Generation of interaction diagrams of pad-reinforced and non-padded vessel/nozzle structures via employing various plastic collapse techniques
Introduction
Thin-walled cylindrical vessels with radial nozzles are integral pressurized components found in a diversity of substantial heavy and crucial industries such as conventional and nuclear power generation plants, natural gas liquefaction facilities, petrochemical, pharmaceutical and food industries in addition to desalination facilities … etc. On the other hand, small-sized thin-walled cylindrical vessel/radial nozzle structures are extensively found in the fuel and the oxidizer tanks of liquid rocket propulsion systems. Furthermore, thin-walled vessel/nozzle structures presently invade the automotive sector with a specific focus on future hydrogen-powered vehicles. Thin-walled vessel/nozzle pressurized structures suffer immense stress concentration due to the near-geometric discontinuity located at the vicinity of the vessel/nozzle intersection. Failure in the vessel/nozzle intersection domain leads to undesirable catastrophes. Accordingly, careful design and analysis of such structures are deemed essential. Encompassing the vessel/nozzle intersection region with pad reinforcements significantly reduces the concentration of stresses associated with the various applied loading conditions and affords a practical and economic solution as compared to assigning larger wall thicknesses for the entire vessel and the nozzle. The thin-walled vessel/nozzle structure presently analyzed is subjected to a spectrum of steady internal pressures and in-plane and out-of-plane bending moments applied on the nozzle end once at a time. The key objective of the present research is to apply the Plastic Work Curvature (PWC) and the Plastic Work (PW) criteria in addition to the Twice-Elastic-Slope (TES) Method to generate the plastic collapse moment boundaries versus a spectrum of steady internal pressures concerning both pad-reinforced and non-padded vessel/nozzle structures. The PWC and the PW criteria are almost not applied to such intricate structures, to the best knowledge of the author.
Section snippets
Scope of work
Initially, a finite element (FE) model is constructed for validation against recordings of two experimental test setups of a cylindrical vessel/radial nozzle structure with pad reinforcement subjected to out-of-plane bending applied on the nozzle end in the absence of internal pressure, section 5. The experimental test is conducted by Sang et al. [1], where load-deflection curves are plotted and the plastic collapse moment is determined via the American Society of Mechanical Engineers (ASME)
Literature review
Sang et al. [4] pointed out that research is more focused on thin-walled spherical vessels with radial nozzles as compared to cylindrical vessels with radial and oblique nozzles. Additionally, Sang et al. [4] stated that most design codes do not provide clear procedures for computing stresses within the pad-reinforced regions. In specific, only the effect of internal pressure is accounted for in computing local stresses within the padded region, whereas the effects due to bending, torsional,
The employed plastic collapse load techniques
This section provides a concise description concerning the three plastic collapse load techniques employed in the present study, namely, the Plastic Work Curvature (PWC) criterion, the Plastic Work (PW) criterion, and the Twice-Elastic-Slope (TES) Method. It is essential to mention that the finite element analyses conducted in the present research adopt both large displacement formulation and strain hardening material model. Computation of plastic collapse loads indicates that significant
Experimental setup description
Sang et al. [1] tested three thin-walled non-pressurized pad-reinforced cylindrical vessels with radial nozzle models for determining the out-of-plane (OP) plastic collapse bending moment loads on the nozzles utilizing the Twice-Elastic-Slope (TES) Method. The three experimental vessel/nozzle models tested by Sang et al. [1] possess the same cylindrical vessel geometry, but with different nozzle and pad reinforcement diameters. In the present research, two experimental models are utilized for
Analysis of the pressurized pad-reinforced model and mathematical computation of plastic collapse moments utilizing the PWC and the PW criteria
This section further elaborates on the analysis of the model by applying a spectrum of steady internal pressures and their resulting axial thrust loads in addition to the rotation/angular displacements applied on the nozzle end, thus achieving IP and OP bending. Additionally, this section also provides ample explanation and systematic mathematical steps to calculate the plastic collapse moments via employing the PWC and the PW criteria respectively. As previously performed in the validation
Results and discussion
Subsequent to the performed validation study in addition to the presented systematic mathematical approaches for computing plastic collapse moments via both the PWC and the PW criteria, the present study is extended to analyze the thin-walled pad-reinforced model subjected to the combined effect of steady internal pressure spectra and IP/OP bending loading on the nozzle along with comparisons and discussion. Plastic collapse load boundaries are generated employing the PWC and the PW
Conclusions
Subsequent to the discussion of results, which included employing the Plastic Work Curvature (PWC) and the Plastic Work (PW) criteria in addition to the Twice-Elastic-Slope (TES) Method, the following concluding remarks are highlighted:
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The application of the PWC criterion resulted in generating relatively higher plastic collapse moment boundaries as compared to the corresponding boundaries generated via the TES Method and the PW criterion. This is mainly because the PWC criterion attains better
Statement of original work and funding
The author affirms that the present research contents have not been previously published nor submitted for publication, in whole or in part, either in a serial, professional journal or as a part of a book that is formally published and made available to the public. The author also affirms that this research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The Canadian International College and the American University in Cairo are greatly acknowledged for providing state-of-the-art computational facilities.
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