

Preface
About The Author
Fundamental Concepts
Introduction
Historical Background
Outline of Presentation
Stresses and Equilibrium
Boundary Conditions
Strain-Displacement Relations
Stress-Strain Relations
Special Cases
Temperature Effects
Potential Energy and Equilibrium: The Rayleigh-Ritz Method
Potential Energy �
Rayleigh-Ritz Method
Galerkin's Method
Saint Venant's Principle
Von Mises Stress
Principle of Superposition
Computer Programs
Conclusion
Historical References
Problems
Matrix Algebra And Gaussian Elimination
Matrix Algebra
Row and Column Vectors
Addition and Subtraction
Multiplication by a Scalar
Matrix Multiplication
Transposition
Differentiation and Integration
Square Matrix
Diagonal Matrix
Identity Matrix
Symmetric Matrix
Upper Triangular Matrix
Determinant of a Matrix
Matrix Inversion
Eigenvalues and Eigenvectors
Positive Definite Matrix
Cholesky Decomposition
Gaussian Elimination
General Algorithm for Gaussian Elimination
Symmetric Matrix
Symmetric Banded Matrices
Solution with Multiple Right Sides
Gaussian Elimination with Column Reduction
Skyline Solution
Frontal Solution
Conjugate Gradient Method for Equation Solving
Conjugate Gradient Algorithm
Input Data/Output
Problems
Program Listings
One-Dimensional Problems
Introduction
Finite Element Modeling
Element Division
Numbering Scheme
Shape Functions and Local Coordinates
The Potential-Energy Approach
Element Stiffness Matrix
Force Terms
The Galerkin Approach
Element Stiffness
Force Terms
Assembly of the Global Stiffness Matrix and Load Vector
Properties of K
The Finite Element Equations: Treatment of Boundary Conditions
Types of Boundary Conditions
Elimination Approach
Penalty Approach
Multipoint Constraints
Quadratic Shape Functions
Temperature Effects
Problem Modeling and Boundary Conditions
Problem in Equilibrium
Symmetry
Two Elements with Same End Displacements
Problem with a Closing Gap
Input Data/Output
Problems
Program Listing
Trusses
Introduction
Plane Trusses
Local and Global Coordinate Systems
Formulas for Calculating / and m
Element Stiffness Matrix
Stress Calculations
Temperature Effects
Three-Dimensional Trusses
Assembly of Global Stiffness Matrix for the Banded and Skyline
Solutions
Assembly for Banded Solution
Skyline Assembly
Problem Modeling and Boundary Conditions
Inclined Support in Two Dimensions
Inclined Support in Three Dimensions-Line Constraint
Inclined Support in Three Dimensions-Plane Constraint
Symmetry and Antisymmetry
Input Data/Output
Problems
Program Listing
Beams And Frames
Introduction
Potential-Energy Approach
Galerkin Approach
Finite Element Formulation
Element Stiffness-Direct Approach
Load Vector
Boundary Considerations
Shear Force and Bending Moment
Beams on Elastic Supports
Plane Frames
Three-Dimensional Frames
Problem Modeling and Boundary Conditions
Some Comments
Input Data/Output
Problems
Program Listings
Two-Dimensional Problems Using Constant Strain Triangles
Introduction
Finite Element Modeling
Constant Strain Triangle (CST)
Isoparametric Representation
Potential-Energy Approach
Element Stiffness
Force Terms
Integration Formula on a Triangle
Galerkin Approach
Stress Calculations
Temperature Effects
Problem Modeling and Boundary Conditions
Some General Comments on Dividing into Elements
Patch Test and Convergence
Patch Test
Orthotropic Materials
Temperature Effects
Input Data/Output
Problems
Program Listing
Axisymmetric Solids Subjected To Axisymmetric Loading
Introduction
Axisymmetric Formulation
Finite Element Modeling: Triangular Element
Potential-Energy Approach
Body Force Term
Rotating Flywheel
Surface Traction
Galerkin Approach
Stress Calculations
Temperature Effects
Problem Modeling and Boundary Conditions
Cylinder Subjected to Internal Pressure
Infinite Cylinder
Press Fit on a Rigid Shaft
Press Fit on an Elastic Shaft
Belleville Spring
Thermal Stress Problem
Input Data/Output
Problems
Program Listing
Two-Dimensional Isoparametric Elements And Numerical Integration
Introduction
The Four-Node Quadrilateral
Shape Functions
Element Stiffness Matrix
Element Force Vectors
Numerical Integration
Two-Dimensional Integrals
Stiffness Integration
Stress Calculations
Higher Order Elements
Nine-Node Quadrilateral
Eight-Node Quadrilateral
Six-Node Triangle
Integration on a Triangle-Symmetric Points
Integration on a Triangle-Degenerate Quadrilateral
Four-Node Quadrilateral for Axisymmetric Problems
Conjugate Gradient Implementation of the Quadrilateral Element
Concluding Remarks and Convergence
References for Convergence
Input Data/Output
Problems
Program Listings
Three-Dimensional Problems In Stress Analysis
Introduction
Finite Element Formulation
Element Stiffness
Force Terms
Stress Calculations
Mesh Preparation
Hexahedral Elements and Higher Order Elements
Problem Modeling
Frontal Method for Finite Element Matrices
Connectivity and Prefront Routine
Element Assembly and Consideration of Specified dof
Elimination of Completed dof
Backsubstitution
Consideration of Multipoint Constraints
Input Data/Output
Problems
Program Listings
Scalar Field Problems
Introduction
Steady State Heat Transfer
One-Dimensional Heat Conduction
One-Dimensional Heat Transfer in Thin Fins
Two-Dimensional Steady-State Heat Conduction
Two-Dimensional Fins
Preprocessing for Program Heat2D
Torsion
Triangular Element
Galerkin Approach
Potential Flow, Seepage, Electric and Magnetic Fields, and Fluid Flow in Ducts
Potential Flow
Seepage
Electrical and Magnetic Field Problems
Fluid Flow in Ducts
Acoustics
Boundary Conditions
One-Dimensional Acoustics
One-Dimensional Axial Vibrations
Two-Dimensional Acoustics
Conclusion
Input Data/Output
Problems
Program Listings
Dynamic Considerations
Introduction
Formulation
Solid Body with Distributed Mass
Element Mass Matrices
Evaluation of Eigenvalues and Eigenvectors
Properties of Eigenvectors
Eigenvalue-Eigenvector Evaluation
Inverse Iteration Method
Generalized Jacobi Method
Tridiagonalization and Implicit Shift Approach
Bringing Generalized Problem to Standard Form
Tridiagonalization
Implicit Symmetric QR Step with Wilkinson Shift for Diagonalization
Interfacing with Previous Finite Element Programs and a Program for Determining Critical Speeds of Shafts
Guyan Reduction
Rigid Body Modes
Conclusion
Input Data/Output
Problems
Program Listings
Preprocessing And Postprocessing
Introduction

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