Skip to main content
SpringerLink
Log in

On the Reconstruction of the Characteristics of the Plane Initial Stress State

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract—

A model of planar oscillations of a plane region in the presence of prestress fields is formulated. Various formulations of two-dimensional inverse problems on the restoration of the preliminary stress state are presented. Methods and algorithms for solving the stated inverse problems are proposed and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. E. Salvati and A. M. Korsunsky, “A simplified FEM eigenstrain residual stress reconstruction for surface treatments in arbitrary 3D geometries,” Int. J. Mech. Sci. 138–139, 457–466 (2018).

    Article  Google Scholar 

  2. H. Ling, Ch. Yang, Sh. Feng, and H. Lu, Predictive model of grinding residual stress for linear guideway considering straightening history,” Int. J. Mech. Sci. 176, 105536 (2020).

    Article  Google Scholar 

  3. S. Suresh and A. E. Giannakopoulos, “A new method for estimating residual stresses by instrumented sharp indentation,” Acta Mater. 46 (16), 5755–5767 (1998).

    Article  ADS  Google Scholar 

  4. T.- H. Pham and S.- E. Kim, “Determination of equi-biaxial residual stress and plastic properties in structural steel using instrumented indentation,” Mater Sci Eng A. 688, 352–363 (2017).

    Article  Google Scholar 

  5. R. Moharrami and M. Sanayei, “Numerical study of the effect of yield strain and stress ratio on the measurement accuracy of biaxial residual stress in steels using indentation,” J. Mater. Res. Technol. 9 (3), 3950–3957 (2020).

    Article  Google Scholar 

  6. D. Deng and S. Kiyoshima, “Numerical simulation of welding temperature field, residual stress and deformation induced by electro slag welding,” Comp. Mater. Sci. 62, 23–34 (2012).

    Article  Google Scholar 

  7. A. Yonezu, R. Kusano, T. Hiyoshi, and X. Chen, “A method to estimate residual stress in austenitic stainless steel using a microindentation test,” J. Mater. Eng. Perform. 24, 362–72 (2015).

    Article  Google Scholar 

  8. F. Wang, K. Mao, and B. Li, “Prediction of residual stress fields from surface stress measurements,” Int. J. Mech. Sci. 140, 68–82 (2018).

    Article  Google Scholar 

  9. C. A. Truesdell, A First Course in Rational Continuum Mechanics (The John Hopkins Uni., Baltimore, Maryland, 1972).

    Google Scholar 

  10. A. Hoger, “On the determination of residual stress in an elastic body,” J. Elast. 16, 303–324 (1986).

    Article  MathSciNet  Google Scholar 

  11. R.L. Robertson, “Determining residual stress from boundary. Measurements: A linearized approach,” J. Elast. 52, 63–73 (1998).

    Article  MathSciNet  Google Scholar 

  12. A. N. Guz, F. G. Makhort, and O. I. Gushcha, Introduction to Acoustoelasticity (Naukova Dumka, Kiev, 1977) [in Russian].

    Google Scholar 

  13. R. D. Nedin, V. V. Dudarev, and A. O. Vatulyan, “Some aspects of modeling and identification of inhomogeneous residual stress,” Eng. Struct. 151, 391–405 (2017).

    Article  Google Scholar 

  14. R. D. Nedin and A. O. Vatulyan, “Inverse problem of non-homogeneous residual stress identification in thin plates,” Int. J. Solids. Struct. 50, 2107–2114 (2013).

    Article  Google Scholar 

  15. R. D. Nedin and A. O. Vatulyan, “Concerning one approach to the reconstruction of heterogeneous residual stress in plate,” ZAMM 94 (1–2), 142–149 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  16. V. V. Dudarev, R. D. Nedin, and A. O. Vatulyan, “Nondestructive identification of inhomogeneous residual stress state in deformable bodies on the basis of the acoustic sounding method,” Adv. Mater. Res. 996, 409–414 (2014).

    Article  Google Scholar 

  17. A. O. Vatulyan, V. V. Dudarev, and R. D. Nedin, Residual Stress: Modelling and Identification (Izd.YuFU, Rostov-on-Don, 2014) [in Russian].

  18. R. D. Nedin, A. O. Vatulyan, and I. V. Bogachev, “Direct and inverse problems for prestressed functionally graded plates in the framework of the Timoshenko model,” Math. Meth. Appl. Sci. 41 (4), 1600–1618 (2018).

    Article  MathSciNet  Google Scholar 

  19. A. Vatulyan, R. Nedin, and V. Dudarev, “Modelling and analysis of prestress field in a thin plate with a nonuniform coating,” IOP Conf. Series: J. Phys.: Conf. Series. 1203, 012027 (2019).

  20. A. O. Vatulyan and R. D. Nedin, “On the reconstruction of inhomogeneous residual stress,” Vestn. St-Peterburg. Univ. Ser. 1. Mat. Mekh. Astr., No 1, 38–44 (2011).

  21. R. D. Nedin, “Modeling and frequency analysis of prestressed functionally graded plates with holes,” Vychisl. Mekh. Sploshn. Sred 12 (2), 192–201 (2019).

    Google Scholar 

  22. A. O. Vatulyan and L. S. Gukasyan, “On Cauchy problem for first-order partial differential equation and its applications in inversion theory,” Vestn. Don. Gos. Tekh. Univ. 12 (7), 11–20 (2012).

    Google Scholar 

  23. A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  24. N. M. Gunter, Integration of PDEs of the First Order (ONTI, Leningrad, 1934) [in Russian].

    Google Scholar 

Download references

Funding

The research was carried out with the financial support of the Russian Science Foundation (grant no. 18-71-10045).

Author information

Authors and Affiliations

  1. Southern Federal University, 344090, Rostov-on-Don, Russia

    A. O. Vatulyan & R. D. Nedin

  2. Southern Mathematical Institute—the Affiliate of Vladikavkaz Scientific Centre of Russian Academy of Sciences, 362025, Vladikavkaz, Russia

    A. O. Vatulyan

Authors
  1. A. O. Vatulyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. D. Nedin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. O. Vatulyan or R. D. Nedin.

Additional information

Translated by M. Katuev

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vatulyan, A.O., Nedin, R.D. On the Reconstruction of the Characteristics of the Plane Initial Stress State. Mech. Solids 55, 624–632 (2020). https://doi.org/10.3103/S0025654420050143

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654420050143

Keywords:

Search

Navigation