Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research

Applied Mechanics Reviews

Volumn 51, Issue 5, 1998, Pages 343-371

  Guz' A N ^a   Babich, S Yu ^b   Rudnitsky, V B ^c  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

^b KYIV NATIONAL UNIVERSITY OF TRADE AND ECONOMICS   (Ukraine)

^c KHMELNYTSKYI NATIONAL UNIVERSITY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; INTERFACES (MATERIALS); MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; PROBLEM SOLVING; STRAIN; STRESS ANALYSIS;

INITIAL STRESSES;

ELASTICITY;

EID: 0032070826     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3099009     Document Type: Article

References (98)

1. Achenbach JD (1973), Wave Propagation in Elastic Solids, North-Holland Publ, Amsterdam, 427 pp.
2. Achenbach JD and Keshava SP (1967), Free waves in a plate supported by semi-infinite continuum, Trans ASME Ser E J Appl Mech 34(2), 156-162.
3. Achenbach JD, Keshava SP, and Herrmann G (1967), Moving load on a plate resting on an elastic half space, Trans ASME Ser E J Appl Mech 34(4), 183-189.
4. Aleksandrov VM and Arutunyan NKh (1984), Contact problems for prestressed solids, Prikl Mekh 20(3), 9-16 (in Russian).
5. Aleksandrov VM and Brudnyi SR (1982), Two problems with mixed boundary conditions for an incompressible isotropic hyperelastic material, Prikl Math Mekh 46(4), 700-704 (in Russian).
6. Aleksandrov VM and Fillipova LM (1980), Contact problem for a heave half plane, Prikl Mekh 44(3), 535-539 (in Russian).
7. Aleksandrov VM, Kadomtsev IG, and Tsaryuk LB (1984), Axisymmetric contact problems of elastoplastic bodies, Trenie Iznos 5(1), 16-25 (in Russian).
8. Aleksandrov VM and Poroshin VS (1984), Contact problem for a prestressed physically nonlinear elastic layer, hv Akad Nauk SSSR Mekh Tverd Tela (6), 79-85 (in Russian).
9. Aleksandrov VM and Vorotynseva IB (1990), Axisymmetric contact problems for prestressed solids, J Prikl Mekh and Tech Phys (3) 146-153 (in Russian).
10. Anan’ev JV, Kalinchuk W, and Polyakova IV (1983), Excitation of waves by a vibrating punch in a medium with nonuniform initial stresses, Prikl Math Mekh 47(3), 483-489 (in Russian).
11. Babich SYu (1982a), Dynamic contact problems for a half plan with initial stresses, Prikl Math Mekh 18(2), 68-73 (in Russian).
12. Babich SYu (1982b), Axisymmetric contact problems for solids with initial stresses, Dokl Akad Nauk UkrSSR, Ser A Phys Math Tech Sci (6), 32-35 (in Russian).
13. Babich SYu (1984a), Contact problem of elasticity theory for a layer with initial stresses, Prikl Mekh 20(6), 34-40 (in Russian).
14. Babich SYu (1984b), Contact problem for an elastic band with initial stresses, Prikl Mekh 20(12), 34-38 (in Russian).
15. Babich SYu (1985), Axisymmetric contact problem for a layer on an elastic half space with initial stresses, Prikl Mekh 21(11), 32-36 (in Russian).
16. Babich SYu (1986a), Contact problem for a pre-stressed band positioned on an elastic base with initial stresses, Prikl Mekh 22(3), 10-14 (in Russian).
17. Babich SYu (1986b), Effect of initial stresses on the distribution of contact pressure in a pre-stressed half plane with allowance for friction forces, Prikl Mekh 22(8), 163-166 (in Russian).
18. Babich SYu (1987), Investigation of a dynamic contact problem for a halfplane with initial stresses, Prikl Mekh 23(4), 39-43 (in Russian).
19. Babich SYu, Glukhov YuP, and Guz’ AN (1986), Dynamics of a laminated compressible half space under the effect of moving load, Prikl Mekh 22(9), 8-15 (in Russian).
20. Babich SYu, Glukhov YuP, and Guz’ AN (1988), Solution of a problem of the effect of moving load on a two-layer space with initial stresses, Prikl Mekh 24(8), 55-60 (in Russian).
21. Babich SYu, Glukhov YuP, and Chernyshenko II (1990), Contact problem for the pre-stressed half-plane in the case of stiff punch system, taking into account the frictional forces, Prikl Mekh 26(2), 93-98 (in Russian).
22. Babich SYu, Glukhov YuP, and Kindrachuk MV (1990), Contact problem for the pre-stressed layer from compressible material, Prikl Mekh 26(6), 118-121 (in Russian).
23. Babich SYu and Guz’ AN (1981a), Complex potentials of a planar dynamic problem of compressible elastic solids with initial stresses, Prikl Mekh 17(7), 75-83 (in Russian).
24. Babich SYu and Guz’ AN (1981b), Spatial contact problems of an elastic half space with initial stresses, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (9), 35-39, (in Russian).
25. Babich SYu and Guz’ AN (1981c), Complex potentials of planar dynamic problem for elastic incompressible solids with initial stresses, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (11), 41-45, (in Russian).
26. Babich SYu and Guz’ AN (1984), Spatial contact problems for an elastic half space initial stresses, Prikl Mekh 20(5), 3-12 (in Russian).
27. Babich SYu and Guz’ AN (1985), General spatian static contact problems for a pre-stressed elastic half space, Prikl Math Mekh 49(3), 438-444 (in Russian).
28. Babich SYu, Guz’ AN, and Makhort PG (1974), Effect of initial stresses on the velocity of propagation of surface cracks in a cylinder, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (3), 243-245, (in Russian).
29. Babich SYu, Guz’ AN, and Rudnitsky VB (1989), Contact problems for elastic bodies with initial stresses (rigid punches), Prikl Mekh 25(8), 318 (in Russian).
30. Babich SYu, Guz’ AN, and Rudnitsky VB (1991), Contact problems for elastic bodies with initial stresses (elastic punches)(survey), Prikl Mekh 27(9), 3-28 (in Russian).
31. Babich SYu, Guz’ AN, and Zhuk AP (1979), Elastic waves in solids with initial stresses, Prikl Mekh 15(4), 3-23 (in Russian).
32. Babich SYu and Rudnitsky VB (1989), Several planar contact problem for elastic solids with initial stresses, Prikl Mekh 25(1), 93-100 (in Russian).
33. Beatty MF and Usmani SA (1975), Indentation of a highly elastic half space, Quart J Mech Math 28(1), 47-69.
34. Biot MA (1965), Mechanics of Incremental Deformations, Wiley, New York, 506 pp.
35. Borodich, FM (1990), Contact problems of Hertz for the elastic anisotropic half space with initial stresses, Prikl Mekh 26(2), 24-31 (in Russian).
36. Development of the Theory of Contact Problems in the USSR (1976), LA Galin (ed), Nauka, Moscow, 494 pp (in Russian).
37. Dhaliwal RS, Ranjit S, and Singh BM (1978), Axisymmetric Boussinesq problem of an initially stressed neo-Hookean half space for a punch of arbitrary profile, Int J Eng Sci 16(6), 379-385.
38. Dhaliwal RS, Ranjit S, Rokne JG, and Singh BM (1980), Axisymmetric contact and crack problems for an initially stressed neo-Hookean elastic layer, Int J Eng Sci 18(6), 169-179.
39. Filippova LM (1973), Flat contact problem for a pre-stressed elastic solid, Izv Akad Nauk SSSR Mekh Tverd Tela (3), 143-146 (in Russian).
40. Filippova LM (1978), Spatial contact problem for a pre-stressed elastic solids, Prikl Math Mekh 42(6), 1080-1084 (in Russian).
41. Filippova LM and Chebakov MI (1988), Contact problem for a pre-stressed for a pre-stressed finite cylinder, Izv Akad Nauk SSSR Mekh Tverd Tela (2), 62-69 (in Russian).
42. Flavin JN (1963) Surface waves in pre-stressed Mooney material, Quart J Mech Math 16(4), 441-449.
43. Galin, LA (1980), Contact Problems of the Elasticity and Viscoelasticity Theory, Nauka, Moscow, 303 p (in Russian).
44. Glukhov YuP (1986), Determination of critical stresses of movement of load on a plate positioned on an incompressible pre-stressed half space, Prikl Mekh 22(10), 57-62 (in Russian).
45. Green AE and Zema W (1968), Theoretical Elasticity, Oxford, 154 pp.
46. Grigorenko PP and Rudnitsky VB (1990), Layer with initial stresses under the section of two punches, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (9), 35-39 (in Russian).
47. Grigoryan EKh and Ovakimyan AS (1989), Contact problem for half-planes with initial stresses, connected by a semi-infinite inclusion, Izv Akad Nauk Arm SSR, Mech (3), 14-20 (in Russian).
48. Guz’ AN (1971), Stability of Three-Dimensional Bodies, Naukova Dumka, Kiev, 276 pp (in Russian).
49. Guz’ AN (1973), Stability of Elastic Bodies with Finite Strains, Naukova Dumka, Kiev 270 pp (in Russian).
50. Guz’ AN (1977), Principles of the Theory of Stability of Mine Workings, Naukova Dumka, Kiev 204 pp (in Russian).
51. Guz’ AN (1979), Stability of Elastic Bodies in Compression, Naukova Dumka, Kiev 144 pp (in Russian).
52. Guz’ AN (1980a), Complex potentials of a planar linearized problem of elasticity theory: Compressible solids, Prikl Mekh 16(5), 72-83 (in Russian).
53. Guz’ AN (1980b), Complex potentials of a planar linearized problem of elasticity theory: Incompressible solids, Prikl Mekh 16(6), 72-83 (in Russian).
54. Guz’ AN (1980c), Contact problems for elastic compressible bodies with initial stresses, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci, (6), 48-52 (in Russian).
55. Guz’ AN (1980d), Theory of contact problems for elastic incompressible solids with initial stresses, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci, (7), 42-45 (in Russian).
56. Guz’ AN (1980e), Contact problems for elasticity theory for a half plane with initial stresses, Prikl Mekh 16(8), 45-58 (in Russian).
57. Guz’ AN (1980), Complex potentials of a planar linearized problems for elasticity theory, Prikl Mekh 16(9), 83-97 (in Russian).
58. Guz’ AN (1983), Mechanics of Brittle Fracture of Materials with Initial Stresses, Naukova Dumka, Kiev, 296 pp (in Russian).
59. Guz’ AN (1986a), Elastic Waves in Solids with Initial Stresses: General Problems, Naukova Dumka, Kiev 1, 376 pp (in Russian).
60. Guz’ AN (1986b), Elastic Waves in Solids with Initial Stresses: Propagation Relationships, Naukova Dumka, Kiev, 536 pp (in Russian).
61. Guz’ AN (1990), Mechanics Fracture of Composite Materials in Compression, Naukova Dumka, Kiev, 632 pp (in Russian).
62. Guz’ AN and Babich SYu (1981), Planar dynamic problems for elastic solids with initial stresses. Dokl Nauk UkrSSR 261(2), 313-316.(in Russian).
63. Guz’ AN and Babich SYu (1982), Planar dynamic problems for elastic incompressible solids with initial stresses, Prikl Mat Mekh 46(2), 263-271 (in Russian).
64. Guz’ AN and Babich SYu(1983), Axisymmetric contact problem for an elastic layer with initial stresses, Dokl Akad Nauk UkrSSR 273(6), 1329-1332 (in Russian).
65. Guz’ AN and Rudnitsky VB (1984), Contact problem on the pressure of elastic punch upon the elastic half-space with initial stresses, Prikl Mekh 20(8), 3-11 (in Russian).
66. Guz’ AN and Rudnitsky VB (1985a), Contact problems for the half-plane with initial stresses, reinforced by elastic straps, Prikl Mekh 20(3), 6878 (in Russian).
67. Guz’ AN and Rudnitsky VB (1985b), Periodic contact problem for the halfplane with initial stresses, reinforced by elastic straps, Dokl Akad Nauk SSSR 280(4),831-833 (in Russian).
68. Guz’ AN and Rudnitsky VB (1982), Contact interaction of an elastic punch and a pre-stressed layer, Mech TeorStos 25(3), 323-339 (in Russian).
69. Harding JW and Sneddon JN (1945), Elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch, Proc Cambridge Philos Soc 41(1), 16-26.
70. Kalinchuk VV, Lusenko NV, and Polyakova IB (1989), Special features of interaction of the vibrating punch with the inhomogeneous heavy foundations, Prikl Math Mekh 53(2), 301-308 (in Russian).
71. Kalinchuk W and Polyakova IB (1980), Excitation of waves in a layer with initial stresses, Prikl Math Mekh 44(2), 320-326 (in Russian).
72. Kalinchuk VV and Polyakova IB (1981), Excitation of a pre-stressed cylinder, Prikl Math Mekh 45(2), 384-389 (in Russian).
73. Kalinchuk VV and Polyakova IB (1982), Vibration of a punch on the surface of a pre-stressed half-space, Prikl Mekh 18(6), 22-27 (in Russian).
74. Kassir MK and Sih GC (1985), Mechanics of Fracture: Three dimensional Crack Problems, Noordhoff Int Publ, Leyden, Netherlands 2, 252 pp.
75. Kurashige M (1969), Circular crack problem for initially stressed neo-Hookean solid, ZAMM 49(8), 671-678.
76. Lebedev NN and Ufland YaS (1958), Axisymmetric contact problem for the elastic layer, Prikl Math Mekh 22(3), 320-326 (in Russian).
77. Lekhnitsky SG (1950,1977) in Russian, 1963 (in English), Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco CA, Nauka, Moscow, 416 pp.
78. Mindlin, RD (1951), Influence of rotatory inertia and on flexural motions of isotropic elastic plates, Trans ASME Ser E J Mech 18(1), 31-38.
79. Muskhelishvili NI, (1953-in English, 1966-in Russian), Basic problems of the mathematical theory of elasticity, Nordhoff Ltd, Groningen, Nauka, Moscow, 708 pp.
80. Poroshin VS (1986), Penetration of a punch into a pre-stressed physically nonlinear elastic layer, Izv Akad Nauk ArmSSR Mekh 39(2), 24-30 (in Russian).
81. Rudnitsky VB (1985a), Contact interaction of two half-planes with initial stresses of elastic punch: Compressible bodies, Prikl Mekh 21(2), 55-62 (in Russian).
82. Rudnitsky VB (1985b), Plane contact problem for the elastic rectangular punch and the half-planes with initial stresses, Prikl Mekh 21(10), 69-74 (in Russian).
83. Rudnitsky VB (1986), Contact interaction of the half-space with initial stresses and the elastic finite cylinder, Prikl Mekh 22(4), 44-51 (in Russian).
84. Rudnitsky VB (1987a), Solution of the contact problem for the prestressed layer and the punch, Prikl Mekh 23(3), 14-21, (in Russian).
85. Rudnitsky VB (1987b), Axisymmetric three-dimensional contact problem for the elastic half-space with initial stresses, taking into account the adhesion, Prikl Mekh 23(4), 112-115, (in Russian).
86. Rudnitsky VB (1987c), Influence of the initial stresses in the layer on the contact pressure at interaction with the cylindrical punch, Prikl Mekh 23(8), 11-19 (in Russian).
87. Rudnitsky VB (1987d), Contact interaction of the pre-stressed layer with two elastic punches, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (2), 56-61.
88. Rudnitsky VB (1987e), Contact interaction of two pre-stressed half-spaces with the elastic cylindrical punch, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (3), 38-41 (in Russian).
89. Rudnitsky VB (1989a), Influence of the initial stresses in high-elastic materials on the elastic contact with cylindrical punch, Prikl Mekh 25(3), 1420 (in Russian).
90. Rudnitcky VB (1989b), Contact problems for pre-stressed plate reinforced by elastic straps, Prikl Mekh 25(4), 123-126 (in Russian).
91. Rudnitsky VB and Shelestovckaya MYa (1990), Contact interaction of the elastic annular punch with pre-stresses sphere, Dokl Akad Nauk UkrSSR Ser A: Phys Math Tech Sci (6), 54-57 (in Russian).
92. Selvadural APS (1980), Penny-shaped crack problem for finitely deformed incompressible elastic solid, IntJ Fract 16, 327-341.
93. Skuchik E (1971), Simple and Complicated Vibrational Systems, Mir, Moscow, 557 pp (in Russian).
94. Sneddon JN (1952), Stresses produced by a pulse of pressure moving along the surface of a semi-infinitive body, Rendiconti di Palermo 1(7), 5762.
95. Sneddon JN (1955), Fourier Transformations, Inostrannaya literatura, Moscow, 669 pp (in Russian).
96. Vorotintseva IV (1986), Planar contact problems for a physically nonlinear pre-stressed elastic medium, Prikl Math Mekh 50(4), 657-662 (in Russian).
97. Vorotintseva IV and Kovalenko EV (1986), Axisymmetric contact problem for a pre-stressed physically nonlinear half-space and layer of finite depth, In: Analytical and Numerical Methods of Solving Boundary Values in Plasticity and Viscoelasticity, Perm, 33-38 (in Russian).
98. Zelentsov VB and Filippova LM (1989) Contact problems for prestressed half-plane and strip, Izv Akad Nauk SSSR Mech Tverd Tela (2), 73-76 (in Russian).