OPERATOR-RELATED FORMULATION OF THE EIGENVALUE PROBLEM FOR THE BOUNDARY PROBLEM OF ANALYSIS OF THE WALL BEAM WITH PIECEWISE-CONSTANT PHYSICAL AND GEOMETRICAL PARAMETERS ALONGSIDE THE BASIC DIRECTION WITHIN THE FRAMEWORK OF THE DISCRETE-CONTINUAL APPROACH

• Main Authors: Akimov Pavel Alekseevich, Mozgaleva Marina Leonidovna, Sidorov Vladimir Nikolaevich
• Format: Article
• Language: English
• Published: Moscow State University of Civil Engineering (MGSU) 2012-10-01
• Series: Vestnik MGSU
• Subjects: operational formulation; eigenvalue problem; boundary problem; piecewise-constant parameters; two-dimensional problem of elasticity; structural analysis; discrete-continual methods
• Online Access: http://vestnikmgsu.ru/files/archive/issues/2012/5/ru/13.pdf

The paper covers the operator-related formulation of the eigenvalue problem of analysis of the wall beam with piecewise-constant physical and geometrical parameters alongside the so-called basic direction within the framework of the discrete-continual approach (discrete-continual finite element method, discrete-continual variation-difference method). Generally, discrete-continual formulations are contemporary mathematical models which are currently becoming available for computer-based implementation. They allow investigators to consider the boundary effects whenever solution components represent rapidly varying functions. Another feature of discrete-continual methods is the absence of limitations imposed on lengths of structures. Two-dimensional model of elasticity is used as a design model of a structure. In accordance with the so-called extended domain method, the domain is limited by the boundary of arbitrary shape. Corresponding key features at the stage of numerical implementation of discrete-continual methods include convenient mathematical formulas, effective computational patterns and algorithms, simple data processing techniques, etc. The definition of an expression for an operator of the problem under consideration, if resolved in the isotropic medium, is presented; the allowance for supports restrained by elastic members is provided; standard boundary conditions are taken into account