Forced vibrations of a layerwise orthotropic cylindrical shell

In the paper we study forced vibrations of an orthotropic cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs in liquid under the action of inner radial pressure pulsating in time. Based on Hamilton – Ostrogradsky variational principle, we construct a system of equations to determine the displacements of the mid-surface points of an orthotropic cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs under dynamical interaction with liquid. Surface loads acting on the cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs as viewed from liquid are determined from the solutions of liquid motion equations written in potentials. Analytic formulas for finding the displacements of the midsurface points of a liquid-contacting orthotropic cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs, were obtained.

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Stress concentration in a non-linear elastic orthotropic cylindrical shell with rectangular holes

Visnyk of Zaporizhzhya National University Physical and Mathematical Sciences ◽

10.26661/2413-6549-2019-1-10 ◽

2019 ◽

pp. 75-82

Author(s):

Eugen Storozhuk ◽

◽

Volodymyr Maksimyuk ◽

Ivan Chernyshenko ◽

Viktoriia Kornienko ◽

...

Keyword(s):

Cylindrical Shell ◽

Stress Concentration ◽

Orthotropic Cylindrical Shell ◽

Linear Elastic ◽

Non Linear

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Collapse of Arteries Subjected to an External Band of Pressure

Journal of Biomechanical Engineering ◽

10.1115/1.3138203 ◽

1980 ◽

Vol 102 (1) ◽

pp. 8-22 ◽

Cited By ~ 6

Author(s):

A. M. Hecht ◽

H. Yeh ◽

S. M. K. Chung

Keyword(s):

Reynolds Number ◽

Blood Flow ◽

Cylindrical Shell ◽

Orthotropic Cylindrical Shell ◽

Reynolds Numbers ◽

Intraluminal Pressure ◽

Collapse Pressure ◽

Vessel Size ◽

Flow Reynolds Number ◽

Small Band

Collapse of arteries subjected to a band of hydrostatic pressure of finite length is analyzed. The vessel is treated as a long, thin, linearly elastic, orthotropic cylindrical shell, homogeneous in composition, and with negligible radial stresses. Blood in the vessel is treated as a Newtonian fluid and the Reynolds number is of order 1. Results are obtained for effects of the following factors on arterial collapse: intraluminal pressure, length of the pressure band, elastic properties of the vessel, initial stress both longitudinally and circumferentially, blood flow Reynolds number, compressibility, and wall thickness to radius ratio. It is found that the predominant parameter influencing vessel collapse for the intermediate range of vessel size and blood flow Reynolds numbers studied is the preconstricted intraluminal pressure. For pressure bands less than about 10 vessel radii the collapse pressure increases sharply with increasing intraluminal pressure. Initial axial prestress is found to be highly stabilizing for small band lengths. The effects of fluid flow are found to be small for pressure bands of less than 100 vessel radii. No dramatic orthotropic vessel behavior is apparent. The analysis shows that any reduction in intraluminal pressure, such as that produced by an upstream obstruction, will significantly lower the required collapse pressure. Medical implications of this analysis to Legg-Perthes disease are discussed.

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