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1

Effect of Friction on Buckling Behavior in Shallow Spherical to Hemispherical Shells in Contact with Rigid Boundaries under Uniform External Pressure

Nguyen Xuan Cuong, Arai Yoshio, Araki Wakako

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no 1

10--25

EN

This study investigates the influence of friction on the buckling behavior of thin, elastic, spherical shells under uniform external pressure. The study spans a range of geometric parameters, from shallow shells to hemispheres. Three different end-edge boundary conditions—clamped, hinged, and frictional ends—are considered across a wide range of friction coefficients using an axisymmetric model and nonlinear buckling analysis. The spherical shell becomes increasingly susceptible to buckling when the friction coefficient falls below the converged friction coefficient. A formula is developed to estimate this converged friction coefficient for each geometric parameter. Furthermore, a boundary separating the effects of friction on critical pressure into distinct regions is established, and equations predicting critical pressure within each region are provided. The study also finds that friction influences the buckling mode transition in the shells. Due to significant changes in the theta angle of the no-bending point with increasing geometric parameter and friction coefficient, buckling mode transitions occur at lower friction coefficients in wider spherical shells. These findings provide valuable insights into the intricate interplay between geometric parameter, friction, and buckling behavior in shells. In practical applications, this study can be used to assess and enhance the safety and reliability of spherical shells.

2

Novel optimization method for mobile magnetostatic shield and test applications

Ralf Patrick Alexander, Kreischer Christian

Archives of Electrical Engineering

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2022

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Vol. 71, nr 3

627--639

EN

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.

3

Comparision of Numerical Results with Known Solutions of Buckling Problem of Pressured Shallow Spherical Shells

Lykhachova O., Kołakowski Z.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 2

185--190

EN

Buckling problem of pressured shallow spherical shells is studied numerically for two types of finite elements: axisymmetric and non–axisymmetric. A very good correspondence of obtained results and known solutions is revealed in the case of clamed and hinged spherical segments for both types of finite elements. The comparison of results also shows that using non–axisymmetric finite element lets one get full pre– and post– buckling equilibrium path in the range of relative deflections w=h.

4

Investigation of the heat transport during the hollow spheres production from the tin melt

Petrov M., Petrov P., Bast J., Sheypak A.

Computer Methods in Materials Science

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2013

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Vol. 13, No. 2

276--282

EN

The present paper reveals one of the energy efficient ways of the units (hollow spheres) production for cellular structures for their further application in light weight constructions, realized through the metallurgical procedure. The metallurgical method exhibit all known methods in intelligence, because it based on the own physical properties of the used materials and boundary conditions of the process, not involving any organically core and preparation of the powder and slurries. These small hollow spheres made from different materials could change the weight of a construction part essentially, used as acoustic and thermal insulation and also as protection against vibrations. They can be used as a unit cell for big parts and alone filled with an inert gas, e.g. fusion targets. Pure tin shells were produced intransient (thixotropic) state of materials by elevated temperatures (close to the melting point of the pure tin) and several simulation steps were used, to determine the preferable boundary conditions. To one of them belongs the investigation of the temperature fields during the formation process. The heat transport from the tin melt into the semi-solid tin shell influence the nucleation process so the solid wall should be formed before the gas starts to form the inner hollow space. Otherwise the semi-solid shell will be broken by the gas pressure or the inner hollow space does not occur. For these purposes the CFD- (Computational Fluid Dynamic) and FEM-commercial codes such as FLUENT and Solid Works Simulation Package respectively were taken. At the end the data verification of the obtained simulation results with the measurements on the laboratory stand and theoretical calculations were carried out. Current investigation was completed by the determination of the whole temperature fields on the side surface of the form nozzle, which was obtained from a thermogram captured with the help of an infrared camera (IRC).

PL

Praca przedstawia jedną z energooszczędnych metod produkcji zespołów struktur komórkowych (pustych kul) stosowanych w lekkich konstrukcjach. Opisany proces metalurgiczny produkcji kul wykorzystuje fizyczne własności zastosowanych materiałów oraz warunki brzegowe procesu bez wprowadzania proszków czy zawiesin. Puste kulki o małych średnicach wykonane z różnych materiałów mogą znacząco zmniejszyć wagę elementów konstrukcyjnych wykorzystywanych jako izolatory akustyczne i termiczne, a także jako ochrona przed wibracjami. Można je stosować jako komórki jednostkowe dla większych elementów lub jako elementy samodzielne wypełnione gazem obojętnym. Powłoki z czystej cyny produkowane są w temperaturze bliskiej temperatury topnienia materiału (w stanie tiksotropowym). W ramach pracy wykonano szereg symulacji komputerowych, które umożliwiły określenie właściwych warunków brzegowych procesu produkcji. Badano między innymi rozkład temperatury podczas procesu produkcji. Transport ciepła w procesie formowania powłok z cyny od stanu płynnego do stanu pół-stałego ma wpływ na proces zarodkowania, dlatego ścianki będące w stanie stałym powinny być formowane zanim gaz rozpocznie kształtowanie wnętrza powłoki. W przeciwnym wypadku pół-stała powłoka pęknie pod wpływem ciśnienia gazu lub w ogóle nie powstanie. W pracy do symulacji wykorzystano komercyjne programy FLUENT oraz pakiet SolidWorks. Wyniki symulacji zostały porównane z wynikami doświadczeń oraz obliczeń teoretycznych. Ponadto badania uzupełniono o wyznaczenie pola temperatury na powierzchni dyszy formującej dzięki termogramowi zarejestrowanemu kamerą na podczerwień (IRC).

5

Numerical calculations of stability of spherical shells

Niezgodziński T., Świniarski J.

Mechanics and Mechanical Engineering

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2010

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Vol. 14, nr 2

325-337

EN

The results of FEM calculations of stability of thin-walled spherical shells are presented. A static and dynamic stability analysis was conducted. Hemispherical shells and spherical caps with various dilation angles, subjected to external pressure, were considered. For each shell calculated, various boundary conditions of support were analyzed: joint, fixed and elastically fixed support. In the calculations, an axisymmetric and random discretization of the model was accounted for. As a result of the calculations conducted for static loads, values of upper critical pressures and buckling modes of the shells were obtained. The results were presented for various shell thicknesses. The FEM solutions were compared to the available results obtained with analytical and numerical methods, showing a good conformity. Dynamic calculations were conducted for a triangular pulse load. On the basis of the Budiansky-Roth dynamic criterion of stability loss, values of upper dynamic critical pressures were obtained. Shell buckling modes were determined as well.