Research Papers: Design and Analysis

Behavior of Thin Elastic Circular Rings With Large Deformations Under Nonuniform Loads

[+] Author and Article Information
E. Azzuni

Lyles School of Civil Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: eazzuni@purdue.edu

S. Guzey

Lyles School of Civil Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: guzey@purdue.edu

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 22, 2017; final manuscript received November 5, 2018; published online December 7, 2018. Assoc. Editor: Yun-Jae Kim.

J. Pressure Vessel Technol 141(1), 011201 (Dec 07, 2018) (14 pages) Paper No: PVT-17-1163; doi: 10.1115/1.4041939 History: Received August 22, 2017; Revised November 05, 2018

Thin elastic circular rings under uniform pressure have been extensively studied by many researchers. Both the deflection and buckling behavior of rings were considered in these studies, but most have focused on the small deformations analysis approach. Even though the use of the small deformations assumption helps find the deflections of the ring prior to reaching the buckling load, it does not accurately capture the behavior of the ring after buckling. The in-plane large deformations analysis of thin elastic circular rings under nonuniform pressure explored in this paper expands on previous work and investigates varying pressure profiles. The pressure profiles studied here can be described by p=p01+qcosnθ. The large deformations assumption allows for the investigating of buckling loads as well as post-buckling behavior. Nonuniform normal pressure acting on a thin elastic circular ring results in a behavior that is described by a second-order ordinary differential equation (ODE) of the Duffing type, which is solved here through a numerical approach.

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Fig. 1

The pressure profiles for n = 2, 3, and 4. The nonuniformity factor, q, is equal to 0.5. The applied pressure is pθ=1.001+0.5 cosnθ.

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Fig. 2

Difference between deflection with large and smalldeformations assumptions. The applied pressure is pθ=5.621+0.5 cos3θ.

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Fig. 3

Initial and deformed configuration of a ring segment. Resultant forces and loading are shown in the deformed configuration.

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Fig. 4

Values of U0 that create a solution for the differential equation describing the ring's curvature ratio behavior

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Fig. 5

Values of C that create a solution for the differential equation describing the ring's curvature ratio behavior

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Fig. 6

Deflection progression shapes of the rings. The x-axis represents x/R and the y-axis represents y/R of a point on the ring for n = 2.

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Fig. 7

Deflection progression shapes of the rings. The x-axis represents x/R and the y-axis represents y/R of a point on the ring for n = 3.

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Fig. 8

Deflection progression shapes of the rings. The x-axis represents x/R and the y-axis represents y/R of a point on the ring for n = 4.

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Fig. 9

Load deformation plot. The progression of the nondimensional deflection in the x-direction, ux/R, for the point at θ = 0.

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Fig. 10

Load deformation plot. The progression of the nondimensional deflection in the y-direction, uy/R, for the point at θ = π.

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Fig. 11

Deformation in inches obtained through finite element analysis (FEA) for a ring with a radius of 8 in (0.2 m) under the load pθ=3.51+0.1 cos4θ lb/in

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Fig. 12

Comparison between deformations obtained through the method presented in this paper (solid line) compared to the results obtained using FEA (dotted line)



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