Design with Constructal Theory

Bejan, Adrian; Lorente, Sylvie

doi:10.1002/9780470432709

Cited by 488 publications

(144 citation statements)

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“…These studies have a significant importance because they played a basic and a starting point role for the extension and application of Constructal Theory to problems in engineering and other branches of science, Bejan & Lorente [40] and Ghodoossi [41]. Moreover, Constructal Theory has been employed to explain deterministically the generation of shapes in nature, and the lesson taught by the Bejan's Constructal Theory is: geometry matters.…”

Section: Constructal Design Methodsmentioning

confidence: 99%

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Numerical evaluation of the effect of type and shape of perforations on the buckling of thin steel plates by means of the constructal design method

Lorenzini¹,

Helbig²,

Silva³

et al. 2016

IJHT

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Thin steel plates -with or without cutouts -are structural components largely used in several engineering applications as buildings, bridges, ships, airplanes and automobiles. However, if an axial compressive load is imposed to these panels an undesired instability phenomenon can occur: buckling. At a certain load magnitude the limit stress is reached and the plate suffers lateral displacements (out of plane) indicating the buckling occurrence. In plates an elastic buckling or an elastoplastic buckling can occur, depending on dimensional, constructive or operational aspects. Therefore, in the present work, the Constructal Design method was adopted to investigate the influence of the type and shape of the cutout in the plate buckling. To do so, by means the Finite Element Method (FEM), computational models were developed to simulate the elastic (linear) and elasto-plastic (nonlinear) plate buckling. Square and rectangular thin steel plates, simply supported in its four edges, with a centered cutout, were analyzed, being the objective function to maximize the buckling limit stress, avoiding the plate buckling occurrence. The square and rectangular plates have a ratio H/L (ratio between height and length of the plate) of 0.5 and 1.0, respectively. A value of 0.2 for the cutout volume fraction (ratio between the cutout volume and the total plate volume) was adopted for different types of cutout: diamond, longitudinal hexagonal, transversal hexagonal, elliptical, and rectangular. The cutout shape variations were produced by the H0/L0 degree of freedom (which relates the characteristic dimensions of the cutout). The results showed that the cutout shape variation has a fundamental influence in the plate buckling behavior, determining if the buckling is elastic or elasto-plastic, allowing the definition of a buckling stress limit curve for each studied cutout type. In addition, it was observed that the Constructal Design method conduct to the definition of optimal geometries, reaching buckling stress limit improvements around 100%.

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Section: Constructal Design Methodsmentioning

confidence: 99%

“…Being this natural tendency of flowing with better and better configuration is the essence of the Constructal Law, Bejan & Lorente [40].…”

Section: Constructal Design Methodsmentioning

confidence: 99%

Numerical evaluation of the effect of type and shape of perforations on the buckling of thin steel plates by means of the constructal design method

Lorenzini¹,

Helbig²,

Silva³

et al. 2016

IJHT

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“…Apart from number of pixels, the ratio (L/H) of 1280 to 800 is 1.67 while it is 1.33 for 1024 × 768; it means 1.67 is nearer to 1.618 than 1.33. More examples of golden ratio with respect to evolution of technological designs can be found in the book Design with Constructal Theory [5].…”

Section: Introductionmentioning

confidence: 99%

Presence of golden ratio relationships in Fe–Fe3C, Cu–Zn and Cu–Sn alloy systems

Ahmad¹

2015

Int. J. DNE

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Iron-carbon, copper-zinc and copper-tin are the three most significant alloy systems. Iron-carbon system is commonly known for steels, copper-zinc for brasses and copper-tin for bronzes. This paper shows how eutectoid, peritectic, eutectic, cementite-intermetallic, maximum solubility of carbon in ferrite, maximum solubility of carbon in austenite points in Fe-Fe 3 C phase diagram are linked to one another through golden ratio relationships. This paper also shows the ratios between proportions of Cu and Zn at maximum solubility of Zn in Cu at 456 and 0°C and the ratio of proportions of Cu-Sn at ε-Cu 3 Sn (IMC) in Cu-Zn and Cu-Sn phase diagrams, respectively, are related to golden ratio. It is predicted that the occurrence of these relationships at vital points in mentioned systems is in accordance with Constructal law of design in nature and golden ratio is the reason for uniqueness and usefulness of these points. Keywords: cementite, eutectic, eutectoid, ferrite, golden ratio, iron-iron carbide phase diagram, pearlite, peritectic 1 INTRODUCTION Iron-iron carbide phase diagram is the base of steel metallurgy. Almost every steel grade that has been developed has its roots in Fe-Fe 3 C phase diagram. From the simple construction grades of steel, for example, ASTM Grade 40 and Grade 60 [1, 2], which account for more than 65% of the total production of world steel, to a highly advanced M42 High Speed tool steel all are developed after deep understanding of iron-iron carbide phase diagram. It should be noted that eutectoid, peritectic, eutectic, cementite-intermetallic, maximum solubility of carbon in ferrite and maximum solubility of carbon in austenite points are vital in understanding the unique behavior of phases present in iron-carbon system. This paper reveals how the points of concern in Fe-Fe 3 C phase diagram are linked with one another through golden ratio.Similarly, golden ratio relationships are also found at key points of phase diagrams of copper-zinc and copper-tin alloy systems. Cu-Zn and Cu-Sn systems are other two most important systems in material science. This paper also shows that the ratios of proportions of Cu-Zn and Cu-Sn at key points in their respective phase diagrams are associated with golden ratio.

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“…According to this method 'the flow geometry is malleable and it is deduced from a principle of global performance maximization subjected to global constraints' [1,2]. This method is based on constructal theory: 'the view that flow configuration (geometry, design) can be reasoned on the basis of a principle of configuration, generation and evolution in time toward greater global flow access in systems that are free to morph' [3].…”

Section: Introductionmentioning

confidence: 99%

“…According to constructal design [3], this optimization can be subjected to two constraints, namely, the total area,…”

Section: Introductionmentioning

confidence: 99%

Constructal design of a cavity cooled by convection

Rocha¹,

Lorenzini²,

Biserni³

et al. 2010

Int. J. DNE

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This paper applies constructal design to optimize the geometry of a C-shaped cavity that penetrates into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. The total volume and the cavity volume are fixed, but the geometric lengths of the C-shaped cavity can vary. The cavity is cooled by convection heat transfer. The results indicate that the shape of C-cavity is optimal when it penetrates the conducting wall almost completely for the external ratio of the solid wall smaller than 2. For external ratio larger than 2 the optimal cavity ratio is the one that presents the largest cavity aspect ratio H 0 /L 0 . The results also show that the cavities with small or large external ratios H/L are the ones that present better performance. Keywords: cavities, constructal design, enhanced heat transfer, fins.INTRODUCTION 1 This paper reports numerically the optimization of the global performance of a C-shaped cavity that intrudes into a solid conducting wall. The optimization is conducted by applying constructal design. According to this method 'the flow geometry is malleable and it is deduced from a principle of global performance maximization subjected to global constraints' [1, 2]. This method is based on constructal theory: 'the view that flow configuration (geometry, design) can be reasoned on the basis of a principle of configuration, generation and evolution in time toward greater global flow access in systems that are free to morph ' [3].The many applications of constructal theory to generate configuration in nature, and engineering has been reviewed recently [4]. This reference shows how natural configuration -river basins, turbulence, animal design, crack in solids, earth climate, etc. − can be predicted by principle. The same principle can be applied in the engineering realm: packing of electronics, fuel cells, tree networks for transport of people, goods and information, etc.The heat transfer field has dedicated great attention to the study of fins arrays [5,6]. Another class of configurations are the open cavities. These are the regions formed between adjacent fins, and they may represent essential promoters of nucleate boiling: see, for example, the Vapotron effect [7][8][9] that occurs as a consequence of the thermal interaction between a non-isothermal finned surface and a fluid locally subjected to a transient change of phase. The significance of fins and cavities are recognized by the application of constructal method in the pursuit of best shapes of assembly of fins [10,11] and cavities [12][13][14].In this paper we apply constructal design to optimize the geometry of the C-shaped cavity. According to constructal design, the cavity shape is free to change subject to volume constraints in the pursuit of maximal global performance. The global performance indicator is the global thermal resistance between the volume of the entire system (cavity and solid) and the surroundings. For ...

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Design with Constructal Theory

Cited by 488 publications

References 32 publications

Numerical evaluation of the effect of type and shape of perforations on the buckling of thin steel plates by means of the constructal design method

Numerical evaluation of the effect of type and shape of perforations on the buckling of thin steel plates by means of the constructal design method

Presence of golden ratio relationships in Fe–Fe3C, Cu–Zn and Cu–Sn alloy systems

Constructal design of a cavity cooled by convection

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