# PSI - Issue 50

Kirill E. Kazakov et al. / Procedia Structural Integrity 50 (2023) 131–136 Kirill E. Kazakov / Structural Integrity Procedia 00 (2022) 000 – 000

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Thus, in real calculations, it is necessary to take the heterogeneity of the material into account. Analytical methods will allow the further use of the obtained solutions in the construction of mathematical models of other problems of solid mechanics. Acknowledgements The present work was supported by the Ministry of Science and Higher Education within the framework of the Russian State Assignment under contract No. AAAA-A20-120011690132-4. References Horgan, C.O., Chan, A.M., 1999, The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials б Journal of Elasticity 55 (1), 43 – 59, doi: 10.1023/a:1007625401963. Tutuncu, N., Ozturk, M., 2001, Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering 32 (8), 683 – 686, doi:10.1016/s1359-8368(01)00041-5 Xiang, H., Shi, Z., Zhang, T., 2006, Elastic analyses of heterogeneous hollow cylinders, Mechanics Research Communications 33 (5), 681 – 691, doi: 10.1016/j.mechrescom.2006.01.005. Shi, Z., Zhang, T., Xiang, H., 2007, Exact solutions of heterogeneous elastic hollow cylinders, Composite Structures 79, 140 – 147, doi: 10.1016/j.compstruct.2005.11.058. Zwillinger, D., 1997, Handbook of Differential Equations, 3rd ed., Academic Press, Boston, MA. Abramowitz, M., Stegun, I.A., 1964, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, United States Department of Commerce, National Bureau of Standards. Olde Daalhuis, A.B., 2010, Confluent hypergeometric functions, in NIST Handbook of Mathematical Functions, U.S. Dept. Commerce, Washington, DC, pp. 321–349.

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