A justification of the Marguerre-von Kármán equations

The method of asymptotic expansions, with the thickness as the small parameter, is applied to the general three-dimensional equations for the equilibrium of nonlinearly elastic shells with specific geometries, subjected to suitable loadings and boundary conditions. Then it is shown that the leading term of the expansion is the solution of a system of equations equivalent to those of Marguerre-von Karman (the case of a clamped shell is also considered). In addition, without making any a priori assumption regarding the variation of the unknowns across the thickness of the shell, it is found that the displacement field is of Kirchhoff-Love type, and that the stresses have polynomial variations with respect to the thickness.This approach clearly delineates the types of three-dimensional loadings, boundary conditions, and shallowness, for which a three-dimensional problem may be deemed asymptotically equivalent to a two-dimensional shallow shell model.Dedicated to Professor Joachim A. Nitsche on the occasion of his sixtieth birthday     

Application of the boundary-domain element method to the pre/post-buckling problem of von Kármán plates

Based on the BEM formulations for the finite deflection problem of von-Kármán-type plates, this paper presents an incremental boundary-domain element method for the pre/post-buckling problem of thin elastic plates. As the governing equations involve the coupled in-plane and out-of-plane deformations as the nonlinear terms, the boundary integral equations are formulated in terms of the increment by using the fundamental solutions for the linear parts of the differential operators. Some of the innovations are made in order to improve the accuracy and accelerate the convergence of the solution procedure. The load-incrementation method and also the arc-length-incrementation method are employed for each incremental step. Numerical analysis is carried out and the results are compared with the available analytical solutions to demonstrate the effectiveness of the proposed method.     

Absolute instability of the von Kármán, Bödewadt and Ekman flows between a rotating disc and a stationary lid

The stability of a family of boundary-layer flows, which includes the von Kármán, B?dewadt and Ekman flows for a rotating incompressible fluid between a rotating disc and a stationary lid, is investigated. Numerical computations with the use of a spectral method are carried out to analyse absolute and convective instability. It is shown that the stability of the system is enhanced with a decrease in distance between the disc and the lid.     

Active primary mirror support for the 2.1-m telescope at the San Pedro Mártir Observatory

We have designed and installed a new set of actuators for the suspension of the primary mirror of the 2.1-m telescope at San Pedro Mártir. This active optics system has allowed us to correct low-order aberrations identified by several wave-front analysis techniques.     

Reflections around ‘the cautionary use’ of the h-index: response to Teixeira da Silva and Dobránszki

Scientometrics - In a recent Letter to the Editor Teixeira da Silva and Dobránszki (2018) present a discussion of the issues regarding the h-index as an indicator for the evaluation of...     

Optimal defocus distance for testing the 2.1 m telescope at San Pedro Mártir

Within the preliminary development of a low-cost active optics system (AOS), computer simulations have been performed. The general purpose of simulations is to find an optimal scheme for the wavefront control of the primary mirror. We present results for the wavefront sensor of the AOS proposed for the 2.1 m telescope at San Pedro Mártir. The method presented here can be used for any other telescopes as well.     

Photothermal Radiometry Characterization of Limestone Rocks from the Península of Yucatán

Limestone is a sedimentary rock composed of calcium carbonate with minor amounts of silica, iron oxide, clay, dolomite, and organic material. These types of stones have been used extensively as building materials. Due to this, determination of their thermal properties is of the utmost importance. These properties depend on the microstructure and composition of each type of rock. In this study, the effect of the thermal treatment of three different limestone rocks from the Peninsula of Yucatán were studied, in the range from 100?°C up to 600?°C, using photothermal radiometry. These studies were complemented by the characterization of the crystalline phases using X-ray diffraction and effective porosity measurements performed by the saturation technique. It is shown that the thermal diffusivity, thermal conductivity, and specific heat of the limestone decrease as the temperature increases. This behavior can be related to increases in microcracks and effective porosity due to thermal treatments.     

Distribution of copper in the vicinity of a deactivated mining site at Carajás in the Amazon region of Brazil

In this work the re-fixation of mobilized copper (Cu) that was released from a deactivated pilot Cu ore dressing plant in the tropical rain forest at Southeastern Amazon (Carajás) was studied. Samples of top soils, decay leaf litter deposited on soils, roots and leaves of standing biomass were taken for the determination of Cu concentration in order to evaluate the distribution of it between different environmental compartments. In the sampling points near to the now extinct plant, total Cu concentrations in the soil reached an average value of 2140 microg g(-1) above the natural level of about 40 microg g(-1), being that bioavailable Cu estimated by DTPA method varied from 1.9 to 20.7% of this total. From the data was possible to calculate that the soil compartment is able to hold around 10 kg Cu/m(2) of ground. Roots of the standing biomass in that area hold around 17 g Cu/m(2), while the Cu content in leaves showed to be largely independent of the Cu level in the soil. Copper in the leaves was estimated as around 1g/m(2) of ground area. In turn, the decay leaf litter deposited on soil can hold about 1.6 g Cu/m(2). The terrestrial system surrounding the abandoned pilot plant demonstrated great buffer capacity to retain mobile Cu released by anthropogenic activities in the area.     

Prof. Tibor Jávor, M. Sc., PhD. DrSc

RILEM Bulletin

Prof. Tibor Jávor, M. Sc., PhD. DrSc