Open AccessOn the distribution of stresses near the crack in a toroidal shell with a flexible coating
Author(s) -
М. В. Маковійчук,
AUTHOR_ID,
Ivan Shatskyi,
А. Б. Щербій,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2021/3.11
Subject(s) - shell (structure) , curvature , mechanics , materials science , singular integral , tension (geology) , stress intensity factor , displacement (psychology) , boundary value problem , integral equation , structural engineering , fracture mechanics , physics , composite material , geometry , mathematics , mathematical analysis , ultimate tensile strength , engineering , psychology , psychotherapist
Elastic equilibrium of shallow toroidal shell loaded by internal pressure and containing the cross-cutting crack located along equator or throat of the shell has been studied in the two-dimensional formulation. The shell is reinforced by coating on one of the face surfaces. The crack in the shell with a flexible coating is simulated by a cuts with eccentrically hinge joint edges. The boundary problem for equations of classical shell theory with interrelated conditions of tension and bending along the cutting line is formulated within the framework of such model. Singular integral equation for the unknown jump of normal displacement on the crack edges has been elaborated. Based on asymptotical solutions of integral equation obtained using the small parameter method forces and moments intensity factors in the vicinity of the defect tips are defined. Their dependences of on the parameters of shell curvature and form parameter are investigated. It is established that the reinforcement of the shell leads to a decrease in the force intensity factor and to the appearance of a non-zero moment intensity factor.