Determination of stress concentration near the holes under dynamic loadings

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Authors:


O.Maksymovych, orcid.org/0000-0002-2892-7735, University of Technology and Life Science, Bydgoszcz, the Republic of Poland, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

T.Solyar, orcid.org/0000-0003-3826-8881, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

A.Sudakov, orcid.org/0000-0003-2881-2855, Dnipro University of Technology, Dnipro, Ukraine; Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

I.Nazar, orcid.org/0000-0003-2592-3592, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

M.Polishchuk, orcid.org/0000-0002-1218-5925, Lutsk National Technical University, Lutsk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


повний текст / full article



Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2021, (3): 019 - 024

https://doi.org/10.33271/nvngu/2021-3/019



Abstract:



Purpose.
To develop an approach for determining the stress state of plate structural elements with holes under dynamic loads with controlled accuracy.


Methodology.
The study was carried out on the basis of the Laplace transform and the method of integral equations.


Findings.
An approach to determining the dynamic stresses at the holes in the plates is proposed, which includes: the Laplace transform in the time coordinate; a numerical method for determining transformants of displacements and stresses based on the method of integral equations; finding originals on the basis of Prudnikovs formula adapted to dynamic problems of elasticity theory. The problem of determining the Laplace images for displacements is reduced to solving singular integral equations. Integral equations were solved numerically based on the approaches developed in the boundary element method. To find displacements and stresses, the Laplace transform inversion formulas proposed by Prudnikov are adapted to dynamic problems. The study on dynamic stresses at holes of various shapes was carried out.


Originality.
A new approach to the regularization of the Prudnikov formula for inverting the Laplace transform as applied to dynamic problems of the theory of elasticity has been developed. For its implementation: convergence of Fourier series based on pre-set stresses at the initial time is improved; the remainder is taken into account in the conversion formula.


Practical value.
A method has been developed for calculating the stress concentration at holes of arbitrary shape in lamellar structural elements under dynamic loads. The proposed approach makes it possible to determine stresses with controlled accuracy. The studies performed at circular and polygonal holes with rounded tops can be used in strength calculations for dynamically loaded plates. The influence of Poissons ratio on the concentration of dynamic stresses is analyzed.



Keywords:
concentration of dynamic stresses, method of boundary integral equations, Laplace transforms, inversion formulas

References.


1. Brebbia, C.A., & Walker, S. (2016).Boundary element techniques in engineering. Elsevier. ISBN: 9781483102566.

2. Sayas, F.J. (2016).Retarded potentials and time domain boundary integral equations: A road map. Springer. ISBN: 978-3-319-26645-9.

3. Costabel, M., & Sayas, F.J. (2017). Time-dependent problems with the boundary integral equation method. In Encyclopedia of Computational Mechanics (2nd ed., pp. 1-24). https://doi.org/10.1002/9781119176817.ecm2022.

4. Onyshko, L.Yo., Seniuk, M.M., & Onyshko, O.Ye. (2014). Dynamic stress intensity factors in the plane with a circular hole under impact non-symmetric stresses. Physicochemical Mechanics of Materials, (5), 116-121.

5. Bazhenov, V., & Ihumnov, L. (2018). Boundary integral equation and boundary elements methods. Litres. ISBN: 978-5-9221-0953-6.

6. Yang, J.H., Jiang, Q.H., Zhang, Q.B., & Zhao, J. (2018). Dynamic stress adjustment and rock damage during blasting excavation in a deep-buried circular tunnel.Tunnelling and Underground Space Technology,71, 591-604. https://doi.org/10.1016/j.tust.2017.10.010.

7. Kushnir, R.M. (2016). A Numerical-Analytical Approach to the Analysis of Non-Stationary Temperature Fields in Multiply-Connected Solids. Mechanics, Materials Science & Engineering, (3), 90-106. https://doi.org/10.13140/RG.2.1.1167.0165.

8. Ditkin, V.A., & Prudnikov, A.P. (2017). Operational calculus in two variables and its applications. Courier Dover Publications.

9. Solyar, T.Ya. (2016). Efficient approach to the evaluation of dynamic stresses in layered circular plates based on the Prudnikov formula for the inverse Laplace transformation. Journal of Mathematical Sciences, 212(2), 107-120. https://doi.org/10.1007/s10958-015-2652-6.

10. Tao, M., Zhao, R., Du, K., Cao, W., & Li, Z. (2020). Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact loading.International Journal of Solids and Structures,191, 401-417. https://doi.org/10.1016/j.tust.2019.03.008.

11. Hu, C., Cao, T., Zhou, C., & Wang, J. (2017). Dynamic stress concentrations in infinite plates with a circular cutout based on refined theory. Archive of Applied Mechanics, 87(2), 261-277. https://doi.org/10.1007/s00419-016-1192-y.

12. Tanaka, S., Sannomaru, S., Imachi, M., Hagihara, S., Okazawa,S., & Okada, H. (2015). Analysis of dynamic stress concentration problems employing spline-based wavelet Galerkin method. Engineering Analysis with Boundary Elements,58, 129-139. https://doi.org/10.1016/j.enganabound.2015.04.003.

13. Shangguan, Z., Zhu, Z., & Tang, W. (2020). Dynamic impact experiment and numerical simulation of frozen soil with prefabricated holes. Journal of Engineering Mechanics, 146(8), 04020085. https://doi.org/10.1007/s10409-020-00999-4.

14. Maksymovych, O., & Jaroszewicz, J. (2018). Determination of stress state of anisotropic plates with rigid inclusions based on singular integral equations. Engineering Analysis with Boundary Elements, 95, 215-221. https://doi.org/10.1016/j.enganabound.2018.07.004.

15. Pokhmurska, H., Maksymovych, O., Dzyubyk, A., & Dzyubyk, L. (2018). Calculation of trajectories and the rate of growth of curvilinear fatigue cracks in isotropic and composite plates. IOP Conference Series: Materials Science and Engineering, 373(1), 012024. IOP Publishing. https://doi.org/10.1088/1757-899X/373/1/012024.

16. Hetnarski, R.B., & Ignaczak, J. (2016). The mathematical theory of elasticity. CRC Press. ISBN: 9781439828885.

17. Dzyubyk, A., Sudakov, A., Dzyubyk, L., & Sudakova, D. (2019). Ensuring the specified position of multisupport rotating units when dressing mineral resources. Mining of Mineral Deposits, 13(4), 91-98. https://doi.org/10.33271/mining13.04.091.

 

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.

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