On some ways to achieve the absence of thermal stresses in an inhomogeneous through thickness infinite layer under stationary thermal loading

Authors

  • B. M. Kalynyak Pidstryhach Institute for Applied Problems of Mechanics and Mathemtics of the National Academy of Sciences of Ukraine, 79060, L’viv, Naukova str., 3B https://orcid.org/0000-0003-1214-2092

DOI:

https://doi.org/10.17721/1812-5409.2019/1.14

Abstract

A method for determining the characteristics of functional gradient materials (FGM) for providing zero thermal stresses in an infinite layer with given constant thermal loads is proposed. We assume that the classical convective conditions of heat transfer are given on the surfaces of the layer, the temperature field is stationary, the characteristics of the FGM are described by the model of a simple mixture, the characteristics of the thermo-stressed state and the material depend only on the transverse variable. Precise analytical expressions were obtained for the distribution of the concentration of one of the materials on the thickness of the layer in the absence of mass forces and heat sources, which provides zero longitudinal stresses.

Key words: functional-gradient materials, thermomechanical characteristics, layer, model of a simple mixture, absence of stresses, stationary temperature field, composites.

Pages of the article in the issue: 66-69

Language of the article: Ukrainian

References

ABRINIA, K. et al. (2008 New analysis for the FGM thick cylinders under combined pressure and temperature loading. Am. J. Appl. Sci. 5 (7). p. 852–859.

BOHIDAR, S. K., SHARMA, R. & MISHRA, P. R. (2014) Functionally graded materials: a critical review. Int. J. Res.. 1 (7). p. 289–301.

(ed. ICHIKAWA, KIYOSHI) (2001) Functionally Graded Materials in the 21st Century: a Workshop on Trends and Forecasts. XVI.

KALYNYAK, B. M. (2016) Guaranteeing the Absence of Radial Stresses in a Long Hollow Cylinder by the Inhomogeneity of Material. Materials Science. 52(2).p.261–268.

KUSHNIR R.M., POPOVYCH V.S. (2009) Termopruzhnist termochutlyvych til V.3 in Modeluvannya ta optymizaciya v termomechanizi electroprovidnych til: v 4-ch tomach / pid zah red. Ya. Y. Buraka, R.M. Kushnira. Spolom, L’viv:

SHEN, H.-S. (2009) Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. CRC Press.

CORLESS, R et al. (1996) On the Lambert W function. Adv. Comp. Math. 5. p. 329–359.

UYSAL M. U. (2013) Investigation of Thermal and Mechanical Loading on Functional Graded Material Plates. World Academy of Scienc. Engineering and Technology. International Journal of Aerospace and Mechanical Engineering. 7(11). p. 2283–2289.

No 1 (2019)

Downloads

How to Cite

Kalynyak, B. M. (2019). On some ways to achieve the absence of thermal stresses in an inhomogeneous through thickness infinite layer under stationary thermal loading. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 66–69. https://doi.org/10.17721/1812-5409.2019/1.14

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).