in this paper, the deformation of a thick-walled circular cylindrical shell of incompressible isotropic elastic material is considered. the shell, which is made of three-term strain energy function is subjected to the combined external and axial loading pressure. in order to obtain the relevant eigenvalues, which is the main objective of the work, the incremental equilibrium equations are so...

The Boussinesq equations for Rayleigh–Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to timedependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25000, the axisymmetric flow becomes unstable to standing or travelling azimu...

The Boussinesq equations for Rayleigh–Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25 000, the axisymmetric flow becomes unstable to standing or travelling azi...

The bifurcation structure is presented for an axisymmetric swirling flow in a constricted pipe, using the pipe geometry of Beran and Culick [J. Fluid Mech. 242, 491 (1992)]. The flow considered has been restricted to a two-dimensional parameter space comprising the Reynolds number Re and the relative swirl V, of the incoming swirling flow. The bifurcation diagram is constructed by solving the t...

Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat et al. J. Fluid Mech. 438, 363 2001 , which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynami...

We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Hölder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetr...

Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equili...

Streamline patterns and their local and global bifurcations in a two-dimensional peristaltic flow for an incompressible Newtonian fluid have been investigated. An analytical solution for the stream-function is found under a long-wavelength and low-Reynolds number approximation. The problem is solved in a moving coordinate system where a system of nonlinear autonomous differential equations can ...

I Buckling and postbuckling behavior under axial compression is analyzed for a long circular cylinder containing an axisymmetric imperfection. Bifurcation I stresses are investigated for all possible modes, both periodic and aperiodic, and postbuckling analysis reveals that bifurcation is not always associated with a loss of load-carrying capacity. The results provide some theoretical foundatio...

A study is presented of the post-buckling behavior and imperfection-sensitivity of complete spherical shells subject to uniform external pressure. The study builds on and extends the major contribution to spherical shell buckling by W.T. Koiter in the 1960’s. Numerical results are presented for the axisymmetric large deflection behavior of perfect spheres followed by an extensive analysis of th...