Contact Problems in the Classical Theory of Elasticity

Front Cover
Springer Science & Business Media, Jun 30, 1980 - Science - 736 pages
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Selected pages

Contents

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
279
68 Receding contact between a strip and a halfplane
287
69 Further problems concerning a plane strip and a foundation
297
610 The inhomogeneous halfplane
307
611 The method of orthogonal polynomials
314
CHAPTER VII STIFFENED PLATES
318
72 Melans original problems
322
73 Melons problems for stiffeners of finite length
328

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
182
CHAPTER V INTEGRAL TRANSFORMS
194
52 Fourier transforms of functions of one variable
197
53 Relations between Fourier transforms
200
56 Hankel transforms
213
57 Relations betueen Fourier Hankel and Abel transforms
219
58 Applications of the twodimensional Fourier transform
230
CHAPTER VI INTEGRAL EQUATIONS FOR CONTACT PROBLEMS
237
62 Integral equations for the halfplane
238
63 Integral equations for the plane strip
246
64 The solution of some integral equations
255
65 Indentation of a strip resting on a rigid foundation
264
66 Contact with finite friction
271
74 Semiinfinite stiffeners
341
75 Periodically stiffened plates
350
76 Refinements of Melans problems
356
77 Reissners problem and its generalizations
364
CHAPTER VIII PLANE PROBLEMS RELATING TO A CIRCLE
375
82 Complex variable formulation
376
83 Basic functions for circular arcs
389
84 Compression of an elastic cylinder
394
85 Inclusion problems
404
86 Cradling contact problems
421
CHAPTER IX CONTACT PROBLEMS INVOLVING WEDGES AND STRAIGHT EDGES
430
93 The theory of elasticity for a plane wedge
435
94 The application of the Mellin transform to wedge problems
439
95 Stress singularities at a sharp corner
448
CHAPTER X AXISYMMETRIC CONTACT PROBLEMS FOR THE ELASTIC HALFSPACE
457
102 Axisymmetric Hankeltransform solutions for the halfspace
458
103 Some asymmetric problems for the halfspace
473
104 Adhesive problems for the halfspace
481
105 The use of oblate spheroidal coordinates
498
106 Some other integral representations for axisynnetria problems
507
107 Contact problems for the circular annulus
518
CHAPTER XI CONTACT PROBLEMS FOR PLATES AND LAYERS
528
112 Complete contact between infinite plates and foundations
538
113 Complete contact of finite plates with foundations
546
114 Equations for the layer
551
115 Receding contact between circular plates and foundations
560
116 Torsional contact problems
565
117 Receding contact between layers and foundations
571
CHAPTER XII THREEDIMENSIONAL CONTACT PROBLEMS
575
122 Loading over an elliptical region
587
123 The use of ellipsoidal coordinates
596
124 Compliance of elastic bodies in contact
608
125 The inhomogeneous halfspace
617
126 Miscellaneous contact problems
629
JOURNALS CITED IN THE REFERENCES
632
REFERENCES
637
NOTATION
701
INDEX
702
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information