UNSTEADY AXISYMMETRIC DEFORMATION OF AN ELASTIC THICK-WALLED SPHERE UNDER THE ACTION OF VOLUME FORCES
V. A. Vestyak1, D. V. Tarlakovskii2
1Moscow Aviation Institute, Moscow, 125993 Russia
v.a.vestyak@mail.ru
2Research Institute of Mechanics, Moscow, 119192 Russia
tdvhome@mail.ru
Keywords: упругая толстостенная сфера, нестационарные осесимметричные объемные силы, ряды по полиномам Лежандра и Гегенбауэра, преобразование Лапласа, функции Грина, elastic thick-walled sphere, unsteady axisymmetric volume forces, series in Legendre and Gegenbauer polynomials, Laplace transform, Green's functions
Abstract
This paper considers a homogeneous isotropic elastic body bounded by concentric spheres and acted upon by axisymmetric unsteady volume forces. Displacement fields are determined using series expansions in Legendre and Gegenbauer polynomials, Laplace transforms in time, and integral representations with kernels in the form of Green's functions. Explicit formulas for the Green's functions are constructed that allow accurate determination of the originals. Examples of the calculations are presented.
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