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Abstract
The formulation of considering multipoint boundary problem includes three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside subdomains; description of boundary conditions (for boundaries of domain and boundaries between subdomains). These boundary conditions (interface conditions) in under consideration in the distinctive paper.
Highlights
Bk U k where Bk is matrix of boundary conditions of size 4N1 u 4N1, which can be constructed in accordance with algorithm presented at Table 1; Bk is matrix of boundary conditions of size 4N1 u 2N1N2,k, which can be constructed in accordance with so-called method of basis variations [1-5,17]
It should be noted that computing of the elements of the matrix Bk by formula (6) corresponds to the boundary conditions (1)-(2)
It should be noted that computing of the elements of the matrix Bk by formulas (9) corresponds to the boundary conditions (3)-(4)
Summary
In practical applications the following variants of boundary conditions (interface conditions) between subdomains (2) from the first part of this paper are most often encountered (some of them are considered in this paper): interface “discrete-continual model – discrete model”, “internal” boundary condition of the type “perfect contact”; interface “discrete model – discrete-continual model”, “internal” boundary condition of the type “perfect contact”; interface “discrete-continual model – discrete-continual model”, “internal” boundary condition of the type “perfect contact”; interface “discrete model – discrete model”, “internal” boundary condition of the type “perfect contact”; interface “external boundary – discrete model”, boundary condition of the type “hinged support”; interface “external boundary – discrete model”, boundary condition of the type “free edge”; interface “external boundary – discrete-continual model”, boundary condition of the type “hinged support”; interface “external boundary – discrete-continual model”, boundary condition of the type “free edge”; interface “discrete model – external boundary”, boundary condition of the type “hinged support”; interface “discrete model – external boundary”, boundary condition of the type “free edge”; interface “discrete-continual model – external boundary”, boundary condition of the type “hinged support”; interface “discrete-continual model – external boundary, boundary condition of the type “free edge”. 3 Interface “discrete model – discrete-continual model”, “internal” boundary condition of the type “perfect contact”
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