Stability experiments on the strongest columns and circular arches

Wilson, James F.; Holloway, D. M.; Biggers, Sherrill B.

doi:10.1007/bf02320583

Cited by 22 publications

(4 citation statements)

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“…Hence, its buckling resistance can be enhanced by moving material away from its ends, towards its center. This result has been established both theoretically31 and experimentally32. We elaborate on this result further in Section Comparison with the Clausen profile .…”

supporting

confidence: 69%

A new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia that guards against buckling instability

Monn

Kesari

2017

Sci Rep

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We identify a new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia. The skeletal elements, known as spicules, are millimeter-long, axisymmetric, silica rods that are tapered along their lengths. Mechanical designs in other structural biomaterials, such as nacre and bone, have been studied primarily for their benefits to toughness properties. The structure-property connection we identify, however, falls in the entirely new category of buckling resistance. We use computational mechanics calculations and information about the spicules’ arrangement within the sponge to develop a structural mechanics model for the spicules. We use our structural mechanics model along with measurements of the spicules’ shape to estimate the load they can transmit before buckling. Compared to a cylinder with the same length and volume, we predict that the spicules’ shape enhances this critical load by up to 30%. We also find that the spicules’ shape is close to the shape of the column that is optimized to transmit the largest load before buckling. In man-made structures, many strategies are used to prevent buckling. We find, however, that the spicules use a completely new strategy. We hope our discussion will generate a greater appreciation for nature’s ability to produce beneficial designs.

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confidence: 69%

A new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia that guards against buckling instability

Monn

Kesari

2017

Sci Rep

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“…The field of strength of materials is rich in examples of optimal shapes and structures for prescribed stiffness with minimum mass, or prescribed mass with maximum stiffness (Beer et al, 2002), e.g. the cantilever beam (Galilei, 1960) and the column in end compression (Wilson et al, 1971). In heat transfer, there are many examples of shape optimization with a single objective.…”

Section: Flow and Strength Optimization Of Geometrymentioning

confidence: 99%

Constructal multi-scale and multi-objective structures

Bejan

Lorente

2005

Int. J. Energy Res.

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SUMMARYThis is a review of recent progress on constructal design made in two directions: multi-scale flow structures, and multi-objective design. The first direction is associated with the maximization of heat transfer rate density in a fixed volume in the limit of decreasing length scales, where boundary layers touch, and optimized channels are no longer slender. In the first example of this type, spacings are optimized based on the intersection of asymptotes method. In the second, the heat transfer density is further increased by placing progressively smaller plates in the entrances of the channels formed by the first generation of plates. In the third example, the placement of discrete heat sources on a vertical wall with natural and forced convection is optimized. The second direction is the discovery of architectures that result from two competing objectives, for example, mechanical strength and thermal insulation. It is shown that the internal configuration of a cavernous brick wall can be deduced from the clash between the two objectives. The same concept can be used to optimize the shape and structure of support beams that must be strong and, at the same time, must resist sudden attack by intense heating. Copyright # 2005 John Wiley & Sons, Ltd.KEY WORDS: constructal theory; spacings; multi-scale; hierarchical; packing; heat sources; multiobjective; mechanical strength; resistance to terrorist attack CONSTRUCTAL THEORY AND DESIGNA newly emerging body of work (Bejan, 2000;Bejan et al., 2004) is focusing attention on the principle-based generation of optimal geometry (configuration, architecture) in flow systems endowed with global objectives and global constraints. In the beginning of this process, the system geometry is missing. The acquisition of geometry is the mechanism by which the system meets its global objectives under constraints. This mechanism is at work not only in engineered systems but also in naturally occurring systems, animate and inanimate. The view that geometry

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“…First of all, many researchers have studied the column problems: Keller (1960) investigated the strongest column, where the strongest column was defined as the column having the largest buckling load among those having a constant volume; Keller and Niordson (1966) studied the tallest optimal column rather than the strongest one, where the tallest column was defined as the constant volume column having the largest column length without buckling; Taylor (1967) researched the strongest column using energy theory. Wilson et al (1971) investigated and experimented the taper functions of the cross sectional depth of the strongest column with a triangular crosssection; Cox and Overton (1992) studied optimal shapes of the cross-section of a column to resist buckling; Lee and Oh (2000) investigated the cross sectional shape of the strongest column using large deflection theory; Lee et al (2006) studied the cross sectional shape of the strongest column using the dynamic concept rather than the static one. Typical works on the strongest beam include studies by Lee et al (2009a), in which the shear effect was not included and only simple beams were considered in the numerical examples; Lee et al (2009b) also investigated the strongest arches whose maximum extreme stresses in bending are minimized.…”

Section: Introductionmentioning

confidence: 99%

Minimum-weight beams with shear strain energy

Lee

Oh²,

Lee

et al. 2011

KSCE J Civ Eng

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This paper deals with minimum-weight beams built with the minimum volume of beam material that can sustain the subjected load. In order to build a minimum-weight beam, the geometry of the strongest beam is analyzed, for which the values of the maximum beam behaviors are minimized at the given volume of material. For the structural analysis of such a beam, the theorem of least work is employed, considering strain energies of both bending and shear. Further, deflection curves are obtained using the successive integration method. The strongest section ratios, as determined by both the maxi-mini stress and deflection, are obtained from the results of the structural analysis. The beam geometry of the minimum-weight beam, which is described by the taper type, side number, volume, and cross sectional depth, is determined from the given allowable stress and deflection. In numerical examples, three kinds of end constraint are considered: hinged-hinged, hinged-clamped, and clamped-clamped beams.

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Stability experiments on the strongest columns and circular arches

Cited by 22 publications

References 4 publications

A new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia that guards against buckling instability

A new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia that guards against buckling instability

Constructal multi-scale and multi-objective structures

Minimum-weight beams with shear strain energy

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