Термопружність ізотропних тіл із недеформівними нитковими включеннями: Fìz.-mat. model. ìnf. tehnol. 2020, 28:33-41

• Дата: 2020
• Автори: Pasternak, Jaroslav, Sulym, Heorhiy, Ilchuk, Nataliia
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2020
• Теми: ниткове включення; термопружність; інтегральне рівняння; гіперсингулярний
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/132
• Назва журналу: Physico-mathematical modeling and informational technologies

The paper derives integral equations of heat conduction and thermoelasticity of isotropic solids with non-deformable perfectly thermally conducting thread-like inclusions. It is observed that, in spite of the order of singularity, the integral equations obtained are hypersingular due to the symmetry of the kernels. Non-integral terms of these equations are derived. A boundary element method scheme for numerical solution of formulated problems is proposed. A numerical example is provided. References Wang, H., Qin, Q. H., Kang, Y.L. (2005). A new meshless method for steady-state heat conductionproblems in anisotropic and inhomogeneous media. Archive of Applied Mechanics, 74, 563–579. DOI https://doi.org/10.1007/s00419-005-0375-8 Vales, B., Cuartas, V. M., Welemane, H., Pastor, M. L., Trajin, B. (2016). Heat source estimation in anisotropic materials. Composite Structures, 136, 287–296. DOI https://doi.org/10.1016/j.compstruct.2015.09.050 Kushch, V. I., Sevostianov, I., Giraud, A. (2017). Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2207). DOI https://doi.org/10.1098/rspa.2017.0472 Balandin, A A., Ghosh, S., Nika, D. L., Pokatilov, E. P. (2010). Extraordinary thermal conductivity of graphene: possible applications in thermal management. ECS Trans, 28(5), 63–71. DOI https://doi.org/10.1149/1.3367937 Sulim, G. T., Piskozub, J. Z. (2008). Thermoelastic equilibrium of piecewise homogeneous solids with thin inclusions. J. Eng. Math., 61, 315–337. DOI https://doi.org/10.1007/s10665-008-9225-3 Pasternak, Ia., Sulym, H., Ilchuk, N., Angew, Z. (2019). Boundary element analysis of 3D shell-like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids. Math. Mech. DOI https://doi.org/10.1002/zamm.201800319 Anufriev, R., Nomura, M. (2019). Coherent thermal conduction in silicon nanowires with periodic wings. Nanomaterials, 9(142). DOI https://doi.org/10.3390/nano9020142 Im, H., Hwang, Y., Moon, J. H., Lee, S. H., Kim, J. (2013). The thermal conductivity of Al(OH)3 covered MWCNT/epoxy terminated dimethyl polysiloxane composite based on analytical Al(OH)3 covered MWCNT. Composites Part A: Applied Science and Manufacturing, 54, 159–165. DOI https://doi.org/10.1016/j.compositesa.2013.07.020 Pasternak, Ia., Pasternak, R., Pasternak, V., Sulym, H. Boundary element analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids. Engineering Analysis with Boundary Elements, 74, 70–78. DOI https://doi.org/10.1016/j.enganabound.2016.10.009