Journal of Mathematical Sciences

, Volume 90, Issue 2, pp 1972–1977 | Cite as

The linearized equations of propagation of elastic perturbations in a body with free strains

  • V. A. Osadchuk
  • I. B. Prokopovich
  • O. Z. Kravchishin


For a stressed isotropic Murnaghan body with free (“intrinsic”) strains we decluce the equations of propagation of small elastic perturbations in terms of the free strain tensors and the gradient of the displacement. The latter characterizes the total strain, that is, the nonlinear superposition of the free and elastic strains. We write out separately the equations for the case of a spherical free strain tensor.


Residual Stress Elastic Strain Current Configuration Isotropic Body Elastic Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatire Cited

  1. 1.
    A. N. Guz',Elastic Waves in Bodies with Initial Stresses [in Russian], Vol. 1: General Questions, Naukova Dumka, Kiev (1986).Google Scholar
  2. 2.
    A. N. Guz', F. G. Makhort, and O. I. Gushcha,Introduction to Acoustoelasticity [in Russian], Naukova Dumka, Kiev (1977).Google Scholar
  3. 3.
    A. I. Lur'e,The Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).Google Scholar
  4. 4.
    V. A. Osadchuk, R. M. Kushnir, I. B. Prokopovich, and V. F. Chekurin, “Solvable equations of mechanics of bodies with intrinsic stresses,”Dop. Nats. Akad. Nauk Ukr., No. 2, 60–64 (1993).MATHGoogle Scholar
  5. 5.
    Ya. S. Podstrigach, V. A. Osadchuk, and A. M. Margolin,Residual Stresses Extended Durability, and Reliability of Glass Structures [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
  6. 6.
    I. B. Prokopovich, “Nonlinear description of intrinsic stresses caused by free strains,”Dop. Nats. Akad. Nauk Ukr., No. 12, 49–51 (1995).Google Scholar
  7. 7.
    V. A. Osadchuk, R. M. Kushnir, and I. B. Prockopovich, “On the optimal design of polarisation-maintaining optical fibers,”Pat. Rec. Im. Anal.,4, No. 3, 367–370 (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. A. Osadchuk
  • I. B. Prokopovich
  • O. Z. Kravchishin

There are no affiliations available

Personalised recommendations