The analytical solution is obtained in quadratures of the elastic theory dynamic centrally-symmetric boundary problems of the same class for multilayer transtropic spheres, the sonic speed in the radial direction of which tends to infinity. Convergence and accuracy of the derived solutions are analyzed. It is shown that the analytical solutions obtained can be used as the first approximation for the cases where the sonic speed in materials is finite.
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References
S. G. Lekhnitskii, Theory of Elasticity for Anisotropic Bodies [in Russian], Nauka, Moscow (1977).
A. G. Ivanov, M. A. Syrunin, and A. G. Fedorenko, “Effect of the reinforcement structure on the limit deformability and strength of shells from directional fiberglass reinforced plastic under internal blast loading,” Prikl. Mekh. Teor. Fiz., No. 4, 130–135 (1992).
W. Nowacki, Teoria Sprezystosci, PWN, Warszawa (1973).
L. I. Fridman, “Solution of the dynamic problem of elasticity theory in curvilinear coordinates,” Strength Mater., 8, No. 5, 560–565 (1976).
Sh. U. Galiev, Yu. N. Babich, S. V. Zhurakhovskii, et al., Numerical Simulation of Wave Processes in Limited Media [in Russian], Kiev, Naukova Dumka (1989).
V. I. Smirnov, Higher Mathematics [in Russian], Vol. 2, Nauka, Moscow (1974).
V. A. Romashchenko, “Solutions of dynamical problems for incompressible and low-compressible spirally orthotropic nonuniform thick-walled cylinders,” Prikl. Matem. Mekh., 71, Issue 1, 56–65 (2007).
E. K. Ashkenazi and É. V. Ganov, Anysotropy of Structural Materials. Handbook [in Russian], Mashinostroenie, Leningrad (1980).
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Translated from Problemy Prochnosti, No. 2, pp. 93 – 107, March – April, 2011.
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Romashchenko, V.A., Tarasovskaya, S.A. The elastic theory dynamic problem for a transtropic multilayer sphere. Strength Mater 43, 178–189 (2011). https://doi.org/10.1007/s11223-011-9284-y
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DOI: https://doi.org/10.1007/s11223-011-9284-y