Stress-strain state of anisotropic thick-walled cylindrical shells under variable loading
DOI:
https://doi.org/10.17721/1812-5409.2026/1.14Keywords:
thick-walled anisotropic shell, three-dimensional formulation, stress-strain state, variable distributed loadAbstract
Thick-walled cylindrical shell structures are essential components of various modern engineering systems, including pipelines, storage tanks, reactor installations, and aerospace bodies. The operation of such structures under complex mechanical or thermal loading requires reliable analysis of their stress–strain state, particularly in the presence of distributed loads varying along the circumferential direction. Such effects may arise from non-uniform working medium pressure, for example, asymmetric turbulent flow in pipelines or asymmetric aerodynamic loads acting on aerospace hulls. These factors can significantly influence the strength, stability, and service life of the structures.
This study presents a three-dimensional approach to the analysis of the stress–strain state of an anisotropic thick-walled cylindrical boroplastic shell subjected to distributed pressure periodically varying in the circumferential direction. The anisotropy of the elastic properties of the material is determined by the misalignment of its orthotropy axes with the curvilinear coordinate system of the cylindrical shell.
To derive the three-dimensional system of differential equations, a modification of the Hu – Washizu variational principle is applied. The resulting system is solved using the analytical Bubnov – Galerkin method. Within this framework, all stress–strain components are expanded into double Fourier series, ensuring that the longitudinal coordinate satisfies boundary conditions at the shell ends, while circumferential periodicity is preserved. The final system of nonhomogeneous differential equations is solved numerically using the discrete orthogonalization method.
The proposed approach provides accurate results for structures operating under complex loading conditions and can be effectively applied to improve their reliability and safety.
Pages of the article in the issue: 115 - 118
Language of the article: Ukrainian
References
Grigorenko, Y. M., Vasylenko, A. T., & Pankratova, N. D. (1991). Problems of the theory of elasticity of inhomogeneous bodies. Naukova dumka [in Russian].
Novozhilov, V. V. (1961). Theory of elasticity. Elsevier.
Semenyuk, N. P., Trach, V. M., & Podvornyi, A. V. (2023). Stress–strain state of a thick-walled anisotropic cylindrical shell. International Applied Mechanics, 59(1), 79–89. https://doi.org/10.1007/s10778-023-01201-5
Washizu, K. (1982). Variational Methods in Elasticity and Plasticity. Pergamon Press. https://doi.org/10.1002/zamm.19840640121
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Copyright (c) 2026 Alexander Grigorenko, Volodymyr Trach, Andrii Podvornyi, Natalia Zhukova
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