Snap-through Buckling of Shallow Spherical Shells under Ring Loads

Yıl 2021, Cilt: 32 Sayı: 2, 10695 - 10716, 01.03.2021

Esra Eylem Karataş , Receb Faruk Yükseler

https://doi.org/10.18400/tekderg.565095

Cited By: 1

Öz

Snap-through buckling behaviour of rigid vinyl polyethylene shallow spherical shells, undergoing large displacements, subjected to static ring loads is investigated by using finite difference and the Newton-Raphson Method. The load-deflection diagrams corresponding to various values of thickness, depth and ring diameter of the shell with simply supported and clamped edges are sketched and compared. The accuracy of the used algorithm and the prepared computer program are tested by comparing some of the numerical results obtained in this study with those obtained by an experimental study, available in the relevant literature. Further steps on the concerning subject are achieved.

Anahtar Kelimeler

Shallow spherical shell, nonlinear behaviour, large deflection, snap-through buckling, upper-limit point, rigid vinly polyethlene, stability

Destekleyen Kurum

-

Proje Numarası

-

Teşekkür

-

Kaynakça

• Labisch, F. K., On the Axisymmetric Buckling Behavior of Incompressible Nonlinearly Elastic Spherical Shells. Z. Angew. Math. Mech., 86(7), 572-583, 2006.
• Pi, Y. L., Bradford, M. A. and Tin-Loi, F., Nonlinear Analysis and Buckling of Elastically Supported Circular Shallow Arches. International Journal of Solids and Structures, 44, 2401-2425, 2007.
• Guana, F. and Pastrone, F., Axisymmetric Instabilities for Elastic Conical Shells under Compressive End Loadings. Mathematics and Mechanics of Solids, 12, 164-182, 2007.
• Pi, Y. L., Bradford, M. A. and Tin-Loi, F., Non-linear In-plane Buckling of Rotationally Restrained Shallow Arches under a Central Concentrated Load. International Journal of Non-Linear Mechanics, 43, 1-17, 2008.
• Cai, J. and Feng, J., Buckling of Parabolic Shallow Arches When Support Stiffens under Compression. Mechanics Research Communications, 37, 767-471, 2010.
• Coman, C. D., Bifurcation Instabilities in Finite Bending of Circular Cylindrical Shells. International Journal of Engineering Science, 119, 249-264, 2017.
• Hutchinson, J. W., Buckling of Spherical Shells Revisited, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2195), 2016. DOI:https://doi.org/10.1098/rspa.2016.0577.
• Yükseler, R. F., The Strain Energy Density of Compressible, Rubber-Like Shells of Revolution, ASME Journal of Applied Mechanics, 63, 419 – 423, 1996.
• Yükseler, R. F., On the Definition of the Deformed Reference Surface of Rubber-Like Shells of Revolution, ASME Journal of Applied Mechanics, 63, 424 – 428, 1996.
• Yükseler, R. F., A Theory for Rubber-Like Rods, International Journal of Solids and Structures, 69-70, 350–359, 2015.
• Yükseler, R. F., Local and Nonlocal Buckling of Mooney-Rivlin Rods, European Journal of Mechanics - A/ Solids, Volume 78, November-December 2019, ( https://doi.org/10.1016/j.euromechsol.2019.103816)
• Moon, J., Yoon, K. Y., Lee, T. H., et al. In-plane Elastic Buckling of Pin-ended Shallow Parabolic Arches. Engineering Structures, 29:2611-2617, 2017.
• Altekin, M. and Yükseler, R. F., A Parametric Study on Geometrically Nonlinear Analysis of Initially Imperfect Shallow Spherical Shells, Journal of Elastomers and Plastics, 40. DOI: 10.1177/0095244307084907, 2008.
• Yıldırım, B. and Yükseler, R. F., Effect of Compressibility on Nonlinear Buckling of Simply Supported Polyurethane Spherical Shells Subjected to an Apical Load, Journal Of Elastomers And Plastics, 43. DOI: 10.1177/0095244310393930, 2011.
• Pi, Y. L. and Bradford, M. A., Non-linear Buckling and postbuckling Analysis of Arches with unequal Rotational End Restraints under a Central Concentrated Load. International Journal of Solids and Structures, 49:3762-3773, 2012.
• Chen, X. and Meguid, S. A., On the Parameters Which Govern the Symmetric Snap-through Buckling Behavior of an Initially Curved Microbeam. International Journal of Solids and Structures, 66:77-87, 2015.
• Plaut, R. H., Snap-through of Shallow Reticulated Domes under Unilateral Displacement Control. International Journal of Solids and Structures, 148-149:24-34, 2018.
• Tsiatas, G. C. and Babouskos, N. G., Linear and Geometrically Nonlinear Analysis of Non-uniform Shallow Arches under a Central Concentrated Force. International Journal of Non-Linear Mechanics, 92:92-101, 2017.
• Virgin, L. N., Wiebe, R., Spottswood, S. M., et al. Sensitivity in the Structural Behavior of Shallow Arches. International Journal of Non-Linear Mechanics, 58:212-221, 2014.
• Ma, H., Fan, F., Wen, P., et al. Experimental and Numerical Studies on a Single-layer Cylindrical Reticulated Shell with Semi-rigid Joints. Thin-Walled Structures, 86:1-9, 2015.
• Cui, Z., Bhattacharyya, D., Moltschaniwskyj, G., Experimental and Numerical Study of Buckling Response of Composite Shells Compressed Transversely Between Rigid Platens. Composites: Part B., 36:478-486, 2005.
• Ko1odziej, S. and Marcinowski, J., Experimental and Numerical Analyses of the Buckling of Steel, Pressurized, Spherical Shells. Advances in Structural Engineering, 21(16):2416-2432, 2018.
• Made, A. M., Mirmiran, A. and Nelsen, D., Stability Tests of Sandwich Composite Elastica Arches. Journal Of Structural Engıneerıng, 128(5):683-686, 2002.
• Erdölen, A. and Yükseler, R. F., An Approach for Finite Strains and Rotations of Shells of Revolution with Application to a Spherical Shell under a Uniformly Distributed Pressure. Journal of Elastomers and Plastics, 35 (4), 357-365, October 2003, DOI:10.1177/009524403038015.
• Altekin, M. and Yükseler, R. F., Geometrically Nonlinear Analysis of Clamped Shallow Spherical Shells, 8th Int. Congress on Advances in Civil Engineering, Eastern, Mediterranean University, Famagusta, North Cyprus, 2008.
• Yıldırım, B. and Yükseler, R. F., Combined Effect of Compressibility, Height and Thickness on the Nonlinear Behaviour of Polyurethane, Simply-Supported Spherical Shells under Apical Loads, Bitlis Eren Univ J Sci & Technol, 4 (1), 12-19, 2014.
• Koçak, A. and Yükseler, R. F., Finite Axisymmetric Strains and Rotations of Shells of Revolution with Application to the Problem of a Spherical Shell under a Point Load. Sixth Annual International Conference on Composites Engineering, Orlando, Florida, 1999.
• Altekin, M. and Yükseler, R. F., Geometrically Nonlinear Axisymmetric Buckling Analysis of Shallow Spherical Shells. International Civil Engineering & Arcitecture Symposium for Academicians, Side-Antalya, Turkey, 2014.
• Evan-Iwanowski, R. M., Loo, T. C. and Tierney, D. W., Local Buckling of Shells. Developments in Mechanics, 2:221-251, 1963.
• Cagan, J. and Taber, L. A., Large Deflection Stability of Spherical Shells with Ring Loads. J. Appl. Mech., 53:897-901, 1986.
• Ranjan, G. V., Edge Zone Expansions for Thin Shells with Application to (1) Torispherical Pressure Vessel and (2) Large Deflection of Sphere with Point Load, PhD Thesis, Stanford University, USA, 1976.
• Parnell, T. K., Numerical Improvement of Asymptotic Solutions and Nonlinear Shell Analysis. PhD Thesis, Stanford University, USA, 1984.
• Huang, N., Unsymmetrical Buckling of Thin Shallow Spherical Shells, J. Appl. Mech., 31, 447-457, 1964.
• Memon, B. A. and Su, X. Z., Arc-Length Technique for Nonlinear Finite Element Analysis. Journal of Zhejiang University, 5(5), 618-628, 2004.
• Riks, E., The Application of Newton’s Method to the Problem of Elastic Stability. Journal of Applied Mechanics, 39, 1060-1065, 1972.
• Riks, E., An Incremental Approach to the Solution of Snapping and Buckling Problems. International Journal of Solids and Structures, 15(7), 529-551, 1979.
• Wempner, G. A., Discrete Approximation Related to Nonlinear Theories of Solids. International Journal of Solids and Structures, 7(11), 1581-1599, 1971.
• Polat, C., and Calayır Y., Lineer Olmayan Yapı Sistemlerinin Analizi İçin Yay-Boyu Metodu. FÜ Fen ve Mühendislik Bilimleri Dergisi 19.4, 525-530, 2007.
• Polat, C., Co-rotational Formulation of a Solid-shell Element Utilizing the ANS and EAS Methods. Journal of Theoretical and Applied Mechanics 48.3, 771-788, 2010.