Past, present and future mathematical models for buildings (i)

This is the first of two articles presenting a detailed review of the historical evolution of mathematical models applied in the development of building technology, including conventional buildings and intelligent buildings. After presenting the technical differences between conventional and intelligent buildings, this article reviews the existing mathematical models, the abstract levels of these models, and their links to the literature for intelligent buildings. The advantages and limitations of the applied mathematical models are identified and the models are classified in terms of their application range and goal. We then describe how the early mathematical models, mainly physical models applied to conventional buildings, have faced new challenges for the design and management of intelligent buildings and led to the use of models which offer more flexibility to better cope with various uncertainties. In contrast with the early modelling techniques, model approaches adopted in neural networks, expert systems, fuzzy logic and genetic models provide a promising method to accommodate these complications as intelligent buildings now need integrated technologies which involve solving complex, multi-objective and integrated decision problems

Past, present and future mathematical models for buildings (ii)

This article is the second part of a review of the historical evolution of mathematical models applied in the development of building technology. The first part described the current state of the art and contrasted various models with regard to the applications to conventional buildings and intelligent buildings. It concluded that mathematical techniques adopted in neural networks, expert systems, fuzzy logic and genetic models, that can be used to address model uncertainty, are well suited for modelling intelligent buildings. Despite the progress, the possible future development of intelligent buildings based on the current trends implies some potential limitations of these models. This paper attempts to uncover the fundamental limitations inherent in these models and provides some insights into future modelling directions, with special focus on the techniques of semiotics and chaos. Finally, by demonstrating an example of an intelligent building system with the mathematical models that have been developed for such a system, this review addresses the influences of mathematical models as a potential aid in developing intelligent buildings and perhaps even more advanced buildings for the future

Numerical simulation of the solidification of a beam blank in the mould

peer reviewedThe stability of the casting process and the wear of the mould as well as the quality of the product depend strongly on the mould design. This is particularly true when considering the production of beam blanks. If the mould is too tight, thermal contraction can generate considerable contact forces between the product and the mould on the inner surfaces of the flanges. If it is not tight enough, the thermal coupling between the mould and the beam blank is not sufficient to allow the solidification of a skin of the required thickness upon exit from the mould. A finite element model was developed to assist in the mould design. This model takes both the thermal and mechanical interaction between the mould and the product into account. The effect of solidification is implicitly included in the (thermal) finite element formulation while the ferro-static pressure is applied by the means of a specially developed element. The model was applied to a medium gage beam blank cast at ProfilARBED Differdange. The skin thickness as well as the localisation of the wear of the mould predicted by the model are in good agreement with observations made in industrial practice

Modélisation des phénomènes thermomécaniques dans une lingotière de coulée continue

La qualité de surface et interne des produits de coulée continue dépend beaucoup du comportement du brin dans la lingotière durant la solidification. Parmi les paramètres susceptibles d’influencer ce comportement, la conicité de la lingotière tient une place éminente. Nous avons développé un modèle 2D thermomécanique du brin dans la lingotière utilisant le code d’éléments finis Lagamine. Une tranche du brin est définie perpendiculairement à l’axe de coulée avec les conditions limites suivantes : symétrie suivant les axes principaux de la section (double symétrie), contact unilatéral avec frottement le long de la surface de la lingotière et température de lingotière imposée. L’approche utilise l’état plan généralisé qui permet une épaisseur variable dans le temps et fournit une équation pour l’équilibre des forces verticales. La pression ferrostatique est également prise en compte. En raison de sa conicité, la géométrie de la lingotière n’est pas constante, mais varie lorsque la tranche progresse vers le bas. Les conditions d’échange thermique sont également modifiées, en fonction des conditions de contact entre le brin et la lingotière. Après un travail de deux années, le modèle est à présent en cours de validation pour prédire le comportement du brin dans différentes configurations (forme de la section, conicité, etc.).Modelling of the thermomechanical phenomena in a mould of continuous casting. The surface and internal quality of continuous cast products depends very much on the behaviour of the strand in the mould during solidification. Among the parameters likely to influence this behaviour, the mould taper takes a prominent part. We developed a thermomechanical 2D model of the strand in the mould using the finite element code LAGAMINE. A slice of the strand is defined perpendicularly to the casting axis with the following boundary conditions: symmetry with principal axes of the section (double symmetry), frictional unilateral contact with the mould surface and imposed mould temperature. The approach uses the generalised plane strain state that allows a variable thickness of the slice in time, and provides one equation for the vertical force equilibrium. The ferrostatic pressure is also taken into account. Due to the mould taper, the geometry of the mould is not constant, but varies as the slice is moving down. The thermal exchange conditions are also modified, depending on contact condition between the strand and the mould. After a two years work, the model is now in checking to predict behaviour of the strand in different cases (shape of the strand cross section, mould taper, etc.)

Modelling of the cooling of steel pieces

peer reviewe

Generation on Internal and Residual Stresses in Steel Workpieces during cooling

peer reviewe

Finite element modeling of thermo-mechanical behaviour of a steel strand in continuous casting

peer reviewedSurface and internal quality of continuous cast products depends very much upon the behaviour of the strand in the mould. Among the parameters likely to influence this behaviour, the mould taper takes a prominent part. In order to understand better the influence of this parameter, we have build up a thermo-mechanical finite element model. the model includes an elasto-visco-plastic law to describe the behaviour of steel from liquid to solid state, a thermo-mechanical element that takes into account thermal expansion and mechanical behaviour of the strand, a unilateral contact element, a mobile rigid boundary element to model the mould and its taper and an adapted loading element to model the ferrostatic pressure according to the liquid or solid state