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Research Papers: Operations, Applications & Components

Shakedown Limit Load Determination of a Cylindrical Vessel–Nozzle Intersection Subjected to Steady Internal Pressures and Cyclic In-Plane Bending Moments

[+] Author and Article Information
Hany F. Abdalla

Assistant Professor of Mechanical
Design and Solid Mechanics
Faculty of Engineering,
Department of Mechanical Engineering,
The British University in Egypt
e-mail: hany.fayek@bue.edu.eg
or hany_f@aucegypt.edu

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 30, 2013; final manuscript received February 16, 2014; published online June 24, 2014. Assoc. Editor: David L. Rudland.

J. Pressure Vessel Technol 136(5), 051602 (Jun 24, 2014) (9 pages) Paper No: PVT-13-1129; doi: 10.1115/1.4026902 History: Received July 30, 2013; Revised February 16, 2014

In the current research, the elastic shakedown limit loads for a cylindrical vessel–nozzle intersection is determined via a direct noncyclic simplified technique. The cylindrical vessel–nozzle intersection is subjected to a spectrum of steady internal pressure magnitudes and cyclic in-plane bending moments on the nozzle end. The determined elastic shakedown limit loads are utilized to generate the elastic shakedown boundary (Bree diagram) of the cylindrical vessel–nozzle structure. Additionally, the maximum moment carrying capacity (limit moments) and the elastic limit loads are determined and imposed on the Bree diagram of the structure. The simplified technique outcomes showed excellent correlation with the results of full cyclic loading elastic–plastic finite element simulations.

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References

Figures

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Fig. 1

Cyclic moment loading pattern employed within the full cyclic loading elastic–plastic FE simulations right after the steady internal pressure is applied

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Fig. 2

Wu et al. [8] cylindrical vessel nozzle structure schematic

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Fig. 3

Schematic diagram of the cylindrical vessel–nozzle half geometric model

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Fig. 4

The cylindrical vessel–nozzle FE meshing [half model]

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Fig. 5

Moment–deflection curves of the nozzle at the three displacement sensors shown in Fig. 2

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Fig. 6

Normalized limit, elastic shakedown limit, and elastic limit moments of the cylindrical vessel–nozzle intersection subjected to steady internal pressures and cyclic in-plane bending moment loadings

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Fig. 7

Elastic shakedown response of the output critical integration section point 1 (SP1) of the 15% PY case under cyclic in-plane bending moment loading on the nozzle utilizing the elastic shakedown limit moment output by the simplified technique

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Fig. 8

Zoomed view of the location of the critical element on the acute angle side between the vessel and the nozzle of the 15% PY case–SP1 which is representative of the 0–17.5% PY steady internal pressure spectrum (von Mises stress distribution at moment loading Removal–zoomed view)

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Fig. 9

Loading–unloading path inscribed within the normalized material yield surface of the output critical integration section point of the 15% PY case employing an elastic–perfectly–plastic material model (cyclic in-plane bending moment loading, SP1)

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Fig. 10

Reversed plasticity response of the output critical integration section point 1 (SP1) of the 15% PY case under cyclic in-plane bending moment loading on the nozzle upon just exceeding the output elastic shakedown limit moment

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Fig. 11

Ratchetting response of the output critical integration section point 5 (SP5) of the 22% PY case under cyclic in-plane bending moment loading on the nozzle upon just exceeding the output elastic shakedown limit moment

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Fig. 12

Location of the critical element on the obtuse angle side between the vessel and the nozzle of the 22% PY case–SP1 that is representative of the 19 PY–25.6% PY steady internal pressure spectrum (von Mises stress distribution at moment loading removal–zoomed view)

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Fig. 13

Zoomed view of the narrow PEEQ spectrum shown in Fig. 10 illustrating ratchetting of the output critical integration section point 5 (SP5) of the 22% PY case (cyclic in-plane bending moment loading)

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