Contact Problems in the Classical Theory of ElasticitySpringer 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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Kluczowe wyrazy i wyrażenia
adhesive analysis applied approximate axisymmetric beam body forces boundary conditions boundary value Cauchy Principal Value circular complex potentials considered contact pressure contact problems contact region contact stress coordinates corresponding cylinder defined denotes derived Dundurs elastic bodies elastic constants elastic foundation elastic half-space elastic layer elliptic equations governing equilibrium Erdogan Example finite friction function given gives Gladwell Hankel transforms Hölder condition holomorphic indenter infinite infinity isotropic Keer load Melan's Mellin transform Mossakovskii Muskhelishvili nonhomogeneous normal displacement numerical obtained plane strain plane stress plate polynomial Popov radius relation rigid punch Russian satisfies semi-infinite shear stress Show shown in Figure singularity Sneddon solved stiffener stress distribution strip surface symmetric theorem theory of elasticity upper half-plane V.M. Aleksandrov wedge zero θο ди дх Эт Эт

