The nonlinear axisymmetric post-buckling behaviour of perfect, thin, elastic spherical shells subject to external pressure and their asymmetric bifurcations are characterized, providing results for a structure/loading combination with an exceptionally nonlinear buckling response. Immediately after the onset of buckling, the buckling mode localizes into a dimple at the poles. The relations among...

We consider the instability of the steady, axisymmetric thermocapillary convection in cylindrical liquid bridges. Finite-difference method is applied to compute the steady axisymmetric basic solutions, and to examine their linear instability to three-dimensional modal perturbations. The numerical results show that for liquid bridges of O(1) aspect ratio Γ (=length/radius) the first instability ...

A study of the three-dimensional axisymmetry-breaking instability of an axisymmetric convective #ow associated with crystal growth from bulk of melt is presented. Convection in a vertical cylinder with a parabolic temperature pro"le on the sidewall is considered as a representative model. The main objective is the calculation of critical parameters corresponding to a transition from the steady ...

The paper presents the results of a study bifurcation axisymmetric equilibrium forms round plates under various conditions for fixing outer edge. It is shown that case sliding edge, analytical, asymptotic and finite element approaches give close results. When edge plate hinged, buckling to non-axisymmetric state occurs at much higher load with formation smaller number waves than boundary condit...

Landau solutions are special to the stationary incompressible Navier-Stokes equations in three dimensional space excluding origin. They self-similar and axisymmetric with no swirl. In fact, any smooth solution must be a solution. effort of extending this result one for class pointwise scale-invariant bound $|u(x)|\leq C_0|x|^{-1}$ some $C_0>0$, we consider discretely solutions, investigate exis...

We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced Energy Momentum for the stability analysis and the treatment of axisymmetric bodies. We explicitly show the existence of new relative equilibria and study thei...

This paper reexamines orientations of shear bands (fault angles) predicted by a theory of shear localization as a bifurcation from homogeneous deformation. In contrast to the Coulomb prediction, which does not depend on deviatoric stress state, the angle between the band normal and the least (most compressive) principal stress increases as the deviatoric stress state varies from axisymmetric co...

The transition from laminar to complex spatio-temporal dynamics of a plume driven by a localized heat source at the bottom of an enclosed cylinder whose sidewall is maintained at a fixed temperature which varies linearly up the wall is studied. Restricting the dynamics to the axisymmetric subspace, the first instability is to a puffing state. However, for smaller Grashof numbers, the plume beco...