Alphose Zingoni

Group-theoretic insights on the vibration of symmetric structures in engineering

Group theory has been used to study various problems in physics and chemistry for many years. Relatively recently, applications have emerged in engineering, where problems of the vibration, bifurcation and stability of systems exhibiting symmetry have been studied. From an engineering perspective, the main attraction of group-theoretic methods has been their potential to reduce computational effort in the analysis of large-scale problems. In this paper, we focus on vibration problems in structural mechanics and reveal some of the insights and qualitative benefits that group theory affords. These include an appreciation of all the possible symmetries of modes of vibration, the prediction of the number of modes of a given symmetry type, the identification of modes associated with the same frequencies, the prediction of nodal lines and stationary points of a vibrating system, and the untangling of clustered frequencies.

Stresses and deformations in egg-shaped sludge digestors: membrane effects

Relatively recently, egg-shaped containment shells have been adopted as sludge digestor tanks at sewage treatment installations, in place of the conventional squat cylindrical tank with a dome-shaped roof closure. The advantages are superior mixing efficiency resulting in less accumulation of deposits at the bottom, easier removal of the deposits that do settle at the bottom and of the crust that forms at the surface of the sludge, and reduced heat losses. In the long term, the reduced maintenance and operational costs offset the higher initial costs of construction, making egg-shaped digestor shells a more attractive option than conventional cylindrical tanks. Despite many egg-shaped sludge digestors having been built in various countries worldwide, their widespread adoption is hampered by the lack of detailed and systematic information on their structural analysis and design. The present study attempts to reduce this gap in the literature by (i) developing a simple, effective and systematic structural-analysis procedure for egg-shaped sludge digestor tanks of a certain practical combination of shell geometries, (ii) presenting usable closed-form analytical results for stresses and deformations throughout the digestor, and (iii) indicating design implications for the information of the structural engineer. In this paper, the first of two, membrane effects are evaluated, and some useful results are presented and illustrated through an example. The follow-up paper (“Stresses and deformations in egg-shaped sludge digestors: discontinuity effects” J Eng Struct 23 (2001) 1373) will evaluate the discontinuity effects at the junctions of the shell components making up the digestor, present detailed analytical and numerical results, and make design recommendations.  2001 Elsevier Science Ltd. All rights reserved.

Stresses and deformations in egg-shaped sludge digestors: discontinuity effects

In the first part of this study [J. Eng. Struct. 23 (2001) 1365–1372], detailed results for stresses and deformations throughout a hydrostatically-loaded egg-shaped sludge digestor were developed on the basis of the membrane hypothesis for shells. However, and as is well-known, such results are generally unreliable around the junctions of the shell components making up the digestor. A significant amount of bending and shearing will occur in the vicinity of these junctions. In this paper, a simplified but reasonably accurate approach for quantifying discontinuity effects is developed for general shells of revolution of a certain variation of thickness along the shell meridian, and applied to the present problem of the 3-region egg-shaped digestor shell, to yield explicit closed-form results for discontinuity, and hence net, stresses throughout the digestor. These results, being very general (all parameters are kept arbitrary), enable a quick and reasonably accurate estimate of stresses in egg-shaped digestors of the type considered, and will thus be useful to the structural analyst and designer. Any desired parametric studies may also be conducted on the basis of these analytical results. Numerical results are presented, enabling some observations to be made and design recommendations proposed for eggshaped digestors.  2001 Elsevier Science Ltd. All rights reserved.

Discontinuity effects at cone-cone axisymmetric shell junctions

In this paper, the problem of a conical shell axisymmetrically intersecting another conical shell, such that the vertices of the cones lie on opposite sides of the plane of intersection, is considered, and associated discontinuity effects quantified for arbitrary loading and geometric parameters of the intersecting cones. The ensuing very practical closed-form results are based on the one-term asymptotic-series solution for the axisymmetric bending of a non-shallow conical shell, and are intended for use in the quick evaluation of stresses and deformations in double-cone pressure vessels, as well as liquid-retaining vessels with intersecting conical portions. As an example of the application of the developed formulation, the stress distribution in a large liquid-filled elevated rhombic tank is evaluated. The stresses obtained on the basis of the closed-form analytical approach developed in the paper are shown to be in good agreement with those obtained from a finite-element analysis, confirming the reliability of the presented formulation.

Parametric stress distribution in shell-of- revolution sludge digesters of parabolic ogival form

Egg-shaped sludge digesters have become popular in relatively recent times owing to their superior functional performance and lower maintenance costs in comparison with conventional cylindrical digesters. These innovative structures are usually constructed as thin shells of revolution in concrete, designed to withstand principally the hydrostatic pressure loading from the contained liquid. As regards the precise shape of the egg shell, a number of mathematical shell surfaces may be envisaged, and the stress distribution will very much depend on the chosen form. In this paper, it is desired to explore the possible adoption of the parabolic ogival shell as a sludge digester. The stress distribution in such a shell is expressed in terms of a single governing parameter ξ, greatly facilitating the investigation. For various values of ξ covering the most practical range for egg-shaped digester shells, recommendations are made regarding the positioning of supports. Taking into account maximisation of tank capacity, minimisation of peak stress resultants in the shell, and ease of prestressing, the best range of ξ for parabolic ogival digester shells is identified. The overall conclusion is that from a structural and functional point of view, the parabolic ogival profile is suitable for adoption in the design of egg-shaped concrete sludge-digester shells.

Advances in damage detection, repair and rehabilitation of engineering structures

This special section of Engineering Structures contains a selection of papers presented at SEMC 2001, the International Conference on Structural Engineering, Mechanics and Computation, held in Cape Town (South Africa) from 2 to 4 April 2001. Repair, rehabilitation and strengthening of existing infrastructure has become increasingly important within the construction and building industry, not only in Europe, North Africa, the Middle East and Asia, where a considerable proportion of the civil-engineering infrastructure is several hundred years old, but also throughout the rest of the world where buildings, bridges and other structures constructed in the past 50 years are now requiring attention to prolong their service life, or to render them more resistant to fire, earthquake, storm and blast hazards. To ensure the greatest possible effectiveness of such measures at affordable cost, new techniques require to be developed, and much research effort is being expended in this regard. It is also clear that repair and maintenance strategies are most effective when there are reliable mechanisms for detecting or diagnosing structural damage before component or sub-structure failure occurs, which has been another important area of study and investigation. The opening paper by Mazzolani and Mandara addresses the important problem of the restoration and rehabilitation of buildings, bridges, monuments and other structures of historical and/or cultural importance. Metal-based solutions for structural rehabilitation, ranging from stainless steels and aluminium alloys to sophisticated shape-memory alloys, are discussed and their advantages highlighted. Not only are such solutions shown to be applicable to strengthening for static loads, but they may also offer effective seismic protection to buildings when employed in energy dissipation systems. Examples of recent projects in which these new technologies have been applied are drawn mainly from Italy. The contribution by Ko, Sun and Ni outlines the development of a three-stage scheme for the identification of damage in large cable-stayed bridges, by reference to a case study of one such structure in Hong Kong. This interesting approach makes use of an auto-associative memory neural network to detect damage, two modal