ON A HIERARCHICAL MODEL OF ELASTIC RODS WITH VARIABLE CROSS-SECTIONS
Gia Avalishvili, Mariam Avalishvili · 2004
The present paper is devoted to the construction and investigation of one-dimensio-nal hierarchical model of elastic rod with variable non-rectangular cross-sections. The three-dimensional static boundary value problem is reduced to a sequence of one-dimensional ones and the existence and uniqueness of their solutions in suitable spaces are proved. Under the conditions of solvability of the original problem the convergence of the sequence of vector functions of three variables restored from the solutions of the constructed one-dimensional problems is proved and the rate of convergence is estimated. Key words and phrases: Linearly elastic rods, hierarchical modeling, a priori error estimates. AMS subject classification: 74K10, 65N15, 42C10. In recent years heirarchical modeling is widely used while constructing and investigating various lower-dimensional models in the theory of elas-ticity and mathematical physics [1-8]. One of the methods of constructing