Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure

Abstract

International audienceTheoretical and experimental studies of the free vibrations and the loss of stability of thick-walled cylindrical and spherical shells subjected to external pressure are presented. General equations for the oscillations of the shell under pressure are formulated on the basis of a rigorous theory of finite elasticity. Loss of stability is determined when the fundamental natural frequency of the prestressed shell ceases to be real-valued. Numerical solutions are obtained by solving the specialized equations that are applicable to neo-Hookean materials. Experiments using specimens made of silicone rubber closely verify the theoretical results

Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

“…When f"1 and "0)5, Levinson}Burgess material reduces to neo-Hookean material which is incompressible. In this limiting case, the results obtained reduce to those obtained by Wang and Ertepinar [17]. Figure 1 displays the variation of radial stress on the outer surface, as a function of outer stretch ratio for a spherical shell with a thickness ratio "0)90 for three di!erent hyperelastic materials, namely the foam rubber ( f"0, "0)25), the slightly compressible material ( f"1, "0)46), and the nearly incompressible material ( f"1, "0)499).…”

Second-Order Estimates for the Macroscopic Response and Loss of Ellipticity in Porous Rubbers at Large Deformations

“…In this connection, it is relevant to remark that while exact results are available for the effective stored-energy function and porosity evolution in in-plane hydrostatic loading of composite cylinders (with incompressible matrix phase), the loss of strong ellipticity of these structures has not been studied. However, Wang and Ertepinar [34] did study the stability of an isolated cylindrical Neo-Hookean shell under in-plane hydrostatic loading. Results of that work comprising the buckling flexural modes n = 2, which corresponds to the collapse to an oval shape, and n = 3 have been included in Figure 2(b), for reference purposes.…”

“…Similarly, for the case of a random and isotropic distribution of aligned cylindrical pores with initially circular cross section, the corresponding HS type estimate is given by (34) but with P being obtained by setting L (0) equal to L 0 in the expression [35]:…”

Nonlinear axisymmetric deformations of an elastic tube under external pressure

“…Using this theory, Nowinski and Shahinpoor (1969) examined the stability of an infinitely long circular cylinder of neo-Hookean material under external pressure assuming a plane strain deformation, and Wang and Ertepinar (1972) investigated the stability of infinitely long cylindrical shells and spherical shells subjected to both internal and external pressure. On the same basis, but for different (incompressible, isotropic) material models, Haughton and Ogden (1979) examined in some detail the bifurcation behaviour of circular cylindrical tubes of finite length under internal pressure and axial loading.…”