Dynamic buckling

In designing axi-symmetric shell structures such as large-type cooling towers, it is necessary to predict the vibration responses to various external forces. The authors describe the linear vibration response analysis of axi-symmetric shell structures by the finite element method. They also analyze geometric nonlinear (large deflection) vibration which poses a problem in thin shell structures causes dynamic buckling in cooling towers. They present examples of numerical calculation and study the validity of this method. 11 refs, cited. 

It seems that the question of dynamic buckling is still to some extent discussed in the literature, even though the variable temperature experiments seemed to have proven beyond doubt that the flat dimer structure in room temperature experiments is a dynamic effect. Given the large distance between tip and surface, the assumption of current induced buckling [55] or buckling due to tip-surface interactions [56] lack experimental and theoretical confirmation. 

Carbon nanotube. Molecular dynamics. Buckling, Shell... 

The other striking feature of nanotubes is their extreme stiffness and mechanical strength. Such tubes can be bent to small radii and eventually buckled into extreme shapes which in any other material would be irreversible, but here are still in the elastic domain. This phenomenon has been both imaged by electron microscopy and simulated by molecular dynamics by lijima et al. (1996). Brittle and ductile behaviour of nanotubes in tension is examined by simulation (because of the impossibility of testing directly) by Nardelli et al. (1998). Hopes of exploiting the remarkable strength of nanotubes may be defeated by the difficulty of joining them to each other and to any other material. 

The most common conditions of possible failure are elastic deflection, inelastic deformation, and fracture. During elastic deflection a product fails because the loads applied produce too large a deflection. In deformation, if it is too great it may cause other parts of an assembly to become misaligned or overstressed. Dynamic deflection can produce unacceptable vibration and noise. When a stable structure is required, the amount of deflection can set the limit for buckling loads or fractures. 

Fig. 3. In vitro TIRF microscopy can also be employed to visualize complex protein-actin interactions. By attaching F-actin elongating proteins on beads (e.g., VASP, left) or on coverslips (e.g., formins, middle, processive elongation of single filaments can be visualized and analyzed. In these cases, filament buckling (white arrowdf can be observed due to the insertional assembly of actin monomers at the anchored filament barbed end (white circied). Moreover, the dynamic formation of complex structures such as filament bundles induced by VASP, fascin, or other actin-binding proteins in solution can be monitored in real time.

Structural mechanics analyses are used to determined design variables such as displacements, forces, vibrations, buckling loads, and dynamic responses, including application of corresponding special areas of structural mechanics for simple structural elements. General purpose finite element programs such as NASTRAN are used for the structural analysis of complex structural shapes, large structures made from simple structural elements. And structural parts made from combinations of simple elements such as bars, rods and plates. 

Fig. 1.9 Molecular models using Tersoff potentials allow for study of a wide range of static, dynamic and thermodynamics properties of carbon forms here carbon nanotubules are shown in several phases of buckling [389]. Image courtesy Prof. Junichiro Shiomi and Dn Takuma Shiga, Department of Mechanical Engineering, University of Tokyo...

Keywords Bending instability of liquid jets Buckling of liquid jets Electrified liquid jets Electrospinning Elongational rheology Newtonian and rheologically complex liquids Quasi-one-dimensional equations of the dynamics of liquid jets Small and finite perturbations Viscoelastic polymeric liquids... 

Zhang Chen-Li, Shen Hui-Shen. (2006). Buckling and Postbuckling Analysis of Single-Walled Carbon Nanotubes in Thermal Environments Via Molecular Dynamics Simulation. Carbon, 44, 2608-2616. 

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