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Mathematical model of the pipeline with angular joint of elements
Author(s) -
Rukavishnikov Viktor A.,
Tkachenko Oleg P.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5751
Subject(s) - singularity , shell (structure) , bending moment , joint (building) , line (geometry) , transverse plane , rotation (mathematics) , mechanics , mathematics , classical mechanics , moment (physics) , surface (topology) , geometry , bending , oblique case , shear (geology) , mathematical analysis , physics , structural engineering , materials science , engineering , linguistics , philosophy , composite material , thermodynamics
A mathematical model of the pipeline as a Koiter‐Vlasov moment shell with kink lines of the surface at the junctions of the pipe segments was constructed and substantiated. The following tasks are solved: The geometric parameters of the mechanical system as a three‐dimensional elastic body and as a shell are found; force factors of the shell are expressed in terms of displacements of the middle surface of the wall, taking into account the presence of a kink line; equations of pipe equilibrium are derived as Koiter‐Vlasov shells with an edge along the line; forces on oblique sections are expressed as functions of shell movements; the conjugation conditions on the pipe joint line for displacements and the angle of rotation of the normal are imposed and justified; conjugation conditions for bending moments, shear forces, transverse and normal forces are imposed and justified. The presence of the solution singularity at points on the connection line of the pipe segments is theoretically established and illustrated by the numerical example.