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Toward the solution of the problem of the action of a live load on a two- layer half-space with initial stresses. (English. Russian original) Zbl 0711.73022

Sov. Appl. Mech. 24, No. 8, 775-780 (1988); translation from Prikl. Mekh., Kiev 24, No. 8, 55-60 (1988).
We use the method of complex potentials to solve problems for compressible and incompressible bodies with an elastic potential of arbitrary form for the case of unequal roots. It is shown that the results obtained by the complex potentials method agree with the results found by the Fourier method. As examples, we examine the cases of a compressible material with an elastic potential of harmonic type and an incompressible material with a potential of Bartenev-Khazanovich type. Varying the initial stresses, load velocities, and contact conditions, we examined the effect of allowance for the rotational inertia of the cross section of a plate on the values of characteristics of the stress state of a two-layer half-space.

MSC:

74G70 Stress concentrations, singularities in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B10 Linear elasticity with initial stresses
74K20 Plates
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References:

[1] S. Yu. Babich, Yu. P. Glukhov, and A. N. Guz’, ?Dynamics of a layered compressed prestressed half-space subjected to a live load,? Prikl. Mekh.,22, No. 9, 8?15 (1986).
[2] S. Yu. Babich and A. N. Guz’, ?Complex potentials of a plane dynamic problem for compressible elastic bodies with initial stresses,? Prikl. Mekh.,17, No. 7, 75?83 (1981).
[3] S. Yu. Babich and A. N. Guz, ?Complex potentials of plane dynamic problems for elastic incompressible bodies with initial stresses,? Dokl. Akad. Nauk Ukr. RSR Ser. A, No. 11, 35?38 (1981). · Zbl 0468.73005
[4] Yu. P. Glukhov, ?Reaction of a layered compressed half-space with initial stresses to a live load,? Transactions of the XI Scientific Conference of Young Scientists, Institute of Mechanics of the Academy of Sciences, Ukrainian SSR (Kiilov, May 27?30, 1986, Vol. 1, pp. 29?34. Submitted to VINITI 28.07.86; No. 5507-B86.
[5] Yu. P. Glukhov, ?Determination of the critical velocities of a load on a plate lying on an incompressible prestrained half-space,? Prikl. Mekh.,22, No. 10, 57?62 (1986).
[6] A. N. Guz’, Mechanics of Brittle Fracture of Materials with Initial Stresses [in Russian], Naukova Dumka, Kiev (1983). · Zbl 0547.73085
[7] N. I. Muskhelishvili, Some Fundamental Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966). · Zbl 0151.36201
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