First Course in the Finite Element Method

ISBN-10: 0495667919
ISBN-13: 9780495667919
Edition: 4th 2011
Authors: Daryl L. Logan
List price: $361.95
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Book details

List price: $361.95
Edition: 4th
Copyright year: 2011
Publisher: Course Technology
Publication date: 1/27/2010
Binding: Paperback
Pages: 752
Size: 7.50" wide x 9.75" long x 1.75" tall
Weight: 2.684
Language: English

No further information has been provided for this title.

Introduction
Prologue
Brief History
Introduction to Matrix Notation
Role of the Computer
General Steps of the Finite Element of Method
Applications of the Finite Element Methods
Advantages of the Finite Element Method
Computer Programs for the Finite Element Method
References
Problems
Introduction to the Stiffness (Displacement) Method Introduction
Definitions 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
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 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
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
Concepts of Substructure 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 Examples of 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 Problems
Computer Program Results for Some Plane Stress/Strain Problems
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
Solutions of an Axisymmetric Pressure Vessel
Applications of Axisymmetric Elements
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
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
Computer Solutions for a Plate Bending Problem
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 and Examples of Heat-Transfer Program
References
Problems
Fluid Flow
Introduction
Derivation of the Basic Differential Equations
One-Dimensional Finite Element Formulation
Two-Dimensional Finite Element Formulation
Flowchart and Example of a Fluid-Flow Program
References
Problems
Thermal Stress Introduction
Formulation of the Thermal Stress Problems and Examples
References
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
Computer Program Example Solutions for Structural Dynamics
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 Forms of the Equations
Uniqueness, Nonuniqueness, and Nonexistence of Solutions
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
Properties of Structural Steel and Aluminum Shapes
Answer to Selected Problems
Index

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