Mathematical Modeling and Analytical Solution of Thermoelastic Stability Problem of Functionally Graded Nanocomposite Cylinders within Different Theories

Mahmure Avey, Nicholas Fantuzzi and Abdullah Sofiyev
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Mahmure Avey: Department of Mathematical Engineering, Graduate School, Istanbul Technical University, Istanbul 34469, Turkey
Nicholas Fantuzzi: Department of Civil, Chemical, Environmental, and Materials Engineering, University Bologna, 40126 Bologna, Italy
Abdullah Sofiyev: Information Technology Research and Application Center of Consultancy Board of ITRAC Center, Istanbul Commerce University, Istanbul 34445, Turkey

Mathematics, 2022, vol. 10, issue 7, 1-11

Abstract: Revolutionary advances in technology have led to the use of functionally graded nanocomposite structural elements that operate at high temperatures and whose properties depend on position, such as cylindrical shells designed as load-bearing elements. These advances in technology require new mathematical modeling and updated numerical calculations to be performed using improved theories at design time to reliably apply such elements. The main goal of this study is to model, mathematically and within an analytical solution, the thermoelastic stability problem of composite cylinders reinforced by carbon nanotubes (CNTs) under a uniform thermal loading within the shear deformation theory (ST). The influence of transverse shear deformations is considered when forming the fundamental relations of CNT-patterned cylindrical shells and the basic partial differential equations (PDEs) are derived within the modified Donnell-type shell theory. The PDEs are solved by the Galerkin method, and the formula is found for the eigenvalue (critical temperature) of the functionally graded nanocomposite cylindrical shells. The influences of CNT patterns, volume fraction, and geometric parameters on the critical temperature within the ST are estimated by comparing the results within classical theory (CT).

Keywords: mathematical modeling; eigenvalue; PDEs; nanocomposites; cylindrical shell; critical temperature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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