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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
A resource book applying mathematics to solve engineering problems
Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls.
Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors.
Key features:
- Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems.
- Examples and problems of a practical nature with illustrations to enhance student’s self-learning.
- Numerical methods and techniques, including finite element analysis.
- Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC).
Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.
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Seitenzahl: 838
Veröffentlichungsjahr: 2018
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
Suggestions to instructors
About the companion website
Chapter 1: Overview of Engineering Analysis
1.1 Introduction
1.2 Engineering Analysis and Engineering Practices
1.3 “Toolbox” for Engineering Analysis
1.4 The Four Stages in Engineering Analysis
1.5 Examples of the Application of Engineering Analysis in Design
1.6 The “Safety Factor” in Engineering Analysis of Structures
Problems
Chapter 2: Mathematical Modeling
2.1 Introduction
2.2 Mathematical Modeling Terminology
2.3 Applications of Integrals
2.4 Special Functions for Mathematical Modeling
2.5 Differential Equations
Problems
Chapter 3: Vectors and Vector Calculus
3.1 Vector and Scalar Quantities
3.2 Vectors in Rectangular and Cylindrical Coordinate Systems
3.3 Vectors in 2D Planes and 3D Spaces
3.4 Vector Algebra
3.5 Vector Calculus
3.6 Applications of Vector Calculus in Engineering Analysis
3.7 Application of Vector Calculus in Rigid Body Dynamics
Problems
Chapter 4: Linear Algebra and Matrices
4.1 Introduction to Linear Algebra and Matrices
4.2 Determinants and Matrices
4.3 Different Forms of Matrices
4.4 Transposition of Matrices
4.5 Matrix Algebra
4.6 Matrix Inversion, [A]
−1
4.7 Solution of Simultaneous Linear Equations
4.8 Eigenvalues and Eigenfunctions
Problems
Chapter 5: Overview of Fourier Series
5.1 Introduction
5.2 Representing Periodic Functions by Fourier Series
5.3 Mathematical Expression of Fourier Series
5.4 Convergence of Fourier Series
5.5 Convergence of Fourier Series at Discontinuities
Problems
Chapter 6: Introduction to the Laplace Transform and Applications
6.1 Introduction
6.2 Mathematical Operator of Laplace Transform
6.3 Properties of the Laplace Transform
6.4 Inverse Laplace Transform
6.5 Laplace Transform of Derivatives
6.6 Solution of Ordinary Differential Equations Using Laplace Transforms
6.7 Solution of Partial Differential Equations Using Laplace Transforms
Problems
Chapter 7: Application of First-order Differential Equations in Engineering Analysis
7.1 Introduction
7.2 Solution Methods for First-order Ordinary Differential Equations
7.3 Application of First-order Differential Equations in Fluid Mechanics Analysis
7.4 Liquid Flow in Reservoirs, Tanks, and Funnels
7.5 Application of First-order Differential Equations in Heat Transfer Analysis
7.6 Rigid Body Dynamics under the Influence of Gravitation
Problems
Chapter 8: Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis
8.1 Introduction
8.2 Solution Method for Typical Homogeneous, Second-order Linear Differential Equations with Constant Coefficients
8.3 Applications in Mechanical Vibration Analyses
8.4 Mathematical Modeling of Free Mechanical Vibration: Simple Mass–Spring Systems
8.5 Modeling of Damped Free Mechanical Vibration: Simple Mass–Spring Systems
8.6 Solution of Nonhomogeneous, Second-order Linear Differential Equations with Constant Coefficients
8.7 Application in Forced Vibration Analysis
8.8 Near Resonant Vibration
8.9 Natural Frequencies of Structures and Modal Analysis
Problems
Chapter 9: Applications of Partial Differential Equations in Mechanical Engineering Analysis
9.1 Introduction
9.2 Partial Derivatives
9.3 Solution Methods for Partial Differential Equations
9.4 Partial Differential Equations for Heat Conduction in Solids
9.5 Solution of Partial Differential Equations for Transient Heat Conduction Analysis
9.6 Solution of Partial Differential Equations for Steady-state Heat Conduction Analysis
9.7 Partial Differential Equations for Transverse Vibration of Cable Structures
9.8 Partial Differential Equations for Transverse Vibration of Membranes
Problems
Chapter 10: Numerical Solution Methods for Engineering Analysis
10.1 Introduction
10.2 Engineering Analysis with Numerical Solutions
10.3 Solution of Nonlinear Equations
10.4 Numerical Integration Methods
10.5 Numerical Methods for Solving Differential Equations
10.6 Introduction to Numerical Analysis Software Packages
Problems
Chapter 11: Introduction to Finite-element Analysis
11.1 Introduction
11.2 The Principle of Finite-element Analysis
11.3 Steps in Finite-element Analysis
11.4 Output of Finite-element Analysis
11.5 Elastic Stress Analysis of Solid Structures by the Finite-element Method
11.6 General-purpose Finite-element Analysis Codes
Problems
Chapter 12: Statistics for Engineering Analysis
12.1 Introduction
12.2 Statistics in Engineering Practice
12.3 The Scope of Statistics
12.4 Common Concepts and Terminology in Statistical Analysis
12.5 Standard Deviation (
σ
) and Variance (
σ
2
)
12.6 The Normal Distribution Curve and Normal Distribution Function
12.7 Weibull Distribution Function for Probabilistic Engineering Design
12.8 Statistical Quality Control
12.9 Statistical Process Control
12.10 The “Control Charts”
Problems
Bibliography
Appendix 1: Table for the Laplace Transform
Appendix 2: Recommended Units for Engineering Analysis
Appendix 3: Conversion of Units
Appendix 4: Application of MATLAB Software for Numerical Solutions in Engineering Analysis: Contributed by Vaibhav Tank
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Overview of Engineering Analysis
Figure 1.1 The Trans-Alaska Pipeline.
Figure 1.2 A commercial airplane ready for a scheduled flight.
Figure 1.3 Role of engineering analysis in the solution of engineering problems.
Figure 1.4 General engineering design procedures.
Figure 1.5 Four-stage engineering analysis in general engineering design process.
Figure 1.6 Coat hanger with specified geometry and dimensions.
Figure 1.7 Loading on the idealized coat hanger member.
Figure 1.8 A bridge across a narrow creek.
Figure 1.9 Specifications of a bridge over a narrow creek.
Figure 1.10 An idealized structural support of a bridge.
Chapter 2: Mathematical Modeling
Figure 2.1 Translation of a melody into music notes—an analogy to mathematical modeling in engineering.
Figure 2.2 The role of mathematical modeling in engineering analysis.
Figure 2.3 Head loss of fluids passing pipe bends.
Figure 2.4 Convective heat transfer between two fluids at different temperatures.
Figure 2.5 Discrete forces applied to a beam structure. (a) People standing on a beam. (b) Equivalent forces applied to the beam.
Figure 2.6 Typical diurnal variation of the ambient temperature of a location.
Figure 2.7 Discrete and approximated continuous functions. (a) People standing close to each other. (b) Approximate continuous variation of forces.
Figure 2.8 A typical water cooler tank.
Figure 2.9 A qualitative representation of water level in the drinking water tank at different times.
Figure 2.10 Measured temperatures from a fabrication process.
Figure 2.11 Coordinate system for polynomial function curve fitting.
Figure 2.12 The fit of the derived function to the three given data (sample) points.
Figure 2.13 A pressurized process chamber.
Figure 2.14 Variation of pressure in the process chamber.
Figure 2.15 Pressure variations in the process chamber in Figure 2.13.
Figure 2.16 Continuous variation of a continuous function.
Figure 2.17 A deflected beam subject to bending load.
Figure 2.18 A cantilever beam subject to a moving load. (a) Moving load on the beam. (b) The loading function of the beam.
Figure 2.19 Illustration of the concept of integration.
Figure 2.20 Area bounded by a continuous function
P
(
t
). (a) A continuous function
P
(
t
). (b) The elements of area bounded by
P
(
t
).
Figure 2.21 Plane area of a right triangle.
Figure 2.22 Plane area of a quarter circular plate. (a) Plate geometry. (b) The plate in an
x–y
coordinate system.
Figure 2.23 Plate with a curved edge. (a) Plate geometry. (b) The plate in an
x–y
coordinate system.
Figure 2.24 Plate with a curved edge that fits an ellipse. (a) Plate geometry. (b) The plate in an
x–y
coordinate system.
Figure 2.25 Plate with curved edge by a designer. (a) Geometry of the plate. (b) The plate in an
x–y
coordinate system.
Figure 2.26 Plane area between two curves.
Figure 2.27 Area between a half ellipse and a half circle. (a) Plane area defined by two curves. (b) Symmetry of the geometry about the
y
-axis.
Figure 2.28 Solid of revolution. (a) Exterior profile of the solid. (b) The same solid with axis of revolution.
Figure 2.29 Solid volume of revolution about the
y
-axis.
Figure 2.30 A right solid cone.
Figure 2.31 Function describing a cone.
Figure 2.32 A solid volume of revolution of a parabolic curve.
Figure 2.33 A wine bottle. (a) The physical bottle. (b) The profile and dimensions of the bottle.
Figure 2.34 Volume of revolution of the curved section of the wine bottle.
Figure 2.35 The “punt” at the bottom of a wine bottle.
Figure 2.36 Mechanism with a coupler.
Figure 2.37 Cam with follower.
Figure 2.38 Centroid of a plane.
Figure 2.39 Solid of plane geometry with straight edges.
Figure 2.40 Centroid of a semicircular plate.
Figure 2.41 Solid of plane geometry with edges defined by multiple functions.
Figure 2.42 Four-bar linkage with a triangular coupler. (a) The coupler ABC. (b) Dimensions of the coupler.
Figure 2.43 Average value of a continuous function. (a) A continuous function. (b) The average value of the function.
Figure 2.44 Diffusion of substance A into solvent B.
Figure 2.45 Bessel functions. (a) Bessel functions
J
0
(
x
) and
J
1
(
x
). (b) The Neumann functions
Y
0
(
x
) and
Y
1
(
x
).
Figure 2.46 Graphical illustration of modified Bessel functions
I
0
(
x
) and
I
1
(
x
).
Figure 2.47 Graphical description of a step function.
Figure 2.48 General form of a function existing in a finite range in an infinite variable domain.
Figure 2.49 Superposition of two step functions.
Figure 2.50 A cantilever beam subjected to partial distributed loading.
Figure 2.51 Application of a step function to a partially loaded beam.
Figure 2.52 Graphical definition of impulsive function.
Figure 2.53 Impulse at origin of a coordinate system.
Figure 2.54 Off-origin impulsive function.
Figure 2.55 Beam subjected to a concentrated load.
Figure 2.56 Impulsive function with a pulse
P
0
.
Figure 2.57 Freely hung solid cone.
Figure 2.58 Forces on a free fall rigid body.
Figure 2.59 Temperature in a nuclear reactor vessel wall.
Figure 2.60 Variation of diameter of a rod.
Figure 2.61 A Pressure vessel containing liquid.
Figure 2.62 Optimal design of a three-section funnel. (a) Image of the three-section funnel. (b) Dimensions of the funnel.
Figure 2.63 Square tapered chute.
Figure 2.64 Design of a measuring jug. (a) Image of the measuring jug. (b) The overall dimensions of the jug.
Figure 2.65 IV bottle for hospital use.
Figure 2.66 A partially loaded beam.
Figure 2.67 Nonuniformly loaded beam.
Figure 2.68 Partially loaded beam.
Figure 2.69 A beam subjected to concentrated loads.
Figure 2.70 A cantilever beam subjected to a distributed load.
Figure 2.71 A plate with a curved edge.
Figure 2.72 A plate of quarter-circle geometry.
Figure 2.73 A plate of quarter-ellipse geometry.
Figure 2.74 A plate of geometry bounded by a half ellipse and a half circle.
Figure 2.75 Plate coupler of a four-bar linkage.
Figure 2.76 Cross-section of a flywheel with a tapered profile.
Chapter 3: Vectors and Vector Calculus
Figure 3.1 Graphical representation of a vector.
Figure 3.2 Rectangular
x–y
coordinate system for a vector. (a) Vector
A
in
x–y
coordinates. (b) Decomposition of vector
A
.
Figure 3.3 Vector in rectangular and cylindrical coordinate systems. (a) A vector in three-dimensional space. (b) Rectangular unit vectors.
Figure 3.4 Position vectors. (a) In the two-dimensional plane. (b) In three-dimensional space.
Figure 3.5 Summation and subtraction of the two vectors in Example 3.4.
Figure 3.6 Force vectors in a 2D plane. (a) Force acting in a plane. (b) Multiple forces acting in a plane.
Figure 3.7 Force vectors in the
x–y
plane.
Figure 3.8 Vectors in 3D space. (a) A space structure. (b) Force vectors in the structural members.
Figure 3.9 Summations of two plane vectors. (a) Two free vectors. (b) Summation of two vectors. (c) An alternative representation of vector summation.
Figure 3.10 Summation of multiple plane vectors. (a) Four free vectors. (b) Summation of four vectors.
Figure 3.11 Subtraction of two vectors. (a)Two free vectors
A
and
B
. (b) Subtraction of
B
from
A
by addition of −
B
to
A
.
Figure 3.12 Summation of two vectors in the same plane.
Figure 3.13 Navigation routes of a cruise ship.
Figure 3.14 Dot product of two vectors.
Figure 3.15 Work done in a displacing a solid.
Figure 3.16 Cross product of two vectors
A
and
B
in a right-handed coordinate system. (a) Cross product
A × B.
(b) Cross product
B × A
.
Figure 3.17 Cross product of two vectors giving the torque applied to a pipe. (a) Physical interpretation. (b) Numerical situation.
Figure 3.18 Plane areas by cross product of two vectors. (a) Area of a parallelogram. (b) Area of a triangle.
Figure 3.19 A parallelepiped solid.
Figure 3.20 Lombard Street in San Francisco. (a) A narrow and winding street. (b) Breath-taking driving.
Figure 3.21 Faraday's right-hand rule in electromagnetism.
Figure 3.22 Rectilinear motion of a rigid body.
Figure 3.23 Vector functions of instantaneous position, velocity, and acceleration in rectilinear motion of a rigid body. (a) Instantaneous position. (b) Instantaneous velocity.(c) Instantaneous acceleration.
Figure 3.24 Rigid body moving along a curved path. (a) Motion on a curved path. (b) Change of a position vector with variable
u
.
Figure 3.25 Rigid body moving along a curved path in the
x–y
plane. (a) Traveling on a curved path. (b) Change of position with time
t
Figure 3.26 Position, velocity, and acceleration vectors of a rigid body moving on a curved path.
Figure 3.27 Flight path of a projectile.
Figure 3.28 The path of a projectile in a rectangular coordinate system.
Figure 3.29 Vectors in plane cylindrical coordinate system. (a) A plane defined by
r–θ
coordinates. (b) A position vector in the
r–θ
plane.
Figure 3.30 Variation of unit vector functions in plane cylindrical coordinates. (a) Displacement of a body from
P
to
P
′. (b) The net increase of unit vector
u
r
(
t
).
Figure 3.31 Variation of the transverse unit vector function. (a) Displacement of unit vector
u
θ
.
(b) Corresponding variation of unit vector
u
θ
.
Figure 3.32 Acceleration vector in a cylindrical coordinate system.
Figure 3.33 A vehicle traveling along an arc.
Figure 3.34 Magnitudes of the components of the acceleration vector of a vehicle traveling along a circular road.
Figure 3.35 Plane curvilinear motion in a cylindrical coordinate system. (a) General curvilinear motion. (b) Showing the radial and tangential components
Figure 3.36 A vehicle traveling on a circular track.
Figure 3.37 Baggage transportation conveyor. (a) An airport baggage transportation conveyor in Frankfurt, Germany. (b) Dimensions and travel of a piece of baggage [here a box].
Figure 3.38 Volume of a parallelepiped solid.
Figure 3.39 Flight path of an airplane.
Figure 3.40 A jet airplane bombing a target on the ground.
Figure 3.41 Flight path of a fighter jet.
Chapter 4: Linear Algebra and Matrices
Figure 4.1 Linear functions.
Figure 4.2 Diagonal of a square matrix.
Figure 4.3 Transposition of a square matrix.
Figure 4.4 A perforated plate subjected to lateral stretching forces. (a) The perforated plate. (b) Application of force
F
. (c) The stress field.
Figure 4.5 Discretization of a perforated plate with tapered edges. (a) Loading of the tapered plate. (b) Discretized model of the plate.
Figure 4.6 Free vibration of multiple mass–spring system.
Chapter 5: Overview of Fourier Series
Figure 5.1 A mechanism with periodic motions. (a) Riding horse on a merry-go-round. (b) Up-and-down motion of a mechanical pony.
Figure 5.2 Periodic motion of the needle of a sewing machines. (a) A typical sewing machine. (b) The repetitive cyclical motion of the needle.
Figure 5.3 A die stamping machine with a repetitive action.
Figure 5.4 Periodic functions in typical Fourier series. (a) A periodic function with period (−
π
,
π
). (b) A periodic function with period (−
L
,
L
).
Figure 5.5 Measured signals representing periodic physical phenomena.
Figure 5.6 Periodic sine function. (a) Signal on oscilloscope screen. (b) Quantitative details of the signal over one period.
Figure 5.7 A sawtooth signal waveform, such as the signal from an oscilloscope screen (Figure 5.5).
Figure 5.8 A piecewise continuous linear signal waveform, such as the signal from an oscilloscope screen (Figure 5.5).
Figure 5.9 A periodic function with period defined in (−
π
,
π
).
Figure 5.10 A periodic function with period defined in (−5, 5).
Figure 5.11 A periodic function with period of (−
π
,
π
).
Figure 5.12 Correlation of a function with the Fourier series with one term.
Figure 5.13 Correlation of a function with the Fourier series with two terms.
Figure 5.14 Correlation of a function with the Fourier series with three terms.
Figure 5.15 Correlation of a function with the Fourier series with four terms.
Figure 5.16 Fourier series at discontinuities.
Figure 5.17 A piecewise continuous periodic function.
Figure 5.18 Convergence of the Fourier series for a piecewise continuous periodic function.
Figure 5.19 Fourier series of a piecewise continuous periodic function.
Figure 5.20 Fourier series with 3 terms (
n
= 3).
Figure 5.21 Fourier series with 15 terms (
n
= 15).
Figure 5.22 Fourier series with 80 terms (
n
= 80).
Figure 5.23 A step function.
Figure 5.24 A piecewise continuous function.
Figure 5.25 A parabolic function.
Figure 5.26 Evaluation of the Fourier series for a parabolic function.
Figure 5.27 Evaluation of the Fourier series for a step function.
Figure 5.28 Crank–slider linkage.
Chapter 6: Introduction to the Laplace Transform and Applications
Figure 6.1 A ramp function.
Figure 6.2 A unit step function.
Figure 6.3 A unit step function at
t
=
a.
Figure 6.4 A beam deflected under a distributed load.
Figure 6.5 A cantilever beam subjected to uniform distributed load.
Figure 6.6 A cantilever beam subjected to a concentrate force
P
.
Figure 6.7 Uniformly loaded beam with built-in support at both ends.
Figure 6.8 Bending of beams subjected to complicated loading and end conditions.
Figure 6.9 Simple beam subjected to partial uniformly distributed load.
Figure 6.10 Simple beam subjected to variable distributed load.
Figure 6.11 A damped mechanical vibration.
Chapter 7: Application of First-order Differential Equations in Engineering Analysis
Figure 7.1 Fluid flow in a conduit.
Figure 7.2 Fluid in motion from state 1 to state 2.
Figure 7.3 Fluid flow in a large reservoir.
Figure 7.4 Fluid flow through various cross-sections.
Figure 7.5 Drainage of water from a cylindrical tank.
Figure 7.6 Drop of water level in the tank during drainage.
Figure 7.7 Drainage of a Tapered Funnel.
Figure 7.8 Instantaneous radius of the funnel vs. the instantaneous water level.
Figure 7.9 Draining of a tapered funnel.
Figure 7.10 A two-section funnel system. (a) A multisection funnel. (b) The dimensions of a two-section funnel.
Figure 7.11 Profile of a tapered funnel.
Figure 7.12 Drainage of a tapered section of a compound funnel.
Figure 7.13 Filling a wine bottle from a circular funnel. (a) Funnel used for filling a wine bottle. (b) Volume of the tapered cone of the funnel.
Figure 7.14 Conduction of heat in a solid slab.
Figure 7.15 Heat flux in a solid slab.
Figure 7.16 Heat flow in a thermally insulated rod.
Figure 7.17 Temperature variation in a rod with to heat flow.
Figure 7.18 Heat flux in a solid.
Figure 7.19 Two-dimensional heat flow in a solid.
Figure 7.20 Heat flow in a rectangular block.
Figure 7.21 Application of signs in Fourier's law of heat conduction in solids.
Figure 7.22 Heat spreaders of integrated circuits and an internal combustion engine. (a) A typical printed circuit board. (b) Dissipation of heat from an integrated circuit (IC) chip. (c) A motorcycle engine with cooling fins.
Figure 7.23 Heat flow in a cooling fin of a heat spreader. (a) Cross-section of half of a fin. (b) The coordinate system for analysis.
Figure 7.24 Convective heat flow in a bulk fluid.
Figure 7.25 (a) Heating and (b) cooling of small solids.
Figure 7.26 Heat flow between a solid and a fluid in a controlled-temperature enclosure.
Figure 7.27 Heat transfer from a solid to a surrounding fluid.
Figure 7.28 Temperature variations in one cycle of heating and cooling of chip under test.
Figure 7.29 Rise and fall of rigid bodies.
Figure 7.30 Paratroopers. (http://www.westandwithukraine.org/wp-content/uploads/2015/04/Paratroopers-3-596573.jpg)
Figure 7.31 Water in a shallow tapered funnel.
Figure 7.32 A flat chute for filling juice into bottles.
Figure 7.33 A square chute for liquid solvents. (a) A square chute. (b) Dimensions of the chute.
Figure 7.34 A tapered circular funnel for water bottle filling.
Figure 7.35 Drainage of an IV bottle. (a) Patient with IV bottle on stand. (b) Dimensions of idealized IV bottle.
Chapter 8: Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis
Figure 8.1 Forms of vibration. (a) Vibration with regular variable amplitudes and frequencies. (b) Vibration with irregular variable amplitudes but constant frequency. (c) Random vibrations.
Figure 8.2 A mass–spring vibrational system. (a) A simple mass–spring system. (b) Mass–spring systems in general.
Figure 8.3 A mass–spring–dashpot vibrational system.
Figure 8.4 Forced vibration.
Figure 8.5 Simple mass–spring systems. (a) Mass resting on a spring. (b) Mass suspended from a spring.
Figure 8.6 Modeling a vibrating mass. (a) Free-hung spring. (b) Statically stretched spring. (c) A vibrating mass attime
t
.
Figure 8.7 Forces acting on a vibrating mass. (a) Static equilibrium. (b) Dynamic equilibrium of a vibrating mass.
Figure 8.8 Graphical representation of a vibrating mass in simple harmonic motion.
Figure 8.9 Non-coil springs. (a) Rod spring. (b) Cantilever spring.
Figure 8.10 Hoisting a machine by a steel cable.
Figure 8.11 Physical model for damped vibration of a mass–spring system. (a) Vibrating mass supported by a dashpot. (b) Mass supported by spring and dashpot. (c) Mass–dashpot assembly for a motorcycle suspension.
Figure 8.12 Forces acting on a vibrating mass with damping.
Figure 8.13 Amplitudes in over-damped vibration. (a) With +ve initial displacement,
y
0
. (b) With negligible initial displacement.
Figure 8.14 Amplitudes in critically damped vibration. (a) With +ve initial displacement. (b) With negligible initial displacement.
Figure 8.15 Amplitudes in under-damped vibration.
Figure 8.16 Forced vibration of a mass–spring system.
Figure 8.17 Excitation force acting on the mass in a mass–spring system.
Figure 8.18 Amplitude of a resonant vibration.
Figure 8.19 Working principle of a sheet metal stamping machine.
Figure 8.20 A simulated punch machine.
Figure 8.21 Vehicle cruising over rough road surface.
Figure 8.22 Graphical representation of the amplitude of vibration of a motor cycle.
Figure 8.23 Amplitude of vibration of a vehicle in resonance.
Figure 8.24 Amplitudes in near-resonance vibrations.
Figure 8.25 Amplitudes of a vibrating mass in the initial period and over one cycle. (a) Instantaneous amplitudes over 25 seconds. (b) Amplitudes in one complete cycle.
Figure 8.26 Amplitudes of a vibrating mass in near-resonant vibration in two cycles.
Figure 8.27 Amplitude of the vibrating machine in the first 6 seconds.
Figure 8.28 Amplitude of the vibrating machine during the first full cycle.
Figure 8.29 Amplitude of the vibrating machine in the first three cycles.
Figure 8.30 Variation of molecular forces with distance.
Figure 8.31 The Golden Gate Bridge.
Figure 8.32 Structures of complex geometry that may be subjected to intermittent loading. (a) A billboard. (b) A jet fighter. (c) A satellite in orbit.
Figure 8.33 Mode shapes of a flat plate. (a) Mode 1. (b) Mode 3.
Figure 8.34 Suspension system of a light-duty vehicle. (a) Wheel suspension. (b) A small road block,
d
= 2 cm.
Figure 8.35 Vibration of a vehicle induced by passing over a speed bump. (a) A speed bump. (b) Analytical model of the suspension system.
Chapter 9: Applications of Partial Differential Equations in Mechanical Engineering Analysis
Figure 9.1 Graphic representation of an derivative of ordinary function
f
(
x
).
Figure 9.2 Function for Fourier Transformation.
Figure 9.3 Flow of heat in a solid.
Figure 9.4 Energy balance of heat flow in a solid.
Figure 9.5 Heat transfer at the interface of a solid submerged in fluid.
Figure 9.6 Steam flow in a thick wall pipe.
Figure 9.7 Temperature variations in the pipe wall.
Figure 9.8 Conduction of heat across thickness of a slab.
Figure 9.9 Heat Conduction in a Long Solid Cylinder.
Figure 9.10 Temperature distribution in a plate.
Figure 9.11 Steady-state heat conduction in a solid cylinder.
Figure 9.12 Long cables in electric power transmission structures.
Figure 9.13 Guy wire support for a tall radio transmission tower.
Figure 9.14 Golden Gate suspension bridge.
Figure 9.15 A long cable in a static equilibrium state.
Figure 9.16 A vibrating long cable. (a) Shape of the vibrating cable at time
t
. (b) Forces on the cable in Detail A.
Figure 9.17 Dynamic forces acting on a cable segment.
Figure 9.18 A long cable subjected to lateral vibration.
Figure 9.19 Convergence of an infinite series solution.
Figure 9.20 Shapes of the cable in mode 1 vibration.
Figure 9.21 Shapes of the cable in mode 2 vibration.
Figure 9.22 Shapes of the cable in mode 3 vibration.
Figure 9.23 Lateral deformations of thin plates in vibration.
Figure 9.24 Forces on a vibrating element of a thin plate.
Figure 9.25 Plan view of a flexible plate undergoing transverse vibration.
Figure 9.26 Shape of the mouse pad in mode 1 vibration. (a) The initial shape of the pad. (b) Mode shape at time 1/8 second.
Figure 9.27 Mode 3 shapes in vibration of a flexible plate. (a) At time
t
= 0. At time
t
= 1/8 second. (c) At time
t
= 1/4 second.
Figure 9.28 Temperature distribution in a flat plate.
Chapter 10: Numerical Solution Methods for Engineering Analysis
Figure 10.4 Dimensions of a measuring cup.
Figure 10.1 Root of a nonlinear equation .
Figure 10.2 Roots of a nonlinear equation.
Figure 10.3 Newton–Raphson method for solving nonlinear equations.
Figure 10.5 Profile of a measuring cup in the
x–y
coordinate system.
Figure 10.6 Graphical representation of integration of a continuous function.
Figure 10.7 Approximation of the integral of a continuous function
y
(
x
).
Figure 10.8 Numerical integration of a function
y
(
x
) by three trapezoids.
Figure 10.9 Integration of function
y
(
x
) with multiple trapezoids.
Figure 10.10 Integration of a function
y
(
x
) with six trapezoids.
Figure 10.11 Graphical representation of integration of a continuous function. (a) Area defined by a function. (b) Approximation of the area by a trapezoid. (c) Approximation of the area by a parabolic function.
Figure 10.12 Numerical integration by Simpson's one-third rule.
Figure 10.13 Integration of a nonlinear function
y
(
x
) by Simpson's one-third rule.
Figure 10.14 Numerical integration using Simpson's one-third rule with eight function values.
Figure 10.15 Transformation of coordinates for Gaussian integration. (a) With the original coordinates. (b) After transformation of coordinates.
Figure 10.16 Function
f
(
x
) evaluated at three positions.
Figure 10.17 Graphical solution of a second-order ordinary differential equation by MatLAB.
Figure 10.18 Design of a measuring cup. (a) A measuring cup. (b) The overall dimensions of the cup.
Figure 10.19 Plane area of an ellipse.
Chapter 11: Introduction to Finite-element Analysis
Figure 11.1 Discretization of a continuum subjected to loads. (a) Before discretization. (b) After discretization in a rectangular coordinate system.
Figure 11.2 Typical simplex elements.
Figure 11.3 FE model for a three-dimensional solid.
Figure 11.4 FE model for a tapered bar subjected to tensile forces. (a) The tapered bar. (b) An FE model.
Figure 11.5 Relating element values with those at nodes.
Figure 11.6 Triangular plate element with two unknown components.
Figure 11.7 Interpolation function of bar elements.
Figure 11.8 Interpolation function for a triangular plate element with specified nodal coordinates.
Figure 11.9 Triangular plate element with nodal constraints and force.
Figure 11.10 Finite-element model of a quadrilateral plate structure.
Figure 11.11 Map for assembling element coefficient matrices.
Figure 11.12 Contour output of a finite-element analysis. (a) Isoclinic stress contour. (b) Finite-element model.
Figure 11.13 Contours of deformation of a wheel section by finite-element analysis. (a) The solid for FE modeling. (b) Deformation with the FE model. (c) Contours of deformation.
Figure 11.14 Induced stress components in a solid due to external loads. (a) The solid subjected to external loads. (b) Induced stress in the solid.
Figure 11.15 Displacements in a deformed solid.
Figure 11.16 Finite-element model of a cam-shaft assembly.
Figure 11.17 Typical tetrahedral elements.
Figure 11.18 An axially deformed bar.
Figure 11.19 A uniaxially loaded compound bar made of copper and aluminum.
Figure 11.20 Finite-element model for a uniaxially loaded compound bar.
Figure 11.21 Advanced elements for finite-element models.
Figure 11.22 Finite-element analysis on imported solid geometry. (a) Imported solid geometry. (b) Finite-element analytical results.
Figure 11.23 General processes in new product development.
Figure 11.24 Simulation of the vibration of a disk-coupler during braking of a vehicle. (a) New design of braking pad. (b) Mode shape of disk.
Figure 11.25 A compound bar made of three different materials.
Figure 11.26 A triangular plate subjected to a nodal force.
Figure 11.27 A triangular plate subjected to uniform pressure loading.
Figure 11.28 Finite-element model of a triangular plate with two elements.
Chapter 12: Statistics for Engineering Analysis
Figure 12.1 Histogram of measured lengths of chips.
Figure 12.2 Mark distribution of students in an engineering analysis class.
Figure 12.3 Approximated normal distribution of mark distribution of a class.
Figure 12.4 Normal distribution curve.
Figure 12.5 Properties of the normal distribution.
Figure 12.6 Weibull distribution function.
Figure 12.7 Four-point bend test specimens for brittle materials.
Figure 12.8 Determination of Weibull parameters by the log-log plot method.
Figure 12.9 Estimation of Weibull parameters for KT-SiC by the log-log method with chosen values of
σ
u
.
Figure 12.10 Weibull distribution function for the fracture strength of KT-SiC.
Figure 12.11 A ceramic tube subject to internal pressure loading.
Figure 12.12 Cost and product value associated with quality improvement.
Figure 12.13 A rod sample with six measurement stations.
Figure 12.14 Typical control chart for quality control in mass production.
Figure 12.15 Three-sigma control chart.
Figure 12.16 A three-sigma control chart for IC chip output.
Figure 12.17 Control chart using sample ranges (the R-chart).
Figure 12.18 The R-control chart for quality control of chips.
Appendix 4: Application of MATLAB Software for Numerical Solutions in Engineering Analysis: Contributed by Vaibhav Tank
Figure A4.1 Amplitude of the vibrating mass in the first 20 seconds.
Figure A4.3 Amplitude of the vibrating mass after one complete cycle.
Figure A4.4 Improper graphical results due to aliasing.
Figure 4.5 Mode shape at
t
= 1/4 s.
Figure A4.5a Initial shape at
t
= 0 s of the flexible pad.
Figure A4.6a Initial state of the pad (
t
= 0 s).
List of Tables
Chapter 1: Overview of Engineering Analysis
Table 1.1 Greatest engineering achievements of the 20th century
Table 1.2 Typical safety factors for engineering analyses
Chapter 7: Application of First-order Differential Equations in Engineering Analysis
Table 7.1 Rules for assigning signs in Fourier's law of heat conduction
Table 7.2 Conditions of the heating and cooling chambers.
Chapter 8: Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis
Table 8.1 Guidelines for choosing assumed particular solution
u
p
(
x
)
Chapter 9: Applications of Partial Differential Equations in Mechanical Engineering Analysis
Table 9.1 Fourier transform of selected functions
Chapter 10: Numerical Solution Methods for Engineering Analysis
Table 10.1 Function values at designated points.
Table 10.2 Eight values of a function for integration using Simpson one-third rule.
Table 10.3 Weight coefficients of the Gaussian quadrature formula in Equation 10.12 (Kreyszig, 2011; Zwillinger, 2003)
Table 10.4 Coefficients in the fourth-order Runge–Kutta method for solving second-order differential equations
Table 10.5 Solutions of a differential equation by Runge–Kutta methods with three different increment sizes.
Chapter 11: Introduction to Finite-element Analysis
Table 11.1 Nodal description of an FE model of a tapered bar
Table 11.2 Element description of an FE model of a tapered bar
Table 11.3 Typical actions and induced reactions.
Chapter 12: Statistics for Engineering Analysis
Table 12.1 Fracture strength of silicon carbide in 4-pont bending tests
Table 12.2 Reliability of a pressurized tube made of KT-SiC ceramic.
Table 12.3 Working sheet for establishing the R-chart
Table 12.4 Factors for estimating.
.
and lower and upper control limits (Rosenkrantz, 1997)
Applied Engineering Analysis
Tai-Ran Hsu
San Jose State University, San Jose, USA
This edition first published 2018
© 2018 John Wiley & Sons Ltd
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Library of Congress Cataloging-in-Publication Data
Names: Hsu, Tai-Ran, author.
Title: Applied engineering analysis / by Tai-Ran Hsu.
Description: Hoboken, NJ : John Wiley & Sons, 2017. | Includes bibliographical references and index. |
Identifiers: LCCN 2017017185 (print) | LCCN 2017037252 (ebook) | ISBN 9781119071181 (pdf) | ISBN 9781119071198 (epub) | ISBN 9781119071204 (cloth)
Subjects: LCSH: Engineering mathematics-Textbooks.
Classification: LCC TA332.5 (ebook) | LCC TA332.5 .H78 2017 (print) | DDC 620.001/51-dc23
LC record available at https://lccn.loc.gov/2017017185
Cover design by Wiley
Cover image: (Sir Isaac Newton) © duncan1890/Gettyimages; (Hand) © Colin Anderson/Gettyimages
My wife Grace Su-Yong who has supported me for decades with endless encouragement and love, my three loving adult children, Jean, Euginette, and Leigh, for their consistent support, and above all, my motivated students who inspired me to write this book.
Preface
This book is designed to be a textbook for a one-semester course in engineering analysis for both junior and senior undergraduate classes or entry-level graduate programs. It is also designed for practicing engineers who are in need of analytical tools to solve technical problems in their line of duties. Unlike many textbooks adopted for class teaching of engineering analysis, this book introduces fewer additional mathematical topics beyond the courses on calculus and differential equations, but has heavy engineering content. Another unique feature of this book is its strong focus on using mathematics as a tool to solve engineering problems. Theories are presented in the book to show students their connection with practical issues in problem-solving. Overall, this book should be treated as an engineering, not advanced engineering mathematics textbook.
Mathematics and physics are two principal pillars of engineering education of all disciplines. Indeed, courses in mathematics and physics dominate the curricula of lower division engineering education in both the Freshman and Sophomore years in most engineering programs worldwide. Many engineering schools offer a course on engineering analysis that follows classes on precalculus, calculus, and differential equations. Engineering analysis is also offered at the entry level of graduate studies in many universities in the world.
The widespread acceptance of engineering analysis as a core curriculum by many educators is attributed to their conviction that students need to synergistically integrate all of the mathematical subjects that they learned earlier and apply them in solving engineering problems. However, the pedagogy of engineering analysis and its outcome has rarely been discussed in open forums. Many universities offer a course on engineering analysis as a terminal mathematics course with additional advanced mathematics subjects. Consequently, all textbook vendors with whom I have had contact in the last 30 years have consistently published books on advanced engineering mathematics, as textbooks for my course on engineering analysis. Upon close inspection, almost all have little direct relevance to the engineering profession. Additionally, all of these books are close to, or exceed, 1000 printed pages, with overwhelming coverage of detailed and elegant mathematical treatments to mostly mathematical problems. I have also observed that in all of the advanced engineering mathematics books such as those cited in the bibliography of this book, less than 10 percent of the pages have applications to engineering problems. Consequently, a textbook that is designed to teach students to solve engineering problems using mathematics as a tool is truly needed in classes on engineering analysis or those with similar objectives.
Many science and engineering educators are of the opinion that most engineering problems in the real world are of a physical nature. The disconnect in teaching mathematics and physics, as it occurs in lower division engineering education, has resulted in the inability of students to use mathematics as a tool to solve such engineering problems. Many students in my engineering analysis classes are skillful in manipulating mathematics in their assigned problems, including performing integrations and solving differential equations either using classical solution techniques learned previously, or using modern tools such as electronic calculators and computers. However, they are not capable of deriving appropriate equations for solving particular genuine engineering problems. Even more, students cannot apply integrations to determine simple design engineering properties such as areas, volumes, and centroids of solids of given geometry. The situation has worsened in recent years with rapid advances in information technology, which offer students ready access to turnkey software packages such as finite-element and finite-difference codes. This results in obtaining the solutions of engineering problems, in which insight, knowledge, and experience are sacrificed for numbers with seven-decimal point accuracy and fancy graphics. Unfortunately, most of these student users do not know what these numbers and graphs mean as solutions to the problems. These readily available commercial computer codes have actually further prevented engineering students from understanding fundamental engineering principles, worsening an already serious dissociation occurring early in mathematics and physics education.
An encouraging sign in recent years, however, has been the emergence of a consensus among visionary educators that students should relate their mathematics to the engineering subjects they will encounter in their upper division classes, and develop them as tools to solve real-world problems. It was with this conviction that I was motivated to write this book.
The present book intends to develop the analytical capability of students in engineering education. I am convinced that upper division students are not short of exposure to mathematics; what is lacking is the opportunity that they get to use what they learned in solving engineering problems. Consequently, no advanced mathematical subjects need to be added to this book. Rather, I have placed strong emphasis on how students will learn to apply the mathematics that they learned in previous years to solve engineering problems. Another aspect of this book is to include sufficient materials to fit the 3 hours per week in a 15-week timeframe that most engineering schools provide for this course. The topics to be covered were carefully chosen to ensure proper balance between breadth and depth, with lower division mathematics and physics courses as prerequisites.
There are 12 chapters in this book. Chapter 1 offers an overview of engineering analysis, in which students will learn the need for a linkage between physics and mathematics in solving engineering problems. Chapter 2 provides students with basic concepts of mathematical modeling of physical problems. Mathematical modeling often requires setting up functions and variables that represent physical quantities in practical situations. It may involve all forms of mathematical expressions ranging from algebraic equations to integrations and differential equations. Students are expected to apply their skills to determine physical quantities such as areas, volumes, centroids of plane subjects, moments of inertia, and so on as required in many engineering analyses. Special functions and curve-fitting techniques that can model specific engineering effects and phenomena are also presented. Chapter 3 refreshes the topics on vectors and vector calculus, which are viable tools in dealing with complicated engineering problems of different disciplines. Application of vector calculus, in particular, to rigid body dynamics is illustrated. Chapter 4 relates to the application of linear algebra and matrices in the formulation of modern-day analytical tools, and the solution techniques for very large numbers of simultaneous equations such as in the finite-element analysis. Chapter 5 deals with Fourier series, which are used to represent many periodic phenomena in engineering practices. Chapter 6 relates to Laplace transformation for functions that represent physical phenomena covering half of the infinite space or time domain, such as in the case of indeterminate beams subjected to distributed loads in various sections of the spans, or with discrete concentrated forces. Chapters 7 and 8 deal with the derivation, not just solution techniques, of first- and second-order ordinary differential equations with applications in fluid dynamics and heat transfer by conduction and convection in solids interfaced with fluids with applications in heating, cooling, and refrigeration of small solids.Chapter 8 presents the principles and mathematical modeling of free and forced vibrations, as well as resonant and near-resonant vibrations of solids with elastic restraints. Chapter 9 deals with the solutions of partial differential equations, in which equations for heat conduction and mechanical vibrations in solid structures are introduced. This chapter also offers solution methods such as the separation of variables technique and integral transform methods involving Laplace and Fourier transforms with numerical illustrations. Chapter 10 offers numerical solution methods for solving nonlinear and transcendental equations and differential equations and integrals, with examples that will facilitate learning of these techniques. Special descriptions of the overviews of popular Mathematica and MatLAB software are included in this chapter with a special article on the use of MatLAB in one of the appendices of the book. Chapter 11 introduces the principle and mathematical formulation of the finite-element method, which intends to make readers intelligent users of this versatile and powerful numerical technique for obtaining the solutions to many engineering and scientific problems with complicated geometry, loading, and boundary conditions. The book ends with a special chapter on statistics for engineering analysis as Chapter 12, in which the readers will learn the common terminologies in the science of statistics with physical meanings. This chapter will usher the readers to the common practice of statistical process control (SPC) currently adopted by industries involved in mass production. This chapter also includes probabilistic design methods for structures and mechanical systems that would not be otherwise handled using traditional deterministic techniques.
I have taught engineering analysis to senior undergraduate and entry-level graduate students in two major universities in the U.S. and Canada for over 30 years. I have found that most students are not accustomed to the application of mathematics to solving descriptive engineering problems that often require the derivation of equations and mathematical formulae for solutions. I attribute this to a major psychological barrier that many engineering students need to overcome before they can be effective analysts. Consequently, I have included many examples and problems that are descriptive in nature in this book. These problems are drawn from several engineering disciplines and many of them require numerical solutions that relate to theoretical concepts. Most of these problems can be solved using pocket electronic calculators.
It is by no means a trivial job to develop a book of this breadth and depth single-handedly. I wish to thank a number of students who helped me in shaping its content. In particular, my appreciation goes to a former student, Vaibhav Tank, for his contribution of the application of MatLAB software in problem-solving. Such dedicated students made an effort to develop this book into a memorable pleasure for me, and gave me a feeling of accomplishment in engineering education.
Tai-Ran HsuSan Jose, California
Suggestions to instructors
This book is written to be a textbook for upper division undergraduate and entry-level graduate classes. It is also intended to be a reference book for practicing engineers to refresh their experience and skills in using mathematics for their engineering analyses, or to upgrade their understanding of contemporary analytical tools using digital technology in numerical methods as well as the use of commercial software packages such as MatLAB and the finite-element method for advanced engineering analyses.
The content of this book is designed for 3 hours per week in a 15-week long semester at both undergraduate and graduate levels. With significant omission of materials, the book can also be used for classes with well-prepared students for 10-week long quarters.
This textbook would be more effective for students with the following academic experience and backgrounds:
1.
Undergraduate students in good upper division academic standing with sound knowledge and experience in college mathematics that includes calculus, differential equations, fundamental physics, and concurrent learning of engineering subjects in solid and fluid mechanics and heat transfer.
2.
Students with working experience in computer software packages such as Microsoft Office, in particular the MS Excel, and other software packages such as Mathematica and MatLAB over those who do not have such experience.
Teaching a course on engineering analysis with sufficient breadth and depth such as that presented in this textbook in the aforementioned time frames could be a challenge for instructors. This situation may be further compounded by the likelihood of having students who completed their prerequisite mathematics in lower division coursework which often focuses on drilling rather than applications. The following Schedules A and B offer suggested topics from the book that the instructor may cover in either one semester or one quarter. The instructor would use his or her discretion to assign the unlisted sections in the following tables either as omissions or as assigned reading materials to the students.
Schedule A: For 15-week, 3 hours/week-long semesters
Week no.
Undergraduate classes
Graduate classes
1
Sections 1.3
,
1.4
,
2.2.3
,
2.2.4
,
2.3
,
2.5
Sections 1.3
,
1.4
,
2.2.3
,
2.2.4
,
2.3
,
2.4
2
Sections 3.4
,
3.5
,
3.6
,
Sections 3.5
,
3.6
,
3.7
,
4.3
,
4.4
3
Sections 4.2.2
,
4.3
–
4.7
Sections 4.5
–
4.8
4
Sections 5.2
–
5.5
Sections 5.2
–
5.5
,
6.2
,
6.4
,
6.5
5
Sections 6.2
–
6.4
Sections 6.6
,
6.7
,
7.2
6
Sections 6.5
,
6.6
,
7.2
,
7.3
Sections 7.3
–
7.5
7
Sections 7.4
,
7.5
Sections 8.2
,
8.3
. Assigned reading
8.4
–
8.6
8
Sections 8.2
–
8.4
Sections 8.7
–
8.9
9
Sections 8.5
–
8.6
Sections assigned reading
9.2
.,
9.3
,
9.4
10
Sections 8.7
,
8.8
,
8.9
Sections 9.5.2
,
9.6
11
Sections 9.1
,
9.3.1
,
9.4
Sections assigned
9.7
,
9.8
12
Sections 9.5.1
,
9.6.1
,
9.7
Sections assigned reading
10.2
.,
10.3
–
10.6
13
Sections 10.2
–
10.4
Sections 11.3
–
11.6
14
Sections 10.5
,
10.6
,
11.2
–
11.4
Sections assigned reading
11.7
, 11.8.
12.4
–
12.7
15
Sections 11.6
–11.8,
12.1
–
12.6
,
12.8
–
12.10
Sections 12.8
–
12.10
Schedule B: For 10-week, 3 hours/week-long quarters
Week no.
Undergraduate classes
Graduate classes
1
Sections 1.3
,
1.4
,
2.3
,
2.5
,
3.3
Sections 1.3
,
1.4
,
2.3
–
2.5
,
3.4
2
Sections 3.4
–
3.6
Sections 3.5
–
3.7
3
Sections 4.3
,
4.4
,
4.5
,
4.6
Sections 4.5
–
4.8
4
Sections 4.8
,
5.3
–
5.5
Sections 5.2
–
5.5
,
6.2
–
6.4
,
6.6
,
6.7
5
Sections 6.2
–
6.7
Sections 7.3
,
7.4
,
7.5
6
Sections 7.3
–
7.5
Sections 8.4
–
8.9
7
Sections 8.2
,
8.4
,
8.5
Sections 9.3
,
9.4
–
9.6
8
Sections 8.6
–
8.9
Sections 10.3
,
10.4
,
10.5
,
10.6
9
Sections 9.1
,
9.4
–
9.6
,
9.8
,
10.3
,
10.4
,
10.5.2
Sections 11.2
–11.8
10
Sections 10.6.2
,
11.3
, 11.8,
12.4
,
12.5
,
12.6
,
12.8
–
12.10
Sections 12.4
–
12.10
Instructors may, of course, use their discretion in selecting the topics other than those suggested in the above tables to suit their own preferences and schedules.
The author would like to recommend using a black or white board in addition to slide projections for examples that are offered by the textbook. From his own experience, the author found it challenging to have students who develop a mindset to learn to use their skills in math drilling to the applications in solving a wide range of problems in a single 15-week semester. In pursuit of this goal, much effort needs to be made in extra tutoring and advising students outside the classroom to help them acquire this new experience.
Further, a few additional suggestions for the successful teaching of this class include: offering quizzes and examinations in open book format, for which students may bring any reference materials they wish instead of memorizing all formulae and equations required for solving the problems; students are also encouraged to form “study groups” on their own initiative, and above all, bringing “models” for classroom demonstrations, such as wine bottles for determining their volume content, tightening a bolt to a fixture to demonstrate the principle of “cross product of vectors,” etc. These simple classroom demonstrations would not only help students in understanding the subject matter, but also reinforce students' appreciation of the value of applied engineering analysis by using mathematics as a tool for solving real-world problems.
A final remark on stimulating student's interest in learning engineering analysis is to encourage and reward them for using the available online solution methods in mathematical operations in their homework assignments and quizzes and exams at all times.
About the companion website
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There you will find valuable material designed to enhance your learning, including:
1.
Solutions manual
2.
PowerPoint slides
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Chapter 1Overview of Engineering Analysis
Chapter Learning Objectives
Learn the concept and principles of engineering analysis, and the vital roles that engineering analysis plays in professional engineering practices.
Learn the need for the application of engineering analysis in three principal functions of professional engineering practice: creation, problem solving, and decision making.
Learn that engineers are expected to solve problems that relate to protection of properties and public safety and also to make decisions.
Appreciate the roles that mathematics plays in engineering analysis, and acquire the ability to use mathematical modeling in problem solving and decision making in dealing with real physical situations.
