Daryl L. Logan
Publisher: Cengage Learning
eBook
Your students
can pay an additional fee for access to an online version of the textbook that might contain additional interactive features.
Lifetime of Edition (LOE)
Your students are allowed unlimited access to WebAssign courses that use this edition of the textbook at no additional cost.
Textbook Resources
Additional instructional and learning resources are available with the textbook, and might include testbanks, slide presentations, online simulations, videos, and documents.
Access is contingent on use of this textbook in the instructor's classroom.
 Chapter 1: Introduction
 1.1: Brief History (1)
 1.2: Introduction to Matrix Notation (1)
 1.3: Role of the Computer
 1.4: General Steps of the Finite Element Method (2)
 1.5: Applications of the Finite Element Method
 1.6: Advantages of the Finite Element Method (1)
 1.7: Computer Programs for the Finite Element Method
 1: Chapter Quiz
 Chapter 2: Introduction to the Stiffness (Displacement) Method
 2.1: Definition of the Stiffness Matrix
 2.2: Derivation of the Stiffness Matrix for a Spring Element
 2.3: Example of a Spring Assemblage
 2.4: Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
 2.5: Boundary Conditions (3)
 2.6: Potential Energy Approach to Derive Spring Element Equations (1)
 2: Chapter Quiz
 Chapter 3: Development of Truss Equations
 3.1: Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates (4)
 3.2: Selecting a Displacement Function in Step 2 of the Derivation of Stiffness Matrix for OneDimensional Bar Element (1)
 3.3: Transformation of Vectors in Two Dimensions (1)
 3.4: Global Stiffness Matrix for Bar Arbitrarily Oriented in the Plane
 3.5: Computation for Stress for a Bar in the x–y Plane
 3.6: Solution of a Plane Truss (3)
 3.7: Transformation Matrix and Stiffness Matrix for a Bar in ThreeDimensional Space (1)
 3.8: Use of Symmetry in Structures (1)
 3.9: Inclined, or Skewed, Supports
 3.10: Potential Energy Approach to Derive Bar Element Equations (1)
 3.11: Comparison of Finite Element Solution to Exact Solution for Bar
 3.12: Galerkin's Residual Method and Its Use to Derive the OneDimensional Bar Element Equations
 3.13: Other Residual Methods and Their Application to a OneDimensional Bar Problem (2)
 3.14: Flowchart for Solution of ThreeDimensional Truss Problems
 3.15: Computer Program Assisted StepbyStep Solution for Truss Problem
 3: Chapter Quiz
 Chapter 4: Development of Beam Equations
 4.1: Beam Stiffness (4)
 4.2: Example of Assemblage of Beam Stiffness Matrices
 4.3: Examples of Beam Analysis Using the Direct Stiffness Method (5)
 4.4: Distributed Loading (12)
 4.5: Comparison of the Finite Element Solution to the Exact Solution for a Beam
 4.6: Beam Element with Nodal Hinge (3)
 4.7: Potential Energy Approach to Derive Beam Element Equations (3)
 4.8: Galerkin's Method for Deriving Beam Element Equations
 4: Chapter Quiz
 Chapter 5: Frame and Grid Equations
 5.1: TwoDimensional Arbitrarily Oriented Beam Element
 5.2: Rigid Plane Frame Examples (13)
 5.3: Inclined or Skewed Supports—Frame Element
 5.4: Grid Equations (3)
 5.5: Beam Element Arbitrarily Oriented in Space
 5.6: Concept of Substructure Analysis
 5: Chapter Quiz
 Chapter 6: Development of the Plane Stress and Plane Strain Stiffness Equations
 6.1: Basic Concepts of Plane Stress and Plane Strain
 6.2: Derivation of the ConstantStrain Triangular Element Stiffness Matrix and Equations (5)
 6.3: Treatment of Body and Surface Forces (4)
 6.4: Explicit Expression for the ConstantStrain Triangle Stiffness Matrix (2)
 6.5: Finite Element Solution of a Plane Stress Problem (2)
 6.6: Rectangular Plane Element (Bilinear Rectangle, Q4)
 6: Chapter Quiz
 Chapter 7: Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis
 7.1: Finite Element Modeling (2)
 7.2: Equilibrium and Compatibility of Finite Element Results (2)
 7.3: Convergence of Solution and Mesh Refinement (2)
 7.4: Interpretation of Stresses
 7.5: Flowchart for the Solution of Plane Stress/Strain Problems
 7.6: Computer ProgramAssisted StepbyStep Solution, Other Models, and Results for Plane Stress/Strain Problems
 7: Chapter Quiz
 Chapter 8: Development of the LinearStrain Triangle Equations
 8.1: Derivation of the LinearStrain Triangular Element Stiffness
 8.2: Example LST Stiffness Determination (3)
 8.3: Comparison of Elements
 8: Chapter Quiz
 Chapter 9: Axisymmetric Elements
 9.1: Derivation of the Stiffness Matrix (11)
 9.2: Solution of an Axisymmetric Pressure Vessel
 9.3: Applications of Axisymmetric Elements (2)
 9: Chapter Quiz
 Chapter 10: Isoparametric Formulation
 10.1: Isoparametric Formulation of the Bar Element Stiffness Matrix (2)
 10.2: Isoparametric Formulation of the Plane Quadrilateral (Q4) Element Stiffness Matrix (5)
 10.3: NewtonCotes and Gaussian Quadrature (1)
 10.4: Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
 10.5: HigherOrder Shape Functions (Including Q6, Q8, Q9, and Q12 Elements) (4)
 10: Chapter Quiz
 Chapter 11: ThreeDimensional Stress Analysis
 11.1: ThreeDimensional Stress and Strain
 11.2: Tetrahedral Element (1)
 11.3: Isoparametric Formulation and Hexahedral Element
 11: Chapter Quiz
 Chapter 12: Plate Bending Element
 12.1: Basic Concepts of Plate Bending
 12.2: Derivation of a Plate Bending Element Stiffness Matrix and Equations
 12.3: Some Plate Element Numerical Comparisons
 12.4: Computer Solutions for Bending Problems
 12: Chapter Quiz
 Chapter 13: Heat Transfer and Mass Transport
 13.1: Derivation of the Basic Differential Equation
 13.2: Heat Transfer with Convection
 13.3: Typical Units; Thermal Conductivities, K; and Heat Transfer Coefficients, h
 13.4: OneDimensional Finite Element Formulation Using a Variational Method (3)
 13.5: TwoDimensional Finite Element Formulation (1)
 13.6: Line or Point Sources
 13.7: ThreeDimensional Heat Transfer by the Finite Element Method
 13.8: OneDimensional Heat Transfer with Mass Transport
 13.9: Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method
 13.10: Flowchart and Examples of a Heat Transfer Program
 13: Chapter Quiz
 Chapter 14: Fluid Flow in Porous Media and through Hydraulic Networks; and Electrical Networks and Electrostatics
 14.1: Derivation of the Basic Differential Equations
 14.2: OneDimensional Finite Element Formulation
 14.3: TwoDimensional Finite Element Formulation
 14.4: Flowchart and Example of a FluidFlow Program
 14.5: Electrical Networks
 14.6: Electrostatics
 14: Chapter Quiz
 Chapter 15: Thermal Stress
 15.1: Formulation of the Thermal Stress Problem and Examples (1)
 15: Chapter Quiz
 Chapter 16: Structural Dynamics and TimeDependent Heat Transfer
 16.1: Dynamics of a SpringMass System
 16.2: Direct Derivation of the Bar Element Equations
 16.3: Numerical Integration in Time
 16.4: Natural Frequencies of a OneDimensional Bar
 16.5: TimeDependent OneDimensional Bar Analysis
 16.6: Beam Element Mass Matrices and Natural Frequencies
 16.7: Truss, Plane, Frame, Plane Stress, Plane Strain, Axisymmetric, and Solid Element Mass Matrices
 16.8: TimeDependent Heat Transfer (1)
 16.9: Computer Program Example Solutions for Structural Dynamics
 16: Chapter Quiz
 Chapter A: Appendix A: Matrix Algebra
 Appendix A: Matrix Algebra
 Chapter B: Appendix B: Methods for Solution of Simultaneous Linear Equations
 Appendix B: Methods for Solution of Simultaneous Linear Equations
 Chapter D: Appendix D: Equivalent Nodal Forces
 Appendix D: Equivalent Nodal Forces
Clearly introduce the basics of the finite element method (FEM) with this simple, direct—and now updated—approach in Logan's A First Course In The Finite Element Method, Enhanced 6th Edition, SI Version. This unique presentation is written so both undergraduate and graduate students can easily comprehend content without the usual prerequisites, such as structural analysis. This edition is ideal for civil or mechanical engineering students primarily interested in stress analysis and heat transfer. It also offers a strong foundation for applying FEM as a tool in solving practical physical problems. Additional, current realworld examples and problems demonstrate applications in a variety of engineering and mathematical physicsrelated fields. This edition's consistent presentation with stepbystep, workedout examples and a special visual insert further clarify 3D images and FEM concepts.
 Read It links under each question quickly jump to the corresponding section of a complete, interactive eBook.
 Watch It links provide stepbystep instruction with short, engaging videos that are ideal for visual learners.
 A Course Pack with readytouse assignments, built by subject matter experts specifically for this textbook, are designed to save you time, and can be easily customized to meet your teaching goals.
 Customizable Lecture Slides and a complete Instructor Solution Manual are available as textbook resources.
 (Coming Soon) Chapter Quiz (CQ) questions in each chapter encourage students to test and apply what they have learned in each chapter. These questions can serve as a quick and useful selftest to help confirm understanding of each concept.
Questions Available within WebAssign
Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.
Question Availability Color Key
BLACK questions are available now
GRAY questions are under development
Group

Quantity

Questions

Chapter A: Appendix A: Matrix Algebra

A.2 

001
009

A.3 

002

A.4 

003
006

A.5 

004
007
010
011
012

A.6 

005
008

Chapter B: Appendix B: Methods for Solution of Simultaneous Linear Equations

B.2 

008

B.3 

001

B.4 

002
009

B.5 

003

B.6 

004

B.7 

005

B.8 

006

B.9 

007

Chapter D: Appendix D: Equivalent Nodal Forces

D.1 

001

Chapter 1: Introduction

1.0 
1 
001
002

1.1 
1 
003
004

1.2 
1 
005

1.3 

006

1.4 
2 
007
008
009
010
011

1.5 

012

1.6 
1 
013

Chapter 2: Introduction to the Stiffness (Displacement) Method

2.5 
3 
001
002
003
004
005
006
007
008
010
011
012
013
014
015
016
017

2.6 
1 
018
020
022
023

Chapter 3: Development of Truss Equations

3.1 
4 
001
002
003
004
005
007
008
009
010
011

3.2 
1 
013
014

3.3 
1 
017

3.4 

015

3.6 
3 
019
021
023
025
027
028
029
030
031
032
033
035

3.7 
1 
037
038
039
040
041
043
044

3.8 
1 
045
046
047
048

3.9 

049
051

3.10 
1 
053

3.11 

055
057

3.13 
2 
059
061

Chapter 4: Development of Beam Equations

4.1 
4 
001
002
003
004

4.3 
5 
005
006
008
010
011
012
013

4.4 
12 
014
015
016
017
018
019
020
021
022
024
025
026
039
040
041

4.6 
3 
042
043
044

4.7 
3 
046
047
049

Chapter 5: Frame and Grid Equations

5.1 

043

5.2 
13 
001
002
003
005
007
009
010
011
012
013
014
015
016
017
018
021
023
034
038
050

5.4 
3 
046
047
047.alt
048
049
051

Chapter 6: Development of the Plane Stress and Plane Strain Stiffness Equations

6.2 
5 
002
004
005
006
007
008
010

6.3 
4 
011
012
013
016
022

6.4 
2 
018
023

6.5 
2 
019
020

6.6 

026

Chapter 7: Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis

7.1 
2 
001
002

7.2 
2 
003
004
006

7.3 
2 
009
010

Chapter 8: Development of the LinearStrain Triangle Equations

8.2 
3 
001
002
005
006
007

8.3 

008
009

Chapter 9: Axisymmetric Elements

9.1 
11 
002
003
004
005
006
007
008
009
010
011
012

9.2 

001

9.3 
2 
020
021
022
023
024
025
026
027

Chapter 10: Isoparametric Formulation

10.1 
2 
002
003

10.2 
5 
009
010
011
012
013
014

10.3 
1 
015

10.4 

016
017
019
020

10.5 
4 
001
004
005
006
007
008
018
021
022
023

Chapter 11: ThreeDimensional Stress Analysis

11.2 
1 
001
002
003
004
005
006
007
008
009

11.3 

010
011
012
013

Chapter 13: Heat Transfer and Mass Transport

13.4 
3 
001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018

13.5 
1 
021
022

13.6 

019
020

Chapter 14: Fluid Flow in Porous Media and through Hydraulic Networks; and Electrical Networks and Electrostatics

14.0 

001

14.2 

002
003
004
005
006
007

14.3 

008
009
010

14.5 

017
018
019
020

14.6 

021

Chapter 15: Thermal Stress

15.1 
1 
001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021

Chapter 16: Structural Dynamics and TimeDependent Heat Transfer

16.2 

001
002

16.3 

005
006

16.4 

003
004

16.5 

007
008

16.7 

017

16.8 
1 
018
019

Total 
121
(193)

