Numerical analysis of axisymmetric shells by one-dimensional continuum elements suitable for high frequency excitations

Axisymmetric shells are analyzed by means of one-dimensional continuum elements by using the analogy between the bending of shells and the bending of beams on elastic foundation. The mathematical model is formulated in the frequency domain. Because the solution of the governing equations of vibration of beams are exact, the spatial discretization only depends on geometrical or material considerations. For some kind of situations, for example, for high frequency excitations, this approach may be more convenient than other conventional ones such as the finite element method.

Numerical treatment of thick shells with holes

A Boundary Integral Equation Method (B.I.E.M.)formulation is presented. After a general situation of the method among other usual numerical ones, the possibilities of discretization are developed. As this is done only in the boundary the treatment of tridimensional problems is greatly simplified in comparison with other methods. Some results on a simple shell with holes are finally presented.

An algorithm for graphical computer results in shells

A Finite Element technique to interpolate general data (function values and its derivatives) has been developped. The technique can be considered as a generalized solution of the classical polynomial interpolation, because the condition for the interpolating function to be a polynomial is replaced by a minimizing condition of a given “smoothing” functional. In this way it is possible to find interpolating functions with a given level of continuity according to the class of finite elements used. Examples have been presented in order to assess the accuracy and efficiency of the procedure.

Application of global numerical procedures to the analysis of shells

Examples of global solutions of the shell equations are presented, such as the ones based on the well known Levy series expansion. Also discussed are some natural extensions of the Levy method as well as the inherent limitations of these methods concerning the shell model assumptions, boundary conditions and geometric regularity. Finally, some open additional design questions are noted mainly related to the simultaneous use in analysis of these global techniques and the local methods (like the finite elements) to finding the optimal shell shape, and to determining the reinforcement layout.

Design of Reinforcement in Concrete Shells: a unified Approach

The problem of design/verification of reinforcement in concrete shells is reviewed. Methods of analysis are classified, and the elastic-plastic approach is described in detail in the general case of shells subjected to both bending and membrane action. The procedure is then reduced to membrane shells (applicable also to concrete walls) and to pure bending, as in the case of plates. The procedure, which is based on previous research,generally requires the use of a desk-top computer.

Dynamic analysis of translational shells

In this paper a dynamic analysis of transnational shells is presented. The general linear shell theory is used in conjunction with additional shallow and curved plate approximations. In order to apply some type of extended Levy solution, the shell is assumed to be limited by a rectangular plan form, with two opposite edges simply supported (gable boundary conditions). First, the shells free vibrations are studied in the usual way, obtaining for each Fourier term the natural frequencies as solutions of a transcendental equation. However, solving these equations arises enormous computational difficulties. This paper deals specifically with this problem, trying to reduce its dimension by a discretization procedure. In the shell dynamic characteristics, namely the mass. The shell mass is lumped along a family of coordinate lines. Therefore, the natural frequencies for each harmonic term can be found from the solution of a typical matrix eigenvalues problem and standard numerical techniques can be applied. The shell response to forced vibrations, particularly to earthquake excitation, can be determined by using conventional procedure either in the time or in the frequency domain. Finally, extending the above procedure, any system of translational shells under dynamic loading can be studied. Then, by using matrix methods, a general computer program is written and applied to some illustrative examples. Numerical results has been obtained in two cases: circular cylindrical shell and box girder bridge.

Protein diagenesis in Patella shells: implications for amino acid racemisation dating

Se analiza la racemización de aminoácidos en proteínas inter e intracristalinas en conchas de Patella y su utilización como herramienta geocronológica, fundamentalmente empleadas en yacimientos arqueológicos.The inter- and intra-crystalline fractions of Patella vulgata limpets recovered from archaeological sites in Northern Spain (covering Neolithic, Mesolithic, Magdalenian, Solutrean, and Aurignacian periods) were examined for amino acid composition and racemisation over time. The calcitic apex and rim areas of the shells were found to probably be composed of similar proteins, as the D/L values and amino acids were comparable and varied in the same way with increasing age; however, the mineral structures present in these areas differed. The aragonitic intermediate part of the shell showed a distinctly different amino acid composition and mineral structure. The main protein leaching from the inter-crystalline fraction occurred within the first 6000 yr after the death of the organism. In contrast, the intra-crystalline fraction — comprised of a different protein composition than the inter-crystalline fraction — appeared to behave as a closed system for at least 34 ka, as reflected by the lack of a significant decrease in the amino acid content; however, changes in the amino acid percentages occurred during this period. The concentration of aspartic acid remained almost constant with age both in inter- and intra-crystalline proteins, and its contribution to the total amino acid content increased with age at the expense of other amino acids such as glutamic acid, serine, glycine and alanine. Temperature is thought to play a key role in the amino acid racemisation of P. vulgata and could explain why in the localities belonging to the Gravettian and Solutrean period, which formed during relatively cold conditions, D/L values were similar to those detected in shells from sites formed during the Magdalenian.

Dynamic analysis of translational shells

This paper presents a Levy-type solution for the natural frequencies of translational shells. A computer program in FORTRAN IV language corresponding to this solution is described. This direct solution is compared with some indirect solutions utilising Galerkin and Rayleigh methods. An extension to the study of forced vibrations is outlined.

Thermal decomposition of the different particles size fractions of almond shells and olive stones. Thermal behaviour changes due to the milling processes

The aim of this study is to investigate the effect of particle size on the non-isothermal pyrolysis of almond shells (AS) and olive stones (OS) and to show possible differences in the composition of the different fractions obtained after milling and sieving. The results obtained from the study of different particle size of AS and OS samples show significant differences in the solid residue obtained and in the shape and overlapping degree of the peaks, especially with the smaller particle size. These differences can be due to different factors: (a) the amount of inorganic matter, which increases as particle size decreases, (b) heat and mass transfer processes, (c) different sample composition as a consequence of the milling process which may provoke changes in the structure and the segregation of the components (in addition to the ashes) increasingly changes the composition of the sample as the particle size decreases.

Monography of the family Unionidae, or Naiades of Lamarck (fresh water bivalve shells,) of North America, : illustrated by figures drawn on stone from nature. / by T.A. Conrad ...

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