Advertisement

Strength of Materials

, Volume 5, Issue 4, pp 447–452 | Cite as

Use of the method of random walk to solve problems of the theory of elasticity

  • P. P. Voroshko
  • A. L. Kvitka
  • A. S. Tsybenko
Scientific and Technical Section
  • 19 Downloads

Conclusions

  1. 1.

    The results presented here show that the method described can be used to solve the second fundamental problem of the theory of elasticity with an error, in displacements up to 5%, and in stresses up to 10%.

     
  2. 2.

    The effective time of solution together with an estimate of the variance\(\bar D\left| {\bar \psi } \right| \leqslant 0.05\) ≤ 0.05 for a single point varies from 1.5 to 2 min.

     
  3. 3.

    When the number of walks (N > 30,000) increases, the accuracy of the method just described does not increase, owing to the unstable operation of the random number generator (RNDM).

     

Keywords

Random Number Random Walk Single Point Number Generator Fundamental Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    I. A. Bazilevich and A. L. Sinyavskii, “Solution of harmonic problems by the method of random walks along a grid,” in: Strength of Materials and Theory of Structures [in Russian], No. 15, Budivel'nik, Kiev (1971).Google Scholar
  2. 2.
    N. P. Buslenko and Yu. A. Shreider, The Method of Statistical Tests (Monte Carlo) and Its Realization on Digital Computers [in Russian], Gosfizmatizdat, Moscow (1961).Google Scholar
  3. 3.
    V. S. Gladkii, “Probabilistic models of solving partial differential equations,” in; Marine Hydrophysical Investigations [in Russian], No. 4 (46), Izd. MGI AN UkrSSR, Sevastopol' (1969).Google Scholar
  4. 4.
    E. B. Dynkin and A. A. Yushkevich, Theorems and Problems on Markov Processes [in Russian], Nauka, Sevastopol' (1969).Google Scholar
  5. 5.
    I. G. Dyad'kin and V. N. Starkov, “On a possibility of economy of machine time when solving the Laplace equationbythe Monte Carlo method,” Vychislitel'naya Matematika i Matematicheskaya Fizika,No. 5 (1965).Google Scholar
  6. 6.
    B. S, Elenov and G. A. Mikhailov, “On solving the Dirichlet problem for the equation Δu-cu =-q by simulating walk along spheres,” Vychislitel'naya Matematika i Matematicheskaya Fizika, No. 3 (1969).Google Scholar
  7. 7.
    A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).Google Scholar
  8. 8.
    N. I. Muskhelishvili, Certain Basic Problems of the Mathematical Theory of Elasticity [in Russian], Izd. AN SSSR, Moscow (1954).Google Scholar
  9. 9.
    I. A. Bazilevich, “Normals to surfaces of the second order and lines of their intersection,” in: Problems of Applied Geometry. Report of the 30th Scientific-Technical Conference of the Kiev Engineering and Building Institute [in Ukrainian], Vid. KIBI, Kiev (1969).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • P. P. Voroshko
    • 1
  • A. L. Kvitka
    • 1
  • A. S. Tsybenko
    • 1
  1. 1.Institute of the Strength of MaterialsAcademy of Sciences of the Ukrainian SSRKiev

Personalised recommendations