Solutions & Answer Guide
A First Course in the Finite Element Method, Enhanced
6th edition
by Daryl Logan
Chapters 1–16
SC
Course Resource
This complete test bank for Family Practice Guidelines (6th Edition) by Jill C. Cash, Cheryl
A. Glass, and Jenny Mullen provides comprehensive exam-style questions covering all 23
chapters. It includes multiple-choice, true/false, and clinical scenario–based questions
O
focused on evidence-based primary care across the lifespan.
Format: Solutions & Answer Guide
R
Edition: 6th edition
Coverage: Chapters 1–16
EM
© SCOREVAULT
AX
,TABLE OF CONTENT
Chapter 1. Introduction
Chapter 2. Introduction to the Stiffness (Displacement) Method
Chapter 3. Development of Truss Equations
Chapter 4. Development of Beam Equation
Chapter 5. Frame and Grid Equations
Chapter 6. Development of the Plane Stress and Plane Strain Stiffness Equations
Chapter 7. Practical Considerations in Modeling; Interpreting Results; and Examples of Plane
Stress/Strain Analysis
Chapter 8. Development of the Linear-Strain Triangle Equation
SC
Chapter 9. Axisymmetric Elements
Chapter 10. Isoparametric Formulation
Chapter 11. Three-Dimensional Stress Analysis
O
Chapter 12. Plate Bending Element
Chapter 13. Heat Transfer and Mass Transport
R
Chapter 14. Fluid Flow in Porous Media and through Hydraulic Networks; and Electrical
Networks and Electrostatics
EM
Chapter 15. Thermal Stress
Chapter 16. Structural Dynamics and Time-Dependent Heat Transfer
AX
, Chapter 1
1.1. A finite element is a small body or unit interconnected to other units to model a larger
structure or system.
1.2. Discretization means dividing the body (system) into an equivalent system of finite elements
with associated nodes and elements.
1.3. The modern development of the finite element method began in 1941 with the work of
Hrennikoff in the field of structural engineering.
1.4. The direct stiffness method was introduced in 1941 by Hrennikoff. However, it was not
commonly known as the direct stiffness method until 1956.
SC
1.5. A matrix is a rectangular array of quantities arranged in rows and columns that is often used
to aid in expressing and solving a system of algebraic equations.
1.6. As computer developed it made possible to solve thousands of equations in a matter of
minutes.
1.7. The following are the general steps of the finite element method.
Step 1
O
Divide the body into an equivalent system of finite elements with associated
nodes and choose the most appropriate element type.
Step 2
Choose a displacement function within each element.
R
Step 3
Relate the stresses to the strains through the stress/strain law—generally called
the constitutive law.
EM
Step 4
Derive the element stiffness matrix and equations. Use the direct equilibrium
method, a work or energy method, or a method of weighted residuals to relate the
nodal forces to nodal displacements.
Step 5
Assemble the element equations to obtain the global or total equations and
introduce boundary conditions.
AX
Step 6
Solve for the unknown degrees of freedom (or generalized displacements).
Step 7
Solve for the element strains and stresses.
Step 8
Interpret and analyze the results for use in the design/analysis process.
1.8. The displacement method assumes displacements of the nodes as the unknowns of the
problem. The problem is formulated such that a set of simultaneous equations is solved for
nodal displacements.
1.9. Four common types of elements are: simple line elements, simple two-dimensional elements,
simple three-dimensional elements, and simple axisymmetric elements.
1.10 Three common methods used to derive the element stiffness matrix and equations are
(1) direct equilibrium method
(2) work or energy methods
1
© 2023
, (3) methods of weighted residuals
1.11. The term ‘degrees of freedom’ refers to rotations and displacements that are associated with
each node.
1.12. Five typical areas where the finite element is applied are as follows.
(1) Structural/stress analysis
(2) Heat transfer analysis
(3) Fluid flow analysis
(4) Electric or magnetic potential distribution analysis
(5) Biomechanical engineering
1.13. Five advantages of the finite element method are the ability to
(1) Model irregularly shaped bodies quite easily
(2) Handle general load conditions without difficulty
SC
(3) Model bodies composed of several different materials because element equations are
evaluated individually
(4) Handle unlimited numbers and kinds of boundary conditions
(5) Vary the size of the elements to make it possible to use small elements where necessary
O
R
EM
AX
2
© 2023
A First Course in the Finite Element Method, Enhanced
6th edition
by Daryl Logan
Chapters 1–16
SC
Course Resource
This complete test bank for Family Practice Guidelines (6th Edition) by Jill C. Cash, Cheryl
A. Glass, and Jenny Mullen provides comprehensive exam-style questions covering all 23
chapters. It includes multiple-choice, true/false, and clinical scenario–based questions
O
focused on evidence-based primary care across the lifespan.
Format: Solutions & Answer Guide
R
Edition: 6th edition
Coverage: Chapters 1–16
EM
© SCOREVAULT
AX
,TABLE OF CONTENT
Chapter 1. Introduction
Chapter 2. Introduction to the Stiffness (Displacement) Method
Chapter 3. Development of Truss Equations
Chapter 4. Development of Beam Equation
Chapter 5. Frame and Grid Equations
Chapter 6. Development of the Plane Stress and Plane Strain Stiffness Equations
Chapter 7. Practical Considerations in Modeling; Interpreting Results; and Examples of Plane
Stress/Strain Analysis
Chapter 8. Development of the Linear-Strain Triangle Equation
SC
Chapter 9. Axisymmetric Elements
Chapter 10. Isoparametric Formulation
Chapter 11. Three-Dimensional Stress Analysis
O
Chapter 12. Plate Bending Element
Chapter 13. Heat Transfer and Mass Transport
R
Chapter 14. Fluid Flow in Porous Media and through Hydraulic Networks; and Electrical
Networks and Electrostatics
EM
Chapter 15. Thermal Stress
Chapter 16. Structural Dynamics and Time-Dependent Heat Transfer
AX
, Chapter 1
1.1. A finite element is a small body or unit interconnected to other units to model a larger
structure or system.
1.2. Discretization means dividing the body (system) into an equivalent system of finite elements
with associated nodes and elements.
1.3. The modern development of the finite element method began in 1941 with the work of
Hrennikoff in the field of structural engineering.
1.4. The direct stiffness method was introduced in 1941 by Hrennikoff. However, it was not
commonly known as the direct stiffness method until 1956.
SC
1.5. A matrix is a rectangular array of quantities arranged in rows and columns that is often used
to aid in expressing and solving a system of algebraic equations.
1.6. As computer developed it made possible to solve thousands of equations in a matter of
minutes.
1.7. The following are the general steps of the finite element method.
Step 1
O
Divide the body into an equivalent system of finite elements with associated
nodes and choose the most appropriate element type.
Step 2
Choose a displacement function within each element.
R
Step 3
Relate the stresses to the strains through the stress/strain law—generally called
the constitutive law.
EM
Step 4
Derive the element stiffness matrix and equations. Use the direct equilibrium
method, a work or energy method, or a method of weighted residuals to relate the
nodal forces to nodal displacements.
Step 5
Assemble the element equations to obtain the global or total equations and
introduce boundary conditions.
AX
Step 6
Solve for the unknown degrees of freedom (or generalized displacements).
Step 7
Solve for the element strains and stresses.
Step 8
Interpret and analyze the results for use in the design/analysis process.
1.8. The displacement method assumes displacements of the nodes as the unknowns of the
problem. The problem is formulated such that a set of simultaneous equations is solved for
nodal displacements.
1.9. Four common types of elements are: simple line elements, simple two-dimensional elements,
simple three-dimensional elements, and simple axisymmetric elements.
1.10 Three common methods used to derive the element stiffness matrix and equations are
(1) direct equilibrium method
(2) work or energy methods
1
© 2023
, (3) methods of weighted residuals
1.11. The term ‘degrees of freedom’ refers to rotations and displacements that are associated with
each node.
1.12. Five typical areas where the finite element is applied are as follows.
(1) Structural/stress analysis
(2) Heat transfer analysis
(3) Fluid flow analysis
(4) Electric or magnetic potential distribution analysis
(5) Biomechanical engineering
1.13. Five advantages of the finite element method are the ability to
(1) Model irregularly shaped bodies quite easily
(2) Handle general load conditions without difficulty
SC
(3) Model bodies composed of several different materials because element equations are
evaluated individually
(4) Handle unlimited numbers and kinds of boundary conditions
(5) Vary the size of the elements to make it possible to use small elements where necessary
O
R
EM
AX
2
© 2023
