Contact Problems in the Classical Theory of Elasticity

Przednia okładka
Springer Science & Business Media, 30 cze 1980 - 736
 

Spis treści

CHAPTER I THE CLASSICAL THEORY OF ELASTICITY
1
12 The analysis of strain
2
13 Strains in cylindrical and spherical polar coordinates
7
14 The analysis of stress
11
15 Stress in cylindrical and spherical polar coordinates
16
16 The relation between stress and strain
18
17 Strain energy and Bettis reciprocal theorem
21
18 Anisotropic media
25
67 Beams on an elastic halfplane
277
68 Receding contact between a strip and a halfplane
285
69 Further problems concerning a plane strip and a foundation
295
610 The inhomogeneous halfplane
305
611 The method of orthogonal polynomials
312
CHAPTER VII STIFFENED PLATES
316
72 Melans original problems
320
73 Melons problems for stiffeners of finite length
326

19 Uniqueness of solution for static problems
29
110 Solutions of the displacement equations
32
111 Plane strain and plane stress
36
CHAPTER II ELEMENTARY PROBLEMS
45
22 Simple plane punch problems
51
23 Chebyshev polynomials
61
24 Indentation by a frictionless punch of general profile
70
25 The equations of Boussinesq and Cerruti
75
26 Axisyrmetria loading over a circular region
81
27 Loading applied over an elliptical region
87
28 The use of Bettis reciprocal theorem
89
29 Hertzs theory of contact
93
210 Beams on simple foundations
98
CHAPTER III FUNCTIONS OF A COMPLEX VARIABLE
107
32 Cauchy integrals
110
33 Cauchy integrals along the real axis
121
34 The problem of linear relationship
125
35 Integral equations with Cauahy kernels
131
CHAPTER IV PLANE CONTACT PROBLEMS
139
42 The basic equations of the complex variable theory of elasticity
141
43 Conditions satisfied by the complex potentials
146
44 The stress boundaryvalue problem for the halfplane
151
45 Frictionless contact problems for the halfplane
155
46 Adhesive contact problems for the halfplane
159
47 Contact problems with limiting friction
164
48 Problems involving two or more punches
167
49 Problems involving an infinite number of contact regions
176
410 Contact between two elastic bodies
180
CHAPTER V INTEGRAL TRANSFORMS
192
52 Fourier transforms of functions of one variable
195
53 Relations between Fourier transforms
198
56 Hankel transforms
211
57 Relations betueen Fourier Hankel and Abel transforms
217
58 Applications of the twodimensional Fourier transform
228
CHAPTER VI INTEGRAL EQUATIONS FOR CONTACT PROBLEMS
235
62 Integral equations for the halfplane
236
63 Integral equations for the plane strip
244
64 The solution of some integral equations
253
65 Indentation of a strip resting on a rigid foundation
262
66 Contact with finite friction
269
74 Semiinfinite stiffeners
339
75 Periodically stiffened plates
348
76 Refinements of Melans problems
354
77 Reissners problem and its generalizations
362
CHAPTER VIII PLANE PROBLEMS RELATING TO A CIRCLE
373
82 Complex variable formulation
374
83 Basic functions for circular arcs
387
84 Compression of an elastic cylinder
392
85 Inclusion problems
402
86 Cradling contact problems
419
CHAPTER IX CONTACT PROBLEMS INVOLVING WEDGES AND STRAIGHT EDGES
428
93 The theory of elasticity for a plane wedge
433
94 The application of the Mellin transform to wedge problems
437
95 Stress singularities at a sharp corner
446
CHAPTER X AXISYMMETRIC CONTACT PROBLEMS FOR THE ELASTIC HALFSPACE
455
102 Axisymmetric Hankeltransform solutions for the halfspace
456
103 Some asymmetric problems for the halfspace
471
104 Adhesive problems for the halfspace
479
105 The use of oblate spheroidal coordinates
496
106 Some other integral representations for axisynnetria problems
505
107 Contact problems for the circular annulus
516
CHAPTER XI CONTACT PROBLEMS FOR PLATES AND LAYERS
526
112 Complete contact between infinite plates and foundations
536
113 Complete contact of finite plates with foundations
544
114 Equations for the layer
549
115 Receding contact between circular plates and foundations
558
116 Torsional contact problems
563
117 Receding contact between layers and foundations
569
CHAPTER XII THREEDIMENSIONAL CONTACT PROBLEMS
573
122 Loading over an elliptical region
585
123 The use of ellipsoidal coordinates
594
124 Compliance of elastic bodies in contact
606
125 The inhomogeneous halfspace
615
126 Miscellaneous contact problems
627
JOURNALS CITED IN THE REFERENCES
630
REFERENCES
635
NOTATION
699
INDEX
700
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