Combined effect of compressibility, height and thickness on the nonlinear behaviour of polyurethane, simply-supported spherical shells under apical loads

Year 2014, Volume: 4 Issue: 1, 12 - 19, 23.06.2014

Bülent Yıldırım Recep Faruk Yükseler

https://doi.org/10.17678/beujst.30193

Cited By: 2

Abstract

Previously, the effect of compressibility on the nonlinear buckling behaviour of thin, polyurethane, simply-supported spherical shells subjected to apical loads has been presented without considering the orders of the thickness and height of the spherical shells. In the meantime; it has been observed that although the variations of the thickness and height of the spherical shells do not affect the comments made for the effect of the compressibility on the buckling loads, they do affect the comments made for the effect of the compressibility on the buckling deflections considerably. In this study; combined effect of the compressibility, height and thickness on the buckling loads, buckling deflections and the apical load-apical deflection diagrams of polyurethane, thin, simply-supported spherical shells subjected to apical loads is investigated. Comparing the force-deflection diagrams corresponding to various values of the parameters pertaining to the compressibility of the material used, the height and the thickness of the shell; the variations of the buckling loads, buckling deflections and forms of the force-deflection diagrams corresponding to the various combinations of the mentioned parameters are discussed.

Keywords

Compressible material, finite difference method, nonlinear analysis, polyurethane, spherical shell

References

• Akyüz U, Ertepinar A (2001). Stability and breathing motions of pressurized compressible hyperelastic spherical shells. J Sound Vib 247, 293-304.
• Blatz PJ, Ko WL (1962). Application of finite elastic theory to deformation of rubbery materials. Trans Soc Rhe 233-251.
• Chapra SC, Canale RP (1994). Introduction to computing for engineers. Published by the McGraw-Hill, New York.
• Haddow JB, Faulkner MG (1974). Finite expansion of a thick compressible spherical elastic shell. Int J Mech Sci 16, 63-73.
• Koçak AE, Yükseler RF (1999). Finite axisymmetric strains and rotations of shellsof revolution with application to the problem of a spherical shell under a point load, 6th Annual International Conference on Composites Engineering, Florida, 421-422.
• Novozhilov V (1970). Thin shells theory. Wolters- Noordhoff, Groningen.
• Parnell TK (1984). Numerical improvement of asymtotic solutions and non-linear shell analysis. Stanford University, PhD Thesis.
• Pflüger A (1964). Stabilitats probleme der elastostatic. Berlin.
• Ranjan GV, Steele CR (1977). Large deflection of deep under 18th ASME/ASCE/AHS Dynamics and Material Conference, 269-347. load, Structures, Structurals
• Simmonds JG (1987). The strain- energy density of compressible, rubber-like axishells. ASME J App Mech 54, 453-454.
• Taber LA (1982). Large deflection of a fluid-filled spherical shell under a point load. ASME J App Mech 49, 121-128.
• Taber LA (1987). Large elastic deformation of shear deformable shells of revolution. ASME J App Mech 54, 578-584.
• Treloar L.R.G. (1975). The Physics of Rrubber Elasticity. 3nd edition. Published by Clarendon Pres, Oxford.
• Yıldırım B (2007). Nonlinear analysis of the simply supported spherical shells made of a compressible rubber-like material under the effect of an apical load. PhD thesis, YTU , Istanbul.
• Yıldırım B, Yükseler RF (2011). Effect of compressibility on nonlinear buckling of simply supported polyurethane spherical shells subjected to an apical load. J Elast Plast 43, 167-187.
• Yükseler RF (1996a). The strain energy density of compressible, rubber-like shells of revolution. ASME J App Mech 63, 419 – 423.