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Thin-Walled Hollow Shafts01:15

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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
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Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
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Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
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Sequential buckling in fluid-filled cylindrical shells.

Shresht Jain1,2, Finn Box1,2, Martin Quinn1,2

  • 1Physics of Fluids & Soft Matter, Department of Physics & Astronomy, University of Manchester, Manchester, UK.

Communications Physics
|April 23, 2026
PubMed
Summary
This summary is machine-generated.

Researchers studied the buckling of liquid-filled cylindrical shells, like beverage cans. They discovered a sequential buckling instability that forms localized rings above a critical compression level.

Keywords:
Applied mathematicsNonlinear phenomena

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Area of Science:

  • * Physics and Engineering
  • * Materials Science
  • * Applied Mathematics

Background:

  • * Cylindrical shells are widely used for their load-bearing capabilities, found in applications ranging from oil drums to rockets.
  • * Buckling, a phenomenon where shells deform under compression, exhibits diverse forms like diamond patterns and elephant footing.
  • * The buckling behavior of liquid-filled shells remains under-explored despite their prevalence in industrial and daily applications.

Purpose of the Study:

  • * To investigate the largely overlooked buckling phenomenon in liquid-filled cylindrical shells.
  • * To identify and characterize the specific buckling instabilities occurring in such structures.
  • * To link theoretical models of pattern formation with physical observations of shell buckling.

Main Methods:

  • * Experimental compression of beverage cans to observe buckling behavior.
  • * Measurement of anisotropic material properties of the shell.
  • * Nonlinear modeling using the Swift-Hohenberg equations to simulate buckling patterns.

Main Results:

  • * Identification of a sequential buckling instability in fluid-filled shells.
  • * Observation of localized circumferential rings forming above a critical compression threshold.
  • * Demonstration that fluid-filled shells support multiple localized buckling solutions via nonlinear hoop stress and homoclinic snaking.

Conclusions:

  • * Fluid-filled shells exhibit unique buckling behaviors distinct from empty or solid-core shells.
  • * The study establishes a connection between mathematical pattern formation theories and physical buckling phenomena.
  • * Findings provide a framework for studying localized patterns in systems with material nonlinearities and pressurization.