BENDING OF THE PRISMATIC SHELLS WITH THE THICKNESS VANISHING AT INFINITY IN THE N = 0 APPROXIMATION OF HIERARCHICAL MODELS
NATALIA CHINCHALADZE *
Ilia Vekua Institute of Applied Mathematics (VIAM), Faculty of Exact and Natural Sciences of Ivane Javakhishvili Tbilisi State University, 2 University St., 0186, Tbilisi, Georgia
NATIA MCHEDLIDZE
Ilia Vekua Institute of Applied Mathematics (VIAM), Faculty of Exact and Natural Sciences of Ivane Javakhishvili Tbilisi State University, 2 University St., 0186, Tbilisi, Georgia
*Author to whom correspondence should be addressed.
Abstract
The work is devoted to the prismatic shell with the thickness vanishing at infinity as an exponential function. We consider bending equation of the zero approximation of Vekuas hierarchical models. The problem is reduced to the Dirichlet problem for elliptic type partial differential equation in the first quadrant of a two-dimensional Cartesian system. The solution of the setting problem is constructed in an integral form.
Keywords: Cusped plates, cusped prismatic shells, hierarchical models, elliptic type partial differential equations