Practical calculations for uniform external pressure buckling in cylindrical shells with stepped walls

Metal cylindrical storage structures of significant size, such as silos and vertical-axis tanks, are almost always constructed from many short cylindrical shells of different thickness as the stress resultants on the wall progressively increase towards the base. The resulting increases in thickness are always made in step changes using metal sheets of uniform thickness because of the availability of such source materials. The result is a shell with a stepped wall with multiple discrete steps in thickness. Such shells are very susceptible to buckling under external pressure when empty or partially filled, but the buckling mode may involve only part of the shell height due to the changes in shell thickness. These changes must therefore be accounted for within the design process. A new method of determining the critical buckling resistance of such shells was recently developed, and although it has been shown to be valid, the methodology for its application in practical design has not been set out or shown. This paper therefore briefly describes the new method and demonstrates the manner in which it can be used to produce rapid, safe assessments of cylindrical shells with a wide range of patterns of wall thickness changes. The results are then suitable for direct introduction into such documents as the European standard on metal shells [1] and the ECCS Recommendations [2].

Inhomogeneous cloud coverage through the Coulomb explosion of dust in substellar atmospheres

Context. Recent observations of brown dwarf spectroscopic variability in the infrared infer the presence of patchy cloud cover. Aims. This paper proposes a mechanism for producing inhomogeneous cloud coverage due to the depletion of cloud particles through the Coulomb explosion of dust in atmospheric plasma regions. Charged dust grains Coulomb-explode when the electrostatic stress of the grain exceeds its mechanical tensile stress, which results in grains below a critical radius a < a Coul crit being broken up. Methods. This work outlines the criteria required for the Coulomb explosion of dust clouds in substellar atmospheres, the effect on the dust particle size distribution function, and the resulting radiative properties of the atmospheric regions. Results. Our results show that for an atmospheric plasma region with an electron temperature of Te = 10 eV (≈105 K), the critical grain radius varies from 10−7 to 10−4 cm, depending on the grains’ tensile strength. Higher critical radii up to 10−3 cm are attainable for higher electron temperatures. We find that the process produces a bimodal particle size distribution composed of stable nanoscale seed particles and dust particles with a ≥ a Coul crit , with the intervening particle sizes defining a region devoid of dust. As a result, the dust population is depleted, and the clouds become optically thin in the wavelength range 0.1–10 μm, with a characteristic peak that shifts to higher wavelengths as more sub-micrometer particles are destroyed. Conclusions. In an atmosphere populated with a distribution of plasma volumes, this will yield regions of contrasting radiative properties, thereby giving a source of inhomogeneous cloud coverage. The results presented here may also be relevant for dust in supernova remnants and protoplanetary disks.