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A First Course in the Finite Element Method Using Algor

by: Logan, Daryl L.

A First Course in the Finite Element Method Using Algor

by: Logan, Daryl L.

ISBN 13:
9780534380687
ISBN 10:
0534380689
Edition: 2nd
Format: Hardcover
Copyright: 12/07/2000
Publisher: Cengage Learning

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Summary

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

(26)

Prologue

(1)

Brief History

(1)

Introduction to Matrix Notation

(3)

Role of the Computer

(1)

General Steps of the Finite Element Method

(7)

Applications of the Finite Element Method

(5)

Advantages of the Finite Element Method

(1)

Computer Programs for the Finite Element Method

(7)

References

(3)

Problems

(1)

Introduction to the Stiffness (Displacement) Method

(37)

Introduction

(1)

Definition of the Stiffness Matrix

(1)

Derivation of the Stiffness Matrix for a Spring Element

(5)

Example of a Spring Assemblage

(3)

Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)

(2)

Boundary Conditions

(13)

Potential Energy Approach to Derive Spring Element Equations

(13)

References

(1)

Problems

(4)

Development of Truss Equations

(74)

Introduction

(1)

Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates

(6)

Selecting Approximation Functions for Displacements

(2)

Transformation of Vectors in Two Dimensions

(3)

Global Stiffness Matrix

(4)

Computation of Stress for a Bar in the x-y Plane

(2)

Solution of a Plane Truss

(7)

Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space

(5)

Use of Symmetry in Structure

(3)

Inclined, or Skewed, Supports

(6)

Potential Energy Approach to Derive Bar Element Equations

101

(11)

Comparison of Finite Element Solution to Exact Solution for Bar

112

(4)

Galerkin's Residual Method and Its Application to a One-Dimensional Bar

116

(21)

References

119

(1)

Problems

120

(17)

Algor Program for Truss Analysis

137

(49)

Introduction

137

(1)

Overview of the Algor System and Flowcharts for the Solution of a Truss Problem Using Algor

137

(8)

Algor Example Solutions for Truss Analysis

145

(41)

References

177

(1)

Problems

177

(9)

Development of Beam Equations

186

(90)

Introduction

186

(1)

Beam Stiffness

187

(5)

Example of Assemblage of Beam Stiffness Matrices

192

(2)

Examples of Beam Analysis Using the Direct Stiffness Method

194

(9)

Distributed Loading

203

(11)

Comparison of the Finite Element Solution to the Exact Solution for a Beam

214

(6)

Beam Element with Nodal Hinge

220

(5)

Potential Energy Approach to Derive Beam Element Equations

225

(3)

Galerkin's Method for Deriving Beam Element Equations

228

(2)

Algor Example Solutions for Beam Analysis

230

(46)

References

268

(1)

Problems

269

(7)

Frame and Grid Equations

276

(110)

Introduction

276

(1)

Two-Dimensional Arbitrarily Oriented Beam Element

276

(4)

Rigid Plane Frame Examples

280

(19)

Inclined or Skewed Supports---Frame Element

299

(1)

Grid Equations

300

(17)

Beam Element Arbitrarily Oriented in Space

317

(5)

Concept of Substructure Analysis

322

(6)

Algor Example Solutions for Plane Frame, Grid, and Space Frame Analysis

328

(58)

References

362

(1)

Problems

363

(23)

Development of the Plane Stress and Plane Strain Stiffness Equations

386

(43)

Introduction

386

(1)

Basic Concepts of Plane Stress and Plane Strain

387

(5)

Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations

392

(14)

Treatment of Body and Surface Forces

406

(5)

Explicit Expression for the Constant-Strain Triangle Stiffness Matrix

411

(2)

Finite Element Solution of a Plane Stress Problem

413

(16)

References

423

(1)

Problems

423

(6)

Practical Considerations in Modeling; Interpreting Results; and Use of the Algor Program for Plane Stress/Strain Analysis

429

(68)

Introduction

429

(1)

Finite Element Modeling

430

(10)

Equilibrium and Compatibility of Finite Element Results

440

(2)

Convergence of Solution

442

(1)

Interpretation of Stresses

443

(2)

Static Condensation

445

(4)

Flowchart for the Solution of Plane Stress/Strain Problems and Typical Steps Using Algor

449

(4)

Algor Example Solutions for Plane Stress/Strain Analysis

453

(44)

References

484

(1)

Problems

485

(12)

Development of the Linear-Strain Triangle Equations

497

(14)

Introduction

497

(1)

Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations

497

(5)

Example LST Stiffness Determination

502

(3)

Comparison of Elements

505

(6)

References

507

(1)

Problems

508

(3)

Axisymmetric Elements

511

(49)

Introduction

511

(1)

Derivation of the Stiffness Matrix

511

(10)

Solution of an Axisymmetric Pressure Vessel

521

(7)

Applications of Axisymmetric Elements

528

(3)

Algor Example Solutions for Axisymmetric Problems

531

(29)

References

554

(1)

Problems

555

(5)

Isoparametric Formulation

560

(35)

Introduction

560

(1)

Isoparametric Formulation of the Bar Element Stiffness Matrix

560

(6)

Rectangular Plane Stress Element

566

(3)

Isoparametric Formulation of the Plane Element Stiffness Matrix

569

(9)

Gaussian Quadrature (Numerical Integration)

578

(3)

Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature

581

(6)

Higher-Order Shape Functions

587

(8)

References

591

(1)

Problems

591

(4)

Three-Dimensional Stress Analysis

595

(39)

Introduction

595

(1)

Three-Dimensional Stress and Strain

595

(2)

Tetrahedral Element

597

(7)

Isoparametric Formulation

604

(5)

Algor Example Solutions of Three-Dimensional Stress Analysis

609

(25)

References

629

(1)

Problems

630

(4)

Heat Transfer and Mass Transport

634

(67)

Introduction

634

(1)

Derivation of the Basic Differential Equation

635

(3)

Heat Transfer with Convection

638

(1)

Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h

639

(1)

One-Dimensional Finite Element Formulation Using a Variational Method

640

(14)

Two-Dimensional Finite Element Formulation

654

(9)

Line or Point Sources

663

(3)

One-Dimensional Heat Transfer with Mass Transport

666

(1)

Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method

667

(4)

Flowchart of a Heat-Transfer Program

671

(1)

Algor Example Solutions for Heat-Transfer Problems

672

(29)

References

692

(1)

Problems

692

(9)

Fluid Flow

701

(31)

Introduction

701

(1)

Derivation of the Basic Differential Equations

701

(5)

One-Dimensional Finite Element Formulation

706

(8)

Two-Dimensional Finite Element Formulation

714

(4)

Flowchart of a Fluid-Flow Program

718

(1)

Algor Example Solutions for Two-Dimensional Steady-State Fluid Flow

719

(13)

References

727

(1)

Problems

728

(4)

Thermal Stress

732

(46)

Introduction

732

(1)

Formulation of the Thermal Stress Problem and Examples

732

(21)

Algor Example Solutions for Thermal Stress Problems

753

(25)

Reference

772

(1)

Problems

773

(5)

Structural Dynamics and Time-Dependent Heat Transfer

778

(84)

Introduction

778

(1)

Dynamics of a Spring-Mass System

778

(2)

Direct Derivation of the Bar Element Equations

780

(4)

Numerical Integration in Time

784

(12)

Natural Frequencies of a One-Dimensional Bar

796

(4)

Time-Dependent One-Dimensional Bar Analysis

800

(5)

Beam Element Mass Matrices and Natural Frequencies

805

(5)

Truss, Plane Frame, Plane Stress/Strain, Axisymmetric, and Solid Element Mass Matrices

810

(4)

Time-Dependent Heat Transfer

814

(7)

Algor Example Solutions for Structural Dynamics and Transient Heat Transfer

821

(41)

References

856

(1)

Problems

857

(5)

Plate Bending Element

862

(21)

Introduction

862

(1)

Basic Concepts of Plate Bending

862

(4)

Derivation of a Plate Bending Element Stiffness Matrix and Equations

866

(5)

Some Plate Element Numerical Comparisons

871

(1)

Algor Example Solution for Plate Bending Problems

872

(11)

References

878

(1)

Problems

879

(4)

Appendix A Matrix Algebra

883

(14)

Introduction

883

(1)

A.1 Definition of a Matrix

883

(1)

A.2 Matrix Operations

884

(7)

A.3 Cofactor or Adjoint Method to Determine the Inverse of a Matrix

891

(2)

A.4 Inverse of a Matrix by Row Reduction

893

(4)

References

895

(1)

Problems

895

(2)

Appendix B Methods for Solution of Simultaneous Linear Equations

897

(22)

Introduction

897

(1)

B.1 General Form of the Equations

897

(1)

B.2 Uniqueness, Nonuniqueness, and Nonexistence of Solution

898

(1)

B.3 Methods for Solving Linear Algebraic Equations

899

(11)

B.4 Banded-Symmetric Matrices, Bandwidth, Skyline, and Wavefront Methods

910

(9)

References

916

(1)

Problems

917

(2)

Appendix C Equations from Elasticity Theory

919

(8)

Introduction

919

(1)

C.1 Differential Equations of Equilibrium

919

(2)

C.2 Strain/Displacement and Compatibility Equations

921

(2)

C.3 Stress/Strain Relationships

923

(4)

References

926

(1)

Appendix D Equivalent Nodal Forces

927

(3)

Problems

927

(3)

Appendix E Principle of Virtual Work

930

(4)

References

933

(1)

Appendix F Basics of Algor

934

(9)

Introduction

934

(1)

F.1 Hardware Requirements for Windows Installation

934

(1)

F.2 Conventions

934

(1)

F.3 Getting Around the Menu System

935

(1)

F.4 Function Keys

935

(2)

F.5 Algor Processor Names

937

(1)

F.6 File Extensions Generated by the Algor System

938

(1)

F.7 Checking Model for Defects by Using Superview

938

(5)

Answers to Selected Problems

943

(22)

Index

965

Amazon no longer offers textbook rentals. We do!

A First Course in the Finite Element Method Using Algor

A First Course in the Finite Element Method Using Algor

9780534380687

0534380689

Summary

Table of Contents

Supplemental Materials

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