Stable cross sections of multiwalled carbon nanotubes subjected to electron-beam irradiation are investigated in the realm of the continuum mechanics approximation. The self-healing nature of sp 2 graphitic sheets implies that selective irradiation of the outermost walls causes their radial shrinkage with the remaining inner walls undamaged. The shrinking walls exert high pressure on the interior part of nanotubes, yielding a wide variety of radial-corrugation patterns ͑i.e., circumferentially wrinkling structures͒ in the cross section. All corrugation patterns can be classified into two deformation phases for which the corrugation amplitudes of the innermost wall differ significantly.

The elastic radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investigated within the continuum elastic approximation. The thin-shell theory, with accurate elastic constants and interwall couplings, allows us to estimate the critical pressure above which the original circular cross-section transforms into radially corrugated ones. The emphasis is placed on the rigorous formulation of the van der Waals interaction between adjacent walls, which we analyze using two different approaches. Possible consequences of the radial corrugation in the physical properties of pressurized MWNTs are also discussed.

The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in conjunction with variational principles, is presented. In the exact formulation, axisymmetric and inextensional assumptions are not used initially and the elastic medium is modelled as a Winkler foundation, i.e. using uncoupled radial springs with a constant foundation modulus that is independent of wave numbers of shell buckling modes. Simplified approximations based on a Rayleigh-Ritz approach are also introduced for critical buckling pressure and mode number with a considerable degree of accuracy. Characteristic modal shapes are demonstrated for a wide range of material and geometric parameters. A phase diagram is established to obtain the requisite thickness to radius, and stiffness ratios for a desired mode profile. The present exact formulation can be readily extended to apply to more general cases of nonaxisymmetric buckling problems.

The present paper investigates the cross-sectional morphology of Multiwalled Carbon Nanotubes (MWNTs) restrained radially and circumferentially by an infinite surrounding elastic medium, subjected to uniform external hydrostatic pressure. In this study, a two-dimensional plane strain model is developed, assuming no variation of load and deformation along the tube axis. We find some characteristic cross-sectional shapes from the elastic buckling analysis. The effect of the surrounded elastic medium on the crosssectional shape which occurs due to pressure buckling is focused on by the comparison with the shape for no elastic medium case in our discussion. It is suggested that in no embedded elastic medium cases, the cross-sectional shapes of inner tubes maintain circle or oval; on the other hand, an embedded medium may cause inner tube corrugation modes especially when the number of shells for MWNTs is small.

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The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are presented. A model based on small deflection thin shell theory, the equations of which are solved using exact methods in conjunction with variational principles, is presented. In the current formulation, axisymmetric and inextensional assumptions are not used initially and the elastic medium is modelled as a Winkler foundation, i.e. using uncoupled radial springs with a constant foundation modulus that is independent of wave numbers of shell buckling modes. Critical buckling pressures and characteristic modal shapes are demonstrated for a wide range of material and geometric parameters. A phase diagram is established to obtain the requisite thickness to radius, and stiffness ratios for a desired mode profile. The present formulation can be readily extended to apply to more general cases of non-axisymmetric buckling problems.