Gömbhéjak poligonális horpadási alakjának vizsgálata

Examination of Polygonal Buckling Shapes of Spherical Shells / Studiul pierderii stabilității locale sub forma poligonală ale învelitorilor sferice

  • VETŐ Dániel
  • SAJTOS István
Keywords: héj, gömbhéj, horpadás, poligom, nyúlásmentes alakváltozás

Abstract

The paper discusses the buckling of spherical shells. Our goal is to determine the buckling shape of spherical shells subjected to concentrated load. The load-deflection diagram, concerning this case, is also to be determined. It is shown that the buckling shapes with axisymmetry and discrete symmetry of revolution have no direct connection between each other through inextensional deformations. The results of the proposed model, which is able to treat buckling shapes with discrete symmetry of revolution (i.e. polygonal shapes), show good agreement with experiments.

Kivonat

A cikk gömbhéjak horpadásával foglalkozik, célja a koncentrált erővel terhelt gömbhéjak horpadási alakjának
meghatározása, illetve a horpadáshoz tartozó teher-elmozdulás összefüggés megállapítása. Bebizonyítottuk, hogy a körszimmetrikus horpadási alak és a diszkrét forgásszimmetrikus (poligonális) horpadási alak nem vihető egymásba a felület nyúlásmentes alakváltozásai segítségével. A cikkben bemutatott, a poligonális horpadási alakok figyelembevételére is alkalmas analitikus modell segítségével kapott eredmények jó egyezést mutatnak a kísérletekben tapasztaltakkal.

References

Audoly, B., Pomeau, Y.: Elasticity and geometry, Oxford University Press, Oxford, 2010

Ben Amar, M., Pomeau, Y.: Crumpled paper, Proceedings of the Royal Society London A, 453, 1997, pp. 729- 755.

Blaise, A., André, S., Delobelle, P., Meshaka, Y., Cunat, C.: Identification of the true elastic modulus of high density polyethylene from tensile tests using an appropriate reduced model of the elastoviscoplastic behavior, arXiv:1206.4268v1, 2012

Bushnell, D.: Bifurcation phenomena in spherical shells under concentrated and ring loads, AIAA Journal, 5/11, 1967, pp. 2034-2040.

Croll, J. G. A.: Towards simple estimates of shell buckling loads, Der Stahlbau, 9, 1975, pp. 283-285.

Csonka P.: Héjszerkezetek, Akadémiai Kiadó, Budapest, 1981

Evkin, A. Yu.: Large deflections of deep orthotropic shells under radial concentrated load: asymptotic solution, International Journal of Solids and Structures, 42, 2005, pp. 1173-1186.

Fitch, J. R.: The buckling and post-buckling behavior of spherical caps under concentrated load, International Journal of Solids and Structures, 4, 1968, pp. 421-446.

Forgács G.: Fizika a biológiában, Fizikai Szemle, 3, 1996, pp. 95-101.

Galpin, B., Grolleau, V., Umiastowski, S., Rio, G., Mahéo, L.: Design and application of an instrumented projectile for load measurements during impact, International Journal of Crashworthiness, 13/2, 2008, pp. 139- 148.

Grolleau, V., Galpin, B., Penin, A., Rio, G.: Modeling the effect of forming history in impact simulations: evaluation of the effect of thickness change and strain hardening based on experiments, International Journal of Crashworthiness, 13/4, 2008, pp. 363-373.

Gupta, N. K., Mohamed Sheriff, N., Velmurugan, R.: Experimental and theoretical studies on buckling of thin spherical shells under axial loads, International Journal of Mechanical Sciences, 50, 2008, pp. 422-432.

Hegedűs I., Héjszerkezetek, Műegyetemi Kiadó, Budapest, 1998

Ivanova, J., Pastrone, F.: Geometric method for stability of non-linear elastic thin shells, Kluwer Academic Publishers, Boston, 2002

Knoche, S., Kierfeld, J.: The secondary buckling transition: wrinkling of buckled spherical shells, European Physical Journal E, 37/7, 2014, pp. 1-21.

Kollár, L., Dulácska, E.: Buckling of Shells for Engineers, Akadémiai Kiadó, Budapest, 1984

Lobkovsky, A. E.: Structure of Crumpled Thin Elastic Membranes, PhD disszertáció, University of Chicago, Department of Physics, Chicago, 1996

Menyhárd I.: Héjszerkezetek, Műszaki Könyvkiadó, Budapest, 1966

Moulton, D. E., Goriely, A., Chirat, R.: Mechanical growth and morphogenesis of seashells, Journal of Theoretical Biology, 311, 2012, pp. 69-79.

Niordson, F. I.: Shell theory, Elsevier, Amszterdam, 1985

Pauchard, L., Rica, S.: Contact and compression of elastic spherical shells: the physics of a ’ping-pong’ ball, Philosophical Magazine B, 78/2, 1998, pp. 225-233.

Penning, F. A.: Nonaxisymmetric behavior of shallow shells loaded at the apex, Journal of Applied Mechanics, 33, 1966, pp. 699-700.

Pogorelov, A. V.: Die Verbiegung konvexer Flächen, Akademie-Verlag, Berlin, 1957

Pogorelov, A. V.: Stability of axially symmetric deformations of spherical shells under axially symmetric load, NASA Contract TT F-8628, ST-SM-10050, Arlington, 1963

Pogorelov, A. V.: Bendings of Surfaces and Stability of Shells, American Mathematical Society, Providence, 1988

Quilliet, C., Zoldesi, C., Riera, C., Blaadaren, A. van, Imhof, A.: Anisotropic colloids through non-trivial buckling, European Physical Journal E, 27, 2008, pp. 13-20.

Ramm, E., Wall, W. A.: Shell structures – a sensitive interrelation between physics and numerics, International Journal for Numerical Methods in Engineering, 60, 2004, pp. 381-427.

Ruan, H. H., Gao, Z. Y., Yu, T. X.: Crushing of thin-walled spheres and sphere arrays, International Journal of Mechanical Sciences, 48, 2006, pp. 117-133.

Tarnai, T.: Buckling patterns of shells and spherical honeycomb structures, Computers and Mathematics with Applications, 17/4-6, 1989, pp. 639-652.

Thang, C. Q.: A gömbhéj szimmetrikus horpadása, Építés-Építészettudomány, 21/1-2, 1989, pp. 95-108.

Vaziri, A., Mahadevan, L.: Localized and extended deformations of elastic shells, Proceedings of the National Academy of Sciences, 105/23, 2008, pp. 7913-7918.

Vaziri, A.: Mechanics of highly deformed elastic shells, Thin-Walled Structures, 47, 2009, pp. 692-700.

Vető, D., Sajtos, I.: Application of geometric method to determine the buckling load of spherical shells, Pollack Periodica, 4/2, 2009, pp. 123-134.

Vető D., Sajtos I.: Geometriai módszer alkalmazása gömbhéjak horpadásának vizsgálatához, Építés- Építészettudomány,

Zhu, E., Mandal, P., Calladine, C. R.: Buckling of thin cylindrical shells: an attempt to resolve a paradox, International Journal of Mechanical Sciences, 44, 2002, pp. 1583-1601.

Published
2018-08-03
How to Cite
Dániel, V., & István, S. (2018). Gömbhéjak poligonális horpadási alakjának vizsgálata. Műszaki Szemle, (68), 37-48. Retrieved from http://ojs.emt.ro/index.php/muszakiszemle/article/view/35
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Articles