Abstract
The paper addresses a plane problem: a concentrated force acts on a plate resting on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is assumed to be incompressible and isotropic in the natural state. The elastic potential is given in general form and is only specified for numerical purposes. The dependence of the critical velocity of the load and the stress-strain state on the prestresses is analyzed for different ratios between the stiffnesses of the layer and half-space and different contact conditions. The calculations are carried out for a half-space with Bartenev-Khazanovich potential
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A. N. Guz, Stability of Elastic Bodies under Finite Strains [in Russian], Naukova Dumka, Kyiv (1973).
A. N. Guz, Mechanics of Brittle Fracture of Prestressed Materials [in Russian], Naukova Dumka, Kyiv (1983).
I. O. Osipov, “Propagation of elastic waves in an anisotropic medium from a point source: A plane problem,” Prikl. Mat. Mekh., 33, No. 3, 543–555 (1969).
J. D. Achenbach, S. P. Keshawa, and G. Herrmann, “Moving load on a plate resting on an elastic half space,” Trans. ASME, Ser. E, J. Appl. Mech., 34, No. 4, 183–189 (1967).
S. Yu. Babich, A. N. Guz, and V. B. Rudnitsky, “Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research,” Appl. Mech. Rev., 51, No. 5, 343–371 (1998).
S. Yu. Babich, A. N. Guz, and V. B. Rudnitsky, “Contact problems for prestressed elastic bodies and rigid and elastic punches,” Int. Appl. Mech., 40, No. 7, 744–765 (2004).
A. N. Guz, “Constructing the three-dimensional theory of stability of deformable bodies,” Int. Appl. Mech., 37, No. 1, 1–37 (2001).
A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23–59 (2002).
A. N. Guz, “Establishing the fundamentals of the theory of stability of mine workings,” Int. Appl. Mech., 39, No. 1, 20–48 (2003).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 1. Problem statement and general relationships,” Int. Appl. Mech., 34, No. 12, 1175–1186 (1998).
A. N. Guz, “Dynamic problems of the mechanics of brittle fracture of materials with initial stresses for moving cracks. 2. Cracks of normal separation (Mode I),” Int. Appl. Mech., 35, No. 1, 1–12 (1999).
A. N. Guz, “Dynamic problems of the mechanics of brittle fracture of materials with initial stresses for moving cracks. 3. Transverse-shear (mode II) and longitudinal-shear (mode III) cracks,” Int. Appl. Mech., 35, No. 2, 109–119 (1999).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 4. Wedge problems,” Int. Appl. Mech., 35, No. 3, 225–232 (1999).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 1. Problem formulation and basic relations,” Int. Appl. Mech., 38, No. 4, 423–431 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 2. Exact solution. The case of unequal roots,” Int. Appl. Mech., 38, No. 5, 548–555 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 3. Exact solution. The case of equal roots,” Int. Appl. Mech., 38, No. 6, 693–700 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 4. Exact solution. The combined case of unequal and equal roots,” Int. Appl. Mech., 38, No. 7, 806–814 (2002).
A. N. Guz and I. A. Guz, “Mixed plane problems in linearized solid mechanics: Exact solutions,” Int. Appl. Mech., 40, No. 1, 1–29 (2004).
A. N. Guz and F. G. Makhort, “The physical fundamentals of the ultrasonic nondesrtuctive stress analysis of solids,” Int. Appl. Mech., 36, No. 9, 1119–1149 (2000).
A. N. Guz and V. B. Rudnitsky, “Contact interaction of an elastic punch and an elastic half-space with initial (residual) stresses,” Int. Appl. Mech., 43, No. 12, 1325–1335 (2007).
Yu. V. Skosarenko, “Natural vibrations of a cylindrical shell reinforced with rectangular plates,” Int. Appl. Mech., 42, No. 3, 325–330 (2006).
I. L. Solov’ev, “Rotation of rigid and elastic cylindrical shells elastically coupled with a platform,” Int. Appl. Mech., 42, No. 7, 818–824 (2006).
J. P. Wright and M. L. Baron, “Exponentially decaying pressure pulse moving with contact velocity on the surface of a layered elastic material (superseismic half space),” Trans. ASME, Ser. E, J. Appl. Mech., 37, No. 1, 148–159 (1970).
A. V. Yarovaya, “Thermoelastic bending of a sandwich plate on a deformable foundation,” Int. Appl. Mech., 42, No. 2, 206–213 (2006).
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 36–54, March 2008.
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Babich, S.Y., Glukhov, Y.P. & Guz, A.N. Dynamics of a prestressed incompressible layered half-space under moving load. Int Appl Mech 44, 268–285 (2008). https://doi.org/10.1007/s10778-008-0043-0
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DOI: https://doi.org/10.1007/s10778-008-0043-0