Summary
A new theory is presented for shells of revolution undergoing axisymmetric arbitrarily large strain deformations. The material of the shell is assumed to be hyperelastic incompressible. The formulated theory is applied to analyse the flexural buckling of circular plates under uniform radial loads.
Übersicht
Eine neue Theorie zur Berechnung achsensymmetrischer Verformungen von Rotationsschalen unter Berücksichtigung beliebig großer Dehnungen wird angegeben. Das Material der Schale wird hyperelastisch und inkompressibel angenommen. Die Theorie wird zur Berechnung des Beulens von Kreisplatten unter gleichmäßiger Radialbelastung angewandt.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Reissner, E.: On axisymmetrical deformations of thin shells of revolution. In: Proc. Symp. Appl. Math. 3, pp. 27–52. New York: McGraw-Hill 1950
Alumäe, N. A.: On theory of finite deflections of axisymmetric shells of revolutions (in Russian). Prikl. Mat. Mekh. 16 (1952) 419–428
Makowski, J.; Nolte, L.-P.: Simple equations in terms of displacements for finite axisymmetric deflections of shells of revolution. Int. J. Non-Linear Mech. 1 (1987) 1–13
Simmonds, J. G.: A new displacement form for the nonlinear equations of motion of shells of revolution. J. Appl. Mech. 52 (1985) 507–509
Reissner, E.: On finite symmetrical deflections of thin shells of revolution. J. Appl. Mech. 36 (1969) 267–270
Reissner, E.: On finite symmetrical strain in thin shells of revolution. J. Appl. Mech. 39 (1972) 1137
Antman, S. S.: Existence and nonuniqueness of axisymmetric equilibrium states of nonlinearly elastic shells. Arch. Ration. Mech. Anal. 40 (1971) 329–371
Cohen, H.; Pastrone, F.: Axisymmetric equilibrium states of non-linear elastic cylindrical shells. Int. J. Non-Linear Mech. 21 (1986) 37–50
Chernykh, K. F.: Nonlinear theory of isotropically elastic thin shells (in Russian). Izv. AN SSSR, MTT 15 (1980) 148–159
Chernykh, K. F.: The theory of thin shells of elastomers (in Russian), Adv. Mech. 6 (1983) 111–147
Taber, L. A.: On approximate large strain relations for a shell of revolution. Int. J. Non-Linear Mech. 20 (1985) 27–39
Brodland, G. W.; Cohen, H.: Deflection and snapping of spherical caps. Int. J. Solids Struct. 23 (1987) 1341–1356
Brodland, G. W.; Cohen, H.: Large-strain axisymmetric deformation of cylindrical shells. J. Appl. Mech. 54 (1987) 287–291
Stumpf, H.; Makowski, J.: On large strain deformations of shells. Acta Mech. 65 (1986) 153–168
Simmonds, J. G.: The strain-energy density of rubber-like shells of revolution undergoing torsionless, axisymmetric deformation (axishells). J. Appl. Mech. 53 (1986) 593–596
Simmonds, J. G.: The strain-energy density of compressible, rubber-like axishells. J. Appl. Mech. 54 (1987) 453–454
Cook, W. A.: A finite element model for nonlinear shells of revolution. Int. J. Numer. Methods Eng. 18 (1982) 135–149
Cook, W. A.: Limitations and possible extensions to a nonlinear finite element shell-of-revolution model based on Reissner's shell theory. Int. J. Numer. Methods Eng. 18 (1982) 1855–1871
Taber, L. A.: Large elastic deformation of shear deformable shells of revolution: theory and analysis. J. Appl. Mech. 54 (1987) 578–584
Libai, A.; Simmonds, J. G.: The nonlinear theory of elastic shells, part 1: spatial dimension. San Diego: Academic Press 1988
Makowski, J.; Stumpf, H.: Finite strains and rotations in shells. In: Pietraszkiewicz, W. (ed.) Finite rotations in structural mechanics, Proc. EUROMECH Colloquium 197, pp. 175–194. Berlin: Springer 1986
Antman, S. S.: Qualitative properties of large buckled states of spherical shells. Arch. Ration. Mech. Anal. 87 (1986) 357–384
Antman, S. S.: Buckled states of nonlinearly elastic plates. Arch. Ration. Mech. Anal. 67 (1977) 111–149
Zee, L.; Sternberg, E.: Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids. Arch. Ration. Mech. Anal. 83 (1983) 53–90
Guo, Z.-H.: Vibration and stability of a cylinder subject to finite deformation. Arch. Mech. 14 (1962) 757–768
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Makowski, J., Stumpf, H. Finite axisymmetric deformation of shells of revolution with application to flexural buckling of circular plates. Ing. arch 59, 456–472 (1989). https://doi.org/10.1007/BF00534312
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00534312