Abstract
Complex potentials in common form for compressible and incompressible elastic bodies are used to formulate and solve the problem of stationary motion of a prestressed two-layer elastic half-space under a moving surface load. The results presented are similar to those obtained earlier using the Fourier transform
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Yu. Babich, Yu. P. Glukhov, and A. N. Guz, “Dynamics of a prestressed incompressible layered half-space under moving load,” Int. Appl. Mech., 44, No. 3, 268–285 (2008).
S. Yu. Babich, Yu. P. Glukhov, and A. N. Guz, “A dynamic problem for a prestressed compressible layered half-space,” Int. Appl. Mech., 44, No. 4, 388–405 (2008).
S. Yu. Babich and A. N. Guz, “Complex potentials of the plane dynamical problem for compressible elastic bodies with initial stresses,” Int. Appl. Mech., 17, No. 7, 662–668 (1981).
S. Yu. Babich and A. N. Guz, “Complex potentials in a plane dynamic problem for elastic incompressible prestressed bodies,” Dokl. AN USSR, Ser. A, No. 11, 35–38 (1981).
A. N. Guz, Mechanics of Brittle Fracture of Prestressed Materials [in Russian], Naukova Dumka, Kyiv (1983).
S. G. Lekhnitskii, Anisotropic Elasticity Theory [in Russian], Nauka, Moscow (1977).
N. I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
J. D. Achenbach and S. P. Keshawa, “Free waves in a plate supported by a semi-infinite continuum,” Trans. ASME, Ser. E, J. Appl. Mech., 34, No. 2, 156–162 (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. Rudnitskii, “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 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 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. Rudnitskii, “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).
A. V. Yarovaya, “Thermoelastic bending of a sandwich plate on a deformable foundation,” Int. Appl. Mech., 42, No. 2, 206–213 (2006).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 3–15, May 2008.
Rights and permissions
About this article
Cite this article
Babich, S.Y., Glukhov, Y.P. & Guz, A.N. Using complex potentials to determine the reaction of a prestressed two-layer elastic half-space to a moving load. Int Appl Mech 44, 481–492 (2008). https://doi.org/10.1007/s10778-008-0060-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-008-0060-z