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Abstract
This paper is devoted to formulation and general principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method (FEM) discrete-continual finite element method (DCFEM). The field of application of DCFEM comprises structures with regular physical and geometrical parameters in some dimension (“basic” dimension). DCFEM presupposes finite element approximation for non-basic dimension while in the basic dimension problem remains continual. DCFEM is based on analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients.
Highlights
Let physical and geometrical parameters within one group of subdomains from (2) is constant in some dimension (“basic” dimension)
finite element method (FEM) [6,8,9,13,24,26,33,34] can be effectively used for approximation here
-called approximation parameter Uk can be introduced in accordance with the following rule : Uk 1 for approximation with the use of FEM ; Uk 2 for approximation with the use of discrete-continual finite element method (DCFEM)
Summary
Let’s consider multipoint boundary problem of static analysis of deep beam (Fig. 1) [7, 10,11,12,14,15,17,18,19,20,21,22,23,25,27,28,29,30,31,32]. Some elements of notation system is presented at Fig. 1. Corresponding design model is two-dimensional theory of elasticity [9]. Let’s : be domain occupied by structure, : { (x1, x2 ) : 0 x1 l1, 0 x2 l2 } or nb 1. 1, 2, ..., nb are coordinates of corresponding boundary points (cross-sections) along basic dimension
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