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Abstract

This paper investigates the effect of friction on the buckling behavior of a thin, shallow, elastic spherical shell under uniform external pressure based on an axisymmetric model of the finite element method. The study examines a combination of different geometric parameters with three different types of boundary conditions: clamped, hinged, and frictional ends with a wide range of friction coefficients. Friction has a significant influence on the buckling response of the spherical shell for all geometric parameters. In general, the critical pressure decreases as the friction coefficient or geometric parameter decreases. The buckling behavior of the frictional end with small friction coefficients presents an obvious difference compared to the results of high coefficients. For certain geometric parameters, the buckling mode of the spherical shell is transited because of changing the friction coefficient. A buckling map that describes the dependence of critical pressure on both friction coefficient and geometric parameter combined with buckling mode is generated. This map can be applied to the design of the spherical shell against buckling.
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Authors and Affiliations

XuanCuong Nguyen
1 2
ORCID: ORCID
Yoshio Arai
1
Wakako Araki
3

  1. Saitama University, Saitama, Japan
  2. Hanoi University of Civil Engineering, Hanoi, Vietnam
  3. Tokyo Institute of Technology, Tokyo, Japan
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Abstract

This article provides an optimized solution to the problem of passive shielding against static magnetic fields with any number of spherical shells. It is known, that the shielding factor of a layered structure increases in contrast to a single shell with the same overall thickness. For the reduction of weight and cost by given material parameters and available space the best system for the layer positions has to be found. Because classic magnetically shielded rooms are very heavy, this system will be used to develop a transportable Zero-Gauss-Chamber. To handle this problem, a new way was developed, in which for the first time the solution with regard to shielding and weight was optimized. Therefore, a solution for the most general case of spherical shells was chosen with an adapted boundary condition. This solution was expanded to an arbitrary number of layers and permeabilities. With this analytic solution a differential evolution algorithm is able to find the best partition of the shells. These optimized solutions are verified by numerical solutions made by the Finite Element Method (FEM). After that the solutions of different raw data are determined and investigated.
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Bibliography

[1] Schiebold K., Zerstörungsfreie Werkstoffprüfung – Magnetpulverprüfung, Springer-Verlag (2015).
[2] Farolfi A., Trypogeorgos D., Colzi G., Fava E., Lamporesi G., Ferrari G., Design and characterization of a compact magnetic shield for ultracold atomic gas experiments, Review of Scientific Instruments, 90.11, 115114 (2019), DOI: 10.48550/arXiv.1907.06457.
[3] Report Buyer Ltd., Degaussing System Market by Solution, End User, Vessel Type and Region – Global Forecast to 2023, June (2018).
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[6] Clerk Maxwell J., Electricity and magnetism, vol. 2, New York: Dover (1954).
[7] David Jackson J., Classical Electrodynamics, American Association of Physics Teachers (1999).
[8] Karaboga D., Ökdem S., A simple and global optimization algorithm for engineering problems: differential evolution algorithm, Turkish Journal of Electrical Engineering and Computer Sciences, 12.1, pp. 53–60 (2004).
[9] Bronstein I.N., Hromkovic J., Luderer B., Schwarz H.R., Blath J., Schied A., Gottwald S., Taschenbuch der Mathematik, compact disc, Springer-Verlag (2008).
[10] Bartelmann M., Feuerbacher B., Krüger T., Lüst D., Rebhan A., Wipf A., Theoretische Physik 2 |Elektrodynamik, Springer-Verlag (2018).
[11] Rohner M., Magnetisch anhaftende Partikel zuverlässig entfernen, JOT Journal für Oberflächentechnik, 53, pp. 51–53 (2013).
[12] Maurer MagneticAG, Restmagnetismus – das verkannte Problem, JOT Journal für Oberflächentechnik, 57, pp. 104–105 (2017).
[13] Wilson E., Nicholson J.W., On the magnetic shielding of large spaces and its experimental measurement, Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, pp. 529–549 (1916).
[14] King L.V., XXI. Electromagnetic shielding at radio frequencies, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 15.97, pp. 201–223 (1933).
[15] Reutov Y.Y., Choice of the number of shells for a spherical magnetostatic shield, Russian Journal of Non-destructive Testing, 37.12, pp. 872–878 (2001).
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Authors and Affiliations

Patrick Alexander Ralf
1
ORCID: ORCID
Christian Kreischer
1

  1. Helmut Schmidt University, University of the Federal Armed Forced Hamburg, Germany
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Abstract

The normal mode solution for the form function and target strength (TS) of a solid-filled spherical shell is derived. The calculation results of the spherical shell’s acoustic TS are in good agreement with the results of the finite element method (FEM). Based on these normal mode solutions, the influences of parameters such as the material, radius, and thickness of the inner and outer shells on the TS of a solid-filled spherical shell are analyzed. An underwater spherical shell scatterer is designed, which uses room temperature vulcanized (RTV) silicone rubber as a solid filling material and does not contain a suspension structure inside. The scatterer has a good TS enhancement effect.
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Authors and Affiliations

Bing Jia
1 2
Jun Fan
1
Gui-Juan Li
2
Bin Wang
1
ORCID: ORCID
Yun-Fei Chen
2

  1. Key Laboratory of Marine Intelligent Equipment and System Ministry of Education Shanghai Jiao Tong University
  2. Science and Technology on Underwater Test and Control Laboratory Dalian, Liaoning, China

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