First Course in the Finite Element Method Using Algor

ISBN-10: 0534380689
ISBN-13: 9780534380687
Edition: 2nd 2001 (Revised)
Authors: Daryl L. Logan
List price: $196.95 Buy it from $44.31
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Description: Daryl Logan's clear and easy to understand text provides a thorough treatment of the finite element method and how to apply it to solve practical physical problems in engineering. Concepts are presented simply, making it understandable for students  More...

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Book details

List price: $196.95
Edition: 2nd
Copyright year: 2001
Publisher: Course Technology
Publication date: 12/7/2000
Binding: Hardcover
Pages: 992
Size: 7.25" wide x 9.25" long x 1.50" tall
Weight: 3.630
Language: English

Daryl Logan's clear and easy to understand text provides a thorough treatment of the finite element method and how to apply it to solve practical physical problems in engineering. Concepts are presented simply, making it understandable for students of all levels of experience. The first edition of this book enjoyed considerable success and this new edition includes a chapter on plates and plate bending, along with additional homework exercise. All examples in this edition have been updated to Algor? Release 12.

Introduction
Prologue
Brief History
Introduction to Matrix Notation
Role of the Computer
General Steps of the Finite Element Method
Applications of the Finite Element Method
Advantages of the Finite Element Method
Computer Programs for the Finite Element Method
References
Problems
Introduction to the Stiffness (Displacement) Method
Introduction
Definition of the Stiffness Matrix
Derivation of the Stiffness Matrix for a Spring Element
Example of a Spring Assemblage
Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
Boundary Conditions
Potential Energy Approach to Derive Spring Element Equations
References
Problems
Development of Truss Equations
Introduction
Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates
Selecting Approximation Functions for Displacements
Transformation of Vectors in Two Dimensions
Global Stiffness Matrix
Computation of Stress for a Bar in the x-y Plane
Solution of a Plane Truss
Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
Use of Symmetry in Structure
Inclined, or Skewed, Supports
Potential Energy Approach to Derive Bar Element Equations
Comparison of Finite Element Solution to Exact Solution for Bar
Galerkin's Residual Method and Its Application to a One-Dimensional Bar
References
Problems
Algor Program for Truss Analysis
Introduction
Overview of the Algor System and Flowcharts for the Solution of a Truss Problem Using Algor
Algor Example Solutions for Truss Analysis
References
Problems
Development of Beam Equations
Introduction
Beam Stiffness
Example of Assemblage of Beam Stiffness Matrices
Examples of Beam Analysis Using the Direct Stiffness Method
Distributed Loading
Comparison of the Finite Element Solution to the Exact Solution for a Beam
Beam Element with Nodal Hinge
Potential Energy Approach to Derive Beam Element Equations
Galerkin's Method for Deriving Beam Element Equations
Algor Example Solutions for Beam Analysis
References
Problems
Frame and Grid Equations
Introduction
Two-Dimensional Arbitrarily Oriented Beam Element
Rigid Plane Frame Examples
Inclined or Skewed Supports--Frame Element
Grid Equations
Beam Element Arbitrarily Oriented in Space
Concept of Substructure Analysis
Algor Example Solutions for Plane Frame, Grid, and Space Frame Analysis
References
Problems
Development of the Plane Stress and Plane Strain Stiffness Equations
Introduction
Basic Concepts of Plane Stress and Plane Strain
Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations
Treatment of Body and Surface Forces
Explicit Expression for the Constant-Strain Triangle Stiffness Matrix
Finite Element Solution of a Plane Stress Problem
References
Problems
Practical Considerations in Modeling; Interpreting Results; and Use of the Algor Program for Plane Stress/Strain Analysis
Introduction
Finite Element Modeling
Equilibrium and Compatibility of Finite Element Results
Convergence of Solution
Interpretation of Stresses
Static Condensation
Flowchart for the Solution of Plane Stress/Strain Problems and Typical Steps Using Algor
Algor Example Solutions for Plane Stress/Strain Analysis
References
Problems
Development of the Linear-Strain Triangle Equations
Introduction
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations
Example LST Stiffness Determination
Comparison of Elements
References
Problems
Axisymmetric Elements
Introduction
Derivation of the Stiffness Matrix
Solution of an Axisymmetric Pressure Vessel
Applications of Axisymmetric Elements
Algor Example Solutions for Axisymmetric Problems
References
Problems
Isoparametric Formulation
Introduction
Isoparametric Formulation of the Bar Element Stiffness Matrix
Rectangular Plane Stress Element
Isoparametric Formulation of the Plane Element Stiffness Matrix
Gaussian Quadrature (Numerical Integration)
Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
Higher-Order Shape Functions
References
Problems
Three-Dimensional Stress Analysis
Introduction
Three-Dimensional Stress and Strain
Tetrahedral Element
Isoparametric Formulation
Algor Example Solutions of Three-Dimensional Stress Analysis
References
Problems
Heat Transfer and Mass Transport
Introduction
Derivation of the Basic Differential Equation
Heat Transfer with Convection
Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h
One-Dimensional Finite Element Formulation Using a Variational Method
Two-Dimensional Finite Element Formulation
Line or Point Sources
One-Dimensional Heat Transfer with Mass Transport
Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method
Flowchart of a Heat-Transfer Program
Algor Example Solutions for Heat-Transfer Problems
References
Problems
Fluid Flow
Introduction
Derivation of the Basic Differential Equations
One-Dimensional Finite Element Formulation
Two-Dimensional Finite Element Formulation
Flowchart of a Fluid-Flow Program
Algor Example Solutions for Two-Dimensional Steady-State Fluid Flow
References
Problems
Thermal Stress
Introduction
Formulation of the Thermal Stress Problem and Examples
Algor Example Solutions for Thermal Stress Problems
Reference
Problems
Structural Dynamics and Time-Dependent Heat Transfer
Introduction
Dynamics of a Spring-Mass System
Direct Derivation of the Bar Element Equations
Numerical Integration in Time
Natural Frequencies of a One-Dimensional Bar
Time-Dependent One-Dimensional Bar Analysis
Beam Element Mass Matrices and Natural Frequencies
Truss, Plane Frame, Plane Stress/Strain, Axisymmetric, and Solid Element Mass Matrices
Time-Dependent Heat Transfer
Algor Example Solutions for Structural Dynamics and Transient Heat Transfer
References
Problems
Plate Bending Element
Introduction
Basic Concepts of Plate Bending
Derivation of a Plate Bending Element Stiffness Matrix and Equations
Some Plate Element Numerical Comparisons
Algor Example Solution for Plate Bending Problems
References
Problems
Matrix Algebra
Introduction
Definition of a Matrix
Matrix Operations
Cofactor or Adjoint Method to Determine the Inverse of a Matrix
Inverse of a Matrix by Row Reduction
References
Problems
Methods for Solution of Simultaneous Linear Equations
Introduction
General Form of the Equations
Uniqueness, Nonuniqueness, and Nonexistence of Solution
Methods for Solving Linear Algebraic Equations
Banded-Symmetric Matrices, Bandwidth, Skyline, and Wavefront Methods
References
Problems
Equations from Elasticity Theory
Introduction
Differential Equations of Equilibrium
Strain/Displacement and Compatibility Equations
Stress/Strain Relationships
Reference
Equivalent Nodal Forces
Problems
Principle of Virtual Work
References
Basics of Algor
Introduction
Hardware Requirements for Windows Installation
Conventions
Getting Around the Menu System
Function Keys
Algor Processor Names
File Extensions Generated by the Algor System
Checking Model for Defects by Using Superview
Answers to Selected Problems
Index

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