Construction and Investigation of the Third-Order Approximation to the Solution of the Heat-Conduction Equation for Thin Shallow Shells by Using Legendre Polynomials in the Case of Stationary Heat Exchange
- 7 Downloads
By using the N th order approximation of temperature function and its first derivative by Legendre polynomials, we construct the solution of problem of heat conduction for a thin-walled shallow isotropic shell and deduce the system of resolving equations for the N th approximation. For the first and third approximations, we solve this problem for the case of concentrated heat sources. In the third approximation, we also construct the plots of the dependences of temperature on the distance to the heat source and on the curvature of the shell under the conditions of symmetric or asymmetric stationary heat exchange.
Unable to display preview. Download preview PDF.
- 1.N. S. Bondarenko and A. S. Gol’tsev, “Solution of the heat-conduction problem for anisotropic plates under concentrated thermal loading using Legendre polynomials,” Mat. Metody Fiz.-Mekh. Polya, 52, No. 4, 216–226 (2009); English translation: J. Math. Sci., 174, No. 3, 400–414 (2011).Google Scholar
- 2.N. S. Bondarenko, A. S. Gol’tsev, and V. P. Shevchenko, “Fundamental solutions of the thermoelastic equations for transversely isotropic plates,” Prikl. Mekh., 46, No. 3, 51–60 (2010); English translation: Int. Appl. Mech., 46, No. 3, 287–295 (2010).Google Scholar
- 3.A. S. Hol’tsev and V. K. Khyzhnyak, G-Function: Methodical Advice for Learning a “Special Functions” Special Course [in Ukrainian], Donets’k Derzh. Univ., Donets’k (1999).Google Scholar
- 4.O. B. Kovalev, A. M. Orishich, V. M. Fomin, and V. B. Shulyat’ev, “Adjoint problems of mechanics of continuous media in gaslaser cutting of metals,” Prikl. Mekh. Tekh. Fiz., 42, No. 6, 106–116 (2001); English translation: J. Appl. Mech. Tech. Phys., 42, No. 6, 1014–1022 (2001).Google Scholar
- 5.B. L. Pelekh and M. A. Sukhorol’skii, Contact Problems of the Theory of Anisotropic Elastic Shells [in Russian], Naukova Dumка, Kiev (1980).Google Scholar
- 6.Ya. S. Podstrigach and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumка, Kiev (1978).Google Scholar
- 7.V. K. Khizhnyak and V. P. Shevchenko, Mixed Problems of the Theory of Plates and Shells: Tutorial [in Russian], Donetsk Gos. Univ., Donetsk (1980).Google Scholar