A Descriptive Listing of Problems in Woo/Hwang

Classic Analytical
Problems
in Mechanical Engineering

Tse-Chien Woo & Charles C.C. Hwang
(both of the University of Pittsburgh)



ISBN 1-930217-00-5

DESCRIPTIVE LISTING OF PROBLEMS

PART I COMPLEX VARIABLES

I.1 Two-Dimensional Fluid Flow

Problem I-1 Flow of a uniform stream around a circular barrier w=U(z+a²/z)
Problem I-2 Flow out of a channel bounded by horizontal straight lines
Problem I-3 Steady plane flow over a flat plate normal to the stream

I.2 Heat Conduction and Electrostatics

Problem I-4 Mapping of a circular segment onto the upper half plane
Problem I-5 Heat conduction in a semi-infinite slab bounded by two planes
Problem I-6 Heat conduction in a long cylindrical wedge
Problem I-7 Heat conduction in a quadrant plate
Problem I-8 Electrostatics of an eccentric cylinder inside another cylinder

I.3 Schwarz Christoffel Transformation

Problem I-9 Mapping of an infinite channel onto the upper half plane
Problem I-10 Mapping of a semi-infinite channel onto the upper half plane
Problem I-11 Mapping of a semi-infinite plane onto the upper half plane
Problem I-12 Mapping of the upper half plane with a slit onto the upper half
Problem I-13 Mapping of a quagrant with a leg onto the upper half plane
Problem I-14 Mapping of a region whose boundary is a circle and its tangent onto the upper half plane

I.4 Two-Dimensional Fluid Flow Using S-C-T

Problem I-15 Flow in a right angle channel
Problem I-16 Flow over a step
Problem I-17 Flow out of the side of a channel
Problem I-18 Flow of a uniform stream past a plate normal to the stream

I.5 Free Streamline Problems

Problem I-19 Flow of a jet from an aperture
Problem I-20 Flow of a jet over a lamina

I.6 Plane Problems in Infinitesimal Elasticity

Problem I-21 Simple tension of an infinite plate with a circular hole
Problem I-22 Simple tension of an infinite plate with a circular hole (Alternative Method)
Problem I-23 A uniformly stretched infinite plate with a circular hole
Problem I-24 An infinite plate with a uniform normal pressure on the circular hole
Problem I-25 An infinite plate with a uniform pressure on parts of the circular hole boundary
Problem I-26 Conditions of vanishing resultant forces and moments on the boundaries of a plate bounded by concentric circles
Problem I-27 A hoolow circular plate with a uniform pressure on part of the outer boundary
Problem I-28 An infinite plate with an elliptic hole under simple tension at an angle with the major axis
Problem I-29 An infinite plate with an elliptic hole under uniform tension in all directions
Problem I-30 An infinite plate with a curvilinear polygonal hole under simple tension at an angle with the major axis
Problem I-31 A square rod under parabolic loadings on the sides
Problem I-32 A circular plate under uniform pressure on its edge
Problem I-33 A circular plate under two opposite concentrated forces on the edge

I.7 Elastic Torsion of Prismatical Bars

Problem I-34 Torsion of a shaft with elliptical cross section
Problem I-35 Torsion of a shaft with equilateral cross section
Problem I-36 Torsion of a shaft with the cross section formed by a hyperbola and a straight line
Problem I-37 Torsion of a circular shaft with a groove of a circular arc
Problem I-38 Torsion of a shaft with the cross section formed by two equal circular arcs
Problem I-39 Torsion of a shaft with the cross section of a Booth's Lemniscate
Problem I-40 Torsion of a shaft with the cross section of a cardiod
Problem I-41 Torsion of a shaft with the cross section of an epitrochoidal curve
Problem I-42 Torsion of a shaft with double grooves

PART II INTEGRAL TRANSFORM

II.1 General

Problems II-1 to II-6 General Problems

II.2 Heat Conduction

Problem II-7 Transient heat conduction in a semi-infinite solid
Problem II-8 Steady two-dimensional heat conduction in a semi-infinite solid with temperature specified at the boundary
Problem II-9 Steady heat conduction in a solid occupying a quadrant
Problem II-10 Steady heat conduction in a solid occupying the upper half plane
Problem II-11 Transient heat conduction in a circular rod
Problem II-12 Transient heat conduction in a plane wall
Problem II-13 Transient heat conduction in a semi-infinite solid with heat source

II.3 Vibration

Problem II-14 Vibration of a finite string with an initial sinusoidal shape
Problem II-15 Vibration of a finite rod with a force applied at one end

II.4 Viscoelasticity

Problem II-16 Wave propagation in a semi-infinite viscoelastic rod
Problem II-17 Wave propagation in a finite viscoelastic rod
Problem II-18 Temperature-induced stresses in an infinite viscoelastic plate

II.5 Elastic Contact

Problem II-19 An elastic half space indented by a rigid spherical indenter

PART III VECTOR AND TENSOR ANALYSIS

III.1 Kinematic and Stress Analysis

Problem III-1 A kinematic problem in the glass forming process
Problem III-2 Determination of the normal component, the shear component, and the shear direction of the traction
Problem III-3 Proof of ...
Problem III-4 Proof that ...
Problem III-5 Determination of the direction of the traction on the plane that contains ...
Problem III-6 Principal stresses determination when the traction does not vanish in only one direction
Problem III-7 Proof of ...
Problem III-8 Ochtahedral shearing stress expression
Problem III-9 Proof of ...
Problem III-10 Stress component determination
Problem III-11 Principal stresses determination
Problem III-12 Principal stresses determination for a strain rosette
Problem III-13 Upper bound of the torsional rigidity for the pure torsion of a uniform bar with an arbitrary cross section
Problem III-14 Expression of the end load that must be applied in order to maintain the plane strain state
Problem III-15 Overall shortening of a prismatic bar with an arbitrary cross section resting on one end on a horizontal plate under its own weight
Problem III-16 Overall volume shrinkage of a prismatic bar with an arbitrary cross section resting on one end on a horizontal plate under its own weight
Problem III-17 Overall length and volume change of a prismatical bar lying on the ground
Problem III-18 Volume change of a body of an arbitrary form compressed between two parallel planes
Problem III-19 Stress displacement relationships in the cylindrical polar coordinates
Problem III-20 Strain displacement relationships in the spherical polar coordinates
Problem III-21 Equations of equilibrium in the cylindrical polar coordinates
Problem III-22 Equations of equilibrium in the spherical polar coordinates

III.2 Finite Elastic Deformation

Problem III-23 Compatibility equations for the finite elastic deformations
Problem III-24 Relationships between Cauchy and Finger strain tensors
Problem III-25 Shear deformation
Problem III-26 A homogeneous deformation
Problem III-27 A rigid body deformation
Problem III-28 Derivation of Cauchy's first equation of motion and the rate of work expression
Problem III-29 Frame indifference of constitutive equations for the Newtonian fluid
Problem III-30 Linear elastic law
Problem III-31 Relationships between the displacement gradients before and after deformation
Problem III-32 Relationships between the Jacobian and the displacement gradients
Problem III-33 Equations of motion in terms of Labrangian stresses
Problem III-34 Force vector expression in terms of undeformed state variables
Problem III-35 Stress expressions in terms of displacement gradiants before and after the deformations
Problem III-36 Constitutive equation derivation
Problem III-37 Stress strain relations for an elastic body with inextensible cords embedded in one direction
Problem III-38 Relationships between strain energy, the tractions, and body forces
Problem III-39 Relationships between strain energy, the tractions, and body forces for incompressible materials
Problem III-40 Further relationships between strain energy, the tractions, and body forces
Problem III-41 Displacement gradiant relationships
Problem III-42 Potential energy stationary theorem
Problem III-43 Stress strain relations for a transversely isotropic material
Problem III-44 A stress strain energy relation for the pure strain case
Problem III-45 Simple tension for a Mooney material
Problem III-46 Simple shear deformation
Problem III-47 Generalized shear deformation
Problem III-48 Inflation of a circular tube for an incompressible material
Problem III-49 Inflation and extension of a thin cylindrical balloon for an incompressible material

SPECIFICATIONS

Classic Analytical Problems in Mechanical Engineering
by Tse-Chien Woo & Charles C.C. Hwang
ISBN: 1-930217-00-5

© 2000, 220 pages, 105 illustrations, $45.00

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PART I COMPLEX VARIABLES
	I.1 Two-Dimensional Fluid Flow
	Problem I-1 Flow of a uniform stream around a circular barrier w=U(z+a²/z) Problem I-2 Flow out of a channel bounded by horizontal straight lines Problem I-3 Steady plane flow over a flat plate normal to the stream
	I.2 Heat Conduction and Electrostatics
	Problem I-4 Mapping of a circular segment onto the upper half plane Problem I-5 Heat conduction in a semi-infinite slab bounded by two planes Problem I-6 Heat conduction in a long cylindrical wedge Problem I-7 Heat conduction in a quadrant plate Problem I-8 Electrostatics of an eccentric cylinder inside another cylinder
	I.3 Schwarz Christoffel Transformation
	Problem I-9 Mapping of an infinite channel onto the upper half plane Problem I-10 Mapping of a semi-infinite channel onto the upper half plane Problem I-11 Mapping of a semi-infinite plane onto the upper half plane Problem I-12 Mapping of the upper half plane with a slit onto the upper half Problem I-13 Mapping of a quagrant with a leg onto the upper half plane Problem I-14 Mapping of a region whose boundary is a circle and its tangent onto the upper half plane
	I.4 Two-Dimensional Fluid Flow Using S-C-T
	Problem I-15 Flow in a right angle channel Problem I-16 Flow over a step Problem I-17 Flow out of the side of a channel Problem I-18 Flow of a uniform stream past a plate normal to the stream
	I.5 Free Streamline Problems
	Problem I-19 Flow of a jet from an aperture Problem I-20 Flow of a jet over a lamina
	I.6 Plane Problems in Infinitesimal Elasticity
	Problem I-21 Simple tension of an infinite plate with a circular hole Problem I-22 Simple tension of an infinite plate with a circular hole (Alternative Method) Problem I-23 A uniformly stretched infinite plate with a circular hole Problem I-24 An infinite plate with a uniform normal pressure on the circular hole Problem I-25 An infinite plate with a uniform pressure on parts of the circular hole boundary Problem I-26 Conditions of vanishing resultant forces and moments on the boundaries of a plate bounded by concentric circles Problem I-27 A hoolow circular plate with a uniform pressure on part of the outer boundary Problem I-28 An infinite plate with an elliptic hole under simple tension at an angle with the major axis Problem I-29 An infinite plate with an elliptic hole under uniform tension in all directions Problem I-30 An infinite plate with a curvilinear polygonal hole under simple tension at an angle with the major axis Problem I-31 A square rod under parabolic loadings on the sides Problem I-32 A circular plate under uniform pressure on its edge Problem I-33 A circular plate under two opposite concentrated forces on the edge
	I.7 Elastic Torsion of Prismatical Bars
	Problem I-34 Torsion of a shaft with elliptical cross section Problem I-35 Torsion of a shaft with equilateral cross section Problem I-36 Torsion of a shaft with the cross section formed by a hyperbola and a straight line Problem I-37 Torsion of a circular shaft with a groove of a circular arc Problem I-38 Torsion of a shaft with the cross section formed by two equal circular arcs Problem I-39 Torsion of a shaft with the cross section of a Booth's Lemniscate Problem I-40 Torsion of a shaft with the cross section of a cardiod Problem I-41 Torsion of a shaft with the cross section of an epitrochoidal curve Problem I-42 Torsion of a shaft with double grooves
PART II INTEGRAL TRANSFORM
	II.1 General
	Problems II-1 to II-6 General Problems
	II.2 Heat Conduction
	Problem II-7 Transient heat conduction in a semi-infinite solid Problem II-8 Steady two-dimensional heat conduction in a semi-infinite solid with temperature specified at the boundary Problem II-9 Steady heat conduction in a solid occupying a quadrant Problem II-10 Steady heat conduction in a solid occupying the upper half plane Problem II-11 Transient heat conduction in a circular rod Problem II-12 Transient heat conduction in a plane wall Problem II-13 Transient heat conduction in a semi-infinite solid with heat source
	II.3 Vibration
	Problem II-14 Vibration of a finite string with an initial sinusoidal shape Problem II-15 Vibration of a finite rod with a force applied at one end
	II.4 Viscoelasticity
	Problem II-16 Wave propagation in a semi-infinite viscoelastic rod Problem II-17 Wave propagation in a finite viscoelastic rod Problem II-18 Temperature-induced stresses in an infinite viscoelastic plate
	II.5 Elastic Contact
	Problem II-19 An elastic half space indented by a rigid spherical indenter
PART III VECTOR AND TENSOR ANALYSIS
	III.1 Kinematic and Stress Analysis
	Problem III-1 A kinematic problem in the glass forming process Problem III-2 Determination of the normal component, the shear component, and the shear direction of the traction Problem III-3 Proof of ... Problem III-4 Proof that ... Problem III-5 Determination of the direction of the traction on the plane that contains ... Problem III-6 Principal stresses determination when the traction does not vanish in only one direction Problem III-7 Proof of ... Problem III-8 Ochtahedral shearing stress expression Problem III-9 Proof of ... Problem III-10 Stress component determination Problem III-11 Principal stresses determination Problem III-12 Principal stresses determination for a strain rosette Problem III-13 Upper bound of the torsional rigidity for the pure torsion of a uniform bar with an arbitrary cross section Problem III-14 Expression of the end load that must be applied in order to maintain the plane strain state Problem III-15 Overall shortening of a prismatic bar with an arbitrary cross section resting on one end on a horizontal plate under its own weight Problem III-16 Overall volume shrinkage of a prismatic bar with an arbitrary cross section resting on one end on a horizontal plate under its own weight Problem III-17 Overall length and volume change of a prismatical bar lying on the ground Problem III-18 Volume change of a body of an arbitrary form compressed between two parallel planes Problem III-19 Stress displacement relationships in the cylindrical polar coordinates Problem III-20 Strain displacement relationships in the spherical polar coordinates Problem III-21 Equations of equilibrium in the cylindrical polar coordinates Problem III-22 Equations of equilibrium in the spherical polar coordinates
	III.2 Finite Elastic Deformation
	Problem III-23 Compatibility equations for the finite elastic deformations Problem III-24 Relationships between Cauchy and Finger strain tensors Problem III-25 Shear deformation Problem III-26 A homogeneous deformation Problem III-27 A rigid body deformation Problem III-28 Derivation of Cauchy's first equation of motion and the rate of work expression Problem III-29 Frame indifference of constitutive equations for the Newtonian fluid Problem III-30 Linear elastic law Problem III-31 Relationships between the displacement gradients before and after deformation Problem III-32 Relationships between the Jacobian and the displacement gradients Problem III-33 Equations of motion in terms of Labrangian stresses Problem III-34 Force vector expression in terms of undeformed state variables Problem III-35 Stress expressions in terms of displacement gradiants before and after the deformations Problem III-36 Constitutive equation derivation Problem III-37 Stress strain relations for an elastic body with inextensible cords embedded in one direction Problem III-38 Relationships between strain energy, the tractions, and body forces Problem III-39 Relationships between strain energy, the tractions, and body forces for incompressible materials Problem III-40 Further relationships between strain energy, the tractions, and body forces Problem III-41 Displacement gradiant relationships Problem III-42 Potential energy stationary theorem Problem III-43 Stress strain relations for a transversely isotropic material Problem III-44 A stress strain energy relation for the pure strain case Problem III-45 Simple tension for a Mooney material Problem III-46 Simple shear deformation Problem III-47 Generalized shear deformation Problem III-48 Inflation of a circular tube for an incompressible material Problem III-49 Inflation and extension of a thin cylindrical balloon for an incompressible material