Two-dimensional Hierarchical Models for Prismatic Shells with Thickness Vanishing at the Boundary

Abstract

We construct variational hierarchical two-dimensional models for elastic, prismatic shells of variable thickness vanishing at boundary. With the help of variational methods, existence and uniqueness theorems for the corresponding two-dimensional boundary value problems are proved in appropriate weighted functional spaces. By means of the solutions of these two-dimensional boundary value problems, a sequence of approximate solutions in the corresponding three-dimensional region is constructed. We establish that this sequence converges in the Sobolev space H 1 to the solution of the original three-dimensional boundary value problem. (2000): 74K20, 74K25. Mathematics Subject Classifications

Concentrated contact interactions in cuspidate prismatic shell-like bodies

“…4); surveys of investigations into elastic cuspidate prismatic shells are found in [1,5,7]. Beginning from Sect.…”

On Some Bending Problems of Prismatic Shell with the Thickness Vanishing at Infinity

“…Problems for cusped plates have been investigated by Khvoles, Jaiani, Tsiskaridze, Khomasuridze, Devdariani, Uzunov, Naguleswaran, Kharibegashvili, Natroshvili, Wendland, and others (see, e.g. [10], [11], [13], [8], [9] and references therein).…”

“…Works of Babuska, Gordeziani, Guliaev, Khoma, Khvoles, Meunargia, Schwab, Vashakmadze, Zhgenti, Jaiani, Tsiskarishvili, M. and G. Avalishvili, Wendland, Natroshvili, Kharibegashvili, Chinchaladze, Gilbert, and others are devoted to further analysis of I.Vekua's models (rigorous estimation of the modeling error, numerical solutions, etc.) and their generalizations (see, e.g., [2], [3], [4], [5], [6], [7], [8], [9], [12], [16] …”

Existence and uniqueness theorems for cusped prismatic shells in the Nth hierarchical model

“…In this direction Schwab's work [7] is also remarkable. The same questions for cusped prismatic shells when the shells occupy a 3D Lipschitz domain were investigated by Jaiani et al [8,9]. Various aspects of I. Vekua's models were studied by Vashakmadze [10], Meunargia [11], Zhgenti [12], Khoma [13], Guliaev et al [14], Khvoles [15], Jaiani [16][17][18][19], Chinchaladze and Gilbert [20], etc.…”