# A First Course in the Finite Element Method (Enhanced Edition), SI Edition 6th edition

Daryl L. Logan
Publisher: Cengage Learning

## Textbook Resources

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• Chapter 1: Introduction
• 1.1: Brief History
• 1.2: Introduction to Matrix Notation
• 1.3: Role of the Computer
• 1.4: General Steps of the Finite Element Method
• 1.5: Applications of the Finite Element Method
• 1.6: Advantages of the Finite Element Method
• 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
• 2.6: Potential Energy Approach to Derive Spring Element Equations
• 2: Chapter Quiz

• Chapter 3: Development of Truss Equations
• 3.1: Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates
• 3.2: Selecting a Displacement Function in Step 2 of the Derivation of Stiffness Matrix for One-Dimensional Bar Element
• 3.3: Transformation of Vectors in Two Dimensions
• 3.4: Global Stiffness Matrix for Bar Arbitrarily Oriented in the Plane
• 3.5: Computation for Stress for a Bar in the xy Plane
• 3.6: Solution of a Plane Truss
• 3.7: Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
• 3.8: Use of Symmetry in Structures
• 3.9: Inclined, or Skewed, Supports
• 3.10: Potential Energy Approach to Derive Bar Element Equations
• 3.11: Comparison of Finite Element Solution to Exact Solution for Bar
• 3.12: Galerkin's Residual Method and Its Use to Derive the One-Dimensional Bar Element Equations
• 3.13: Other Residual Methods and Their Application to a One-Dimensional Bar Problem
• 3.14: Flowchart for Solution of Three-Dimensional Truss Problems
• 3.15: Computer Program Assisted Step-by-Step Solution for Truss Problem
• 3: Chapter Quiz

• Chapter 4: Development of Beam Equations
• 4.1: Beam Stiffness
• 4.2: Example of Assemblage of Beam Stiffness Matrices
• 4.3: Examples of Beam Analysis Using the Direct Stiffness Method
• 4.5: Comparison of the Finite Element Solution to the Exact Solution for a Beam
• 4.6: Beam Element with Nodal Hinge
• 4.7: Potential Energy Approach to Derive Beam Element Equations
• 4.8: Galerkin's Method for Deriving Beam Element Equations
• 4: Chapter Quiz

• Chapter 5: Frame and Grid Equations
• 5.1: Two-Dimensional Arbitrarily Oriented Beam Element
• 5.2: Rigid Plane Frame Examples (8)
• 5.3: Inclined or Skewed Supports—Frame Element
• 5.4: Grid Equations (2)
• 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 Constant-Strain Triangular Element Stiffness Matrix and Equations
• 6.3: Treatment of Body and Surface Forces
• 6.4: Explicit Expression for the Constant-Strain Triangle Stiffness Matrix
• 6.5: Finite Element Solution of a Plane Stress Problem
• 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
• 7.2: Equilibrium and Compatibility of Finite Element Results
• 7.3: Convergence of Solution and Mesh Refinement
• 7.4: Interpretation of Stresses
• 7.5: Flowchart for the Solution of Plane Stress/Strain Problems
• 7.6: Computer Program-Assisted Step-by-Step Solution, Other Models, and Results for Plane Stress/Strain Problems
• 7: Chapter Quiz

• Chapter 8: Development of the Linear-Strain Triangle Equations
• 8.1: Derivation of the Linear-Strain Triangular Element Stiffness
• 8.2: Example LST Stiffness Determination
• 8.3: Comparison of Elements
• 8: Chapter Quiz

• Chapter 9: Axisymmetric Elements
• 9.1: Derivation of the Stiffness Matrix
• 9.2: Solution of an Axisymmetric Pressure Vessel
• 9.3: Applications of Axisymmetric Elements
• 9: Chapter Quiz

• Chapter 10: Isoparametric Formulation
• 10.1: Isoparametric Formulation of the Bar Element Stiffness Matrix
• 10.2: Isoparametric Formulation of the Plane Quadrilateral (Q4) Element Stiffness Matrix
• 10.3: Newton-Cotes and Gaussian Quadrature
• 10.4: Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
• 10.5: Higher-Order Shape Functions (Including Q6, Q8, Q9, and Q12 Elements)
• 10: Chapter Quiz

• Chapter 11: Three-Dimensional Stress Analysis
• 11.1: Three-Dimensional Stress and Strain
• 11.2: Tetrahedral Element
• 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: One-Dimensional Finite Element Formulation Using a Variational Method
• 13.5: Two-Dimensional Finite Element Formulation
• 13.6: Line or Point Sources
• 13.7: Three-Dimensional Heat Transfer by the Finite Element Method
• 13.8: One-Dimensional 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: One-Dimensional Finite Element Formulation
• 14.3: Two-Dimensional Finite Element Formulation
• 14.4: Flowchart and Example of a Fluid-Flow 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
• 15: Chapter Quiz

• Chapter 16: Structural Dynamics and Time-Dependent Heat Transfer
• 16.1: Dynamics of a Spring-Mass System
• 16.2: Direct Derivation of the Bar Element Equations
• 16.3: Numerical Integration in Time
• 16.4: Natural Frequencies of a One-Dimensional Bar
• 16.5: Time-Dependent One-Dimensional 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: Time-Dependent Heat Transfer
• 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 real-world examples and problems demonstrate applications in a variety of engineering and mathematical physics-related fields. This edition's consistent presentation with step-by-step, worked-out examples and a special visual insert further clarify 3-D images and FEM concepts.

• Watch It links provide step-by-step instruction with short, engaging videos that are ideal for visual learners.
• A Course Pack with ready-to-use 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 self-test 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 1: Introduction
1.0 001
1.1 003
1.2 005
1.4 007 009
1.6 013
Chapter 2: Introduction to the Stiffness (Displacement) Method
2.5 001 002 004 005 006 008 010 012 016
2.6 018 020 022
Chapter 3: Development of Truss Equations
3.1 001 003 004 005 007 008 009 011
3.2 013
3.3 017
3.4 015
3.6 019 021 023 025 027 029 031 033 035
3.7 037 041 043
3.8 045 046 047
3.9 049 051
3.10 053
3.11 055 057
3.13 059 061
Chapter 4: Development of Beam Equations
4.1 002 004
4.3 006 008 010 012
4.4 014 016 018 020 022 024 025 039 041
4.6 042 043 044
4.7 046 049
Chapter 5: Frame and Grid Equations
5.1 043
5.2 8 001 002 003 005 007 009 012 013 014 016 017 021 023 034 038 050
5.4 2 046 047 047.alt 048 049 051
Chapter 6: Development of the Plane Stress and Plane Strain Stiffness Equations
6.2 002 004 005 007 008
6.3 011 013 022
6.4 018 023
6.5 020
6.6 026
Chapter 7: Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis
7.1 001 002
7.2 003 004 006
7.3 009 010
Chapter 8: Development of the Linear-Strain Triangle Equations
8.2 001 002 005 006
Total 10 (107)