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Contact Mechanics

:	J.R. Barber
:	Contact Mechanics
:	Springer-Verlag
:	9783319709390
:	1
:	CHF 142.50
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	592
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This book describes the solution of contact problems with an emphasis on idealized (mainly linear) elastic problems that can be treated with elementary analytical methods. General physical and mathematical features of these solutions are highlighted. Topics covered include the contact of rough surfaces and problems involving adhesive (e.g. van der Waals) forces.

he author is a well-known researcher in the subject with hands-on experience of the topics covered and a reputation for lucid explanations. The target readership for the book includes researchers who encounter contact problems but whose primary focus is not contact mechanics. Coverage is also suitable for a graduate course in contact mechanics and end-of-chapter problems are included.

James Richard Barber graduated in Mechanical Sciences from the University of Cambridge in 1963. He then joined British Rail, who later sponsored his research at Cambridge between 1965 and 1968 on the subject of thermal effects in braking systems. In 1969 he became a Lecturer and later Reader in Solid Mechanics at the University of Newcastle upon Tyne, U.K. He moved to the University of Michigan, Department of Mechanical Engineering in 1981. His current research interests are in solid mechanics with particular reference to thermoelasticity, contact mechanics and tribology. He is a Chartered Engineer in the U.K., a Fellow of the Institution of Mechanical Engineers and has engaged extensively in consulting work in the field of stress analysis for engineering design. Dr. Barber is author of two books and numerous articles in the fields of Elasticity, Thermoelasticity, Contact Mechanics, Tribology, Heat Conduction and Elastodynamics and he is a member of the editorial boards of the International Journal of Mechanical Sciences and the Journal of Thermal Stresses.

	Preface	6
	Contents	8
	1 Kinematics of Contact	19
	1.1 Reference Frame and the Initial Gap Function	20
	1.2 Establishment of a Contact Region	21
	1.2.1 Definition of Contact	22
	1.2.2 The Boundary Value Problem	22
	1.2.3 Signorini Problems	23
	1.2.4 Asymptotic Arguments	23
	1.2.5 The Discrete Problem	25
	1.3 Nonlinear Kinematics	26
	1.4 Almost Conformal Contact	27
	2 Three-Dimensional Frictionless Elastic Problems	30
	2.1 The Half-Space Approximation	30
	2.2 Normal Loading of the Half-Space	31
	2.2.1 The Point Force Solution	32
	2.2.2 Similarity, Equilibrium and Anisotropy	33
	2.2.3 The Composite Elastic Modulus	34
	2.3 Integral Equation Formulation	35
	2.3.1 Field-Point Integration	37
	2.3.2 Indentation by a Flat Elliptical Punch	37
	2.4 Galin's Theorem	40
	2.4.1 A Special Case	41
	2.5 Interior Stress Fields	42
	2.5.1 In-Plane Stress Components Near the Surface	42
	3 Hertzian Contact	45
	3.1 Transformation of Coordinates	45
	3.1.1 Cylinders and Spheres	47
	3.1.2 More General Cases	48
	3.2 Hertzian Pressure Distribution	49
	3.3 Strategy for Hertzian Contact Calculations	50
	3.3.1 Eccentricity of the Contact Area	50
	3.3.2 Dimensions of the Contact Area	51
	3.3.3 Highly Elliptical Contacts	54
	3.4 First Yield	55
	4 More General Problems for the Half-Space	58
	4.1 The Electrical--Mechanical Analogy	59
	4.1.1 Other Mathematical Analogies	61
	4.1.2 Boyer's Approximation	63
	4.1.3 Fabrikant's Approximation	64
	4.2 General Theorems for Frictionless Contact	66
	4.3 Superposition by Differentiation	70
	4.4 The Force--Displacement Relation	72
	4.4.1 Non-conformal Contact Problems	73
	5 Axisymmetric Contact Problems	77
	5.1 Green and Collins Solution	77
	5.1.1 The Flat Punch Solution	79
	5.2 Non-conformal Contact Problems	80
	5.3 Annular Contact Regions	82
	5.4 The Non-axisymmetric Cylindrical Punch	83
	5.5 The Method of Dimensionality Reduction (MDR)	84
	6 Two-Dimensional Frictionless Contact Problems	90
	6.1 The Line Force Solution	91
	6.2 Integral Equation Formulation	93
	6.2.1 Edge Conditions	94
	6.3 Incremental Solution of Non-conformal Contact Problems	98
	6.3.1 Symmetric Problems	98
	6.3.2 Bounded-Singular Problems	99
	6.4 Solution by Fourier Series	99
	6.4.1 Rigid-Body Rotation	100
	6.4.2 Galin's Theorem, Chebyshev Polynomials and Recurrence Relations	102
	6.5 Periodic Contact Problems	104
	6.5.1 Sinusoidal Contact Pressure	104
	6.5.2 Fourier Series Methods	105
	6.5.3 The Periodic Green's Function	106
	6.5.4 The Cotangent Transform	106
	6.5.5 Manners' Solution	107
	6.5.6 Westergaard's Problem	109
	6.6 The Smirnov--Sobolev Transform	110
	6.6.1 Inversion of the Transform	111
	6.6.2 Example: Uniform Loading Over the Circle	111
	6.6.3 Anisotropic Problems	112
	6.7 Displacements in Two-Dimensional Problems	113
	6.7.1 Kalker's Line Contact Theory	115
	7 Tangential Loading	121
	7.1 Kinematics	121
	7.1.1 Gross Slip and Microslip	122
	7.2 Green's Functions for Tangential Forces and Displacements	123
	7.2.1 Three-Dimensional [point] Loading	123
	7.2.2 Two-Dimensional [line] Loading	125
	7.2.3 Normal-Tangential Coupling	126
	7.3 Two-Dimensional Flat Rigid Punch with No Slip	127
	7.3.1 Uncoupled Problem	129
	7.3.2 Oscillatory Singularities	129
	7.4 Axisymmetric Flat Rigid Punch with No Slip	131
	7.5 The `Goodman' Approximation	133
	7.6 Uniform Tangential Displacement in a Prescribed Area	135
	7.6.1 Tangential Loading over a Circular Area	135
	7.6.2 Tangential Loading over an Elliptical Area	136
	7.6.3 Two Conjectures	138
	7.7 Non-conformal Contact Problems with No Slip	139
	7.7.1 Uncoupled Hertzian Contact with Tangential Loading	140
	7.7.2 The Coupled Axisymmetric Problem under Purely Normal Loading	141
	7.7.3 The Coupled Two-Dimensional Problem	142
	7.7.4 Relaxation Damping	144
	8 Friction Laws	149
	8.1 Amontons' Law	149
	8.1.1 Continuum Problems	150
	8.1.2 Two-Dimensional Problems	151<