On anticlastic curvature with special reference to plastic bending: A literature survey and some experimental investigations

Horrocks, Don; Johnson, William B.

doi:10.1016/0020-7403(67)90011-2

Cited by 25 publications

(17 citation statements)

References 21 publications

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“…The theory of such elastic surfaces is highly developed in a remarkably successful theory called theory of elasticity [17][18][19][20]. This theory and its sister, theory of plasticity, is the basis of all structural engineering science which gave us shell structures [17][18][19] covering large sports and airport halls without supporting columns and thin fuselages which carry passengers across the Atlantic in a few hours.…”

Section: Negative Gravity As Compactified Dimensionsmentioning

confidence: 99%

“…This theory and its sister, theory of plasticity, is the basis of all structural engineering science which gave us shell structures [17][18][19] covering large sports and airport halls without supporting columns and thin fuselages which carry passengers across the Atlantic in a few hours. When such an elastic or elasto-plastic surface is sufficiently thick, long and narrow then an interesting curvature phenomena takes place called anticlastic curvature [20]. The point is that when the long thick elastic structure is bent, then its cross section curves in the opposite direction.…”

Section: Negative Gravity As Compactified Dimensionsmentioning

confidence: 99%

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A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

Naschie¹

2013

IJMNTA

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The 95.5 percent of discrepancy between theoretical prediction based on Einstein's theory of relativity and the accurate cosmological measurement of WMAP and various supernova analyses is resolved classically using Newtonian mechanics in conjunction with a fractal Menger sponge space proposal. The new energy equation is thus based on the familiar kinetic energy of Newtonian mechanics scaled classically by a ratio relating our familiar three dimensional space homology to that of a Menger sponge. The remarkable final result is an energy equation identical to that of Einstein's but divided by 22 so that our new equation reads as In other words our analysis confirms the cosmological data putting the total value of measured ordinary matter and ordinary energy of the entire universe at 4.5 percent. Thus ordinary positive energy which can be measured using conventional methods is the energy of the quantum particle modeled by the Zero set in five dimensions. Dark energy on the other hand is the absolute value of the negative energy of the quantum Schrödinger wave modeled by the empty set also in five dimensions.

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Section: Negative Gravity As Compactified Dimensionsmentioning

confidence: 99%

Section: Negative Gravity As Compactified Dimensionsmentioning

confidence: 99%

A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

Naschie¹

2013

IJMNTA

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“…In such material space, anticlastic curvature is a natural outcome of any induced curvature [61]. Thus as in the simple elementary demonstration with a long cylindrically rolled paper sheet of Figure 14, Ref.…”

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confidence: 99%

“…Globally our fractal-Cantorian spacetime is a material space like the space of the theory of elasticity, only more sophisticated [60,61]. The nearest known theory to that would be Cartan theory which includes torsion tensors or even better, the theory of polar media of the French electrical engineering brothers Cosserat [62].…”

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confidence: 99%

Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model

Marek-Crnjac

Naschie²

2013

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The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type. Subsequently this analogy is used to deduce the ordinary energy of the quantum particle and the dark energy of the quantum wave. The results agree completely with cosmological measurements. Even more surprisingly the sum of both energy expressions turned out to be exactly equal to Einstein's iconic formula . Consequently Einstein's formula makes no distinction between ordinary and dark energy. E mc

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“…Consequently, the deformation state can be characterized as more plate-like, with plane-strain the limiting approximation. The deformation modes may be interpreted in terms of ''body force'' which tends to suppress the formation of a large circular cross-section (Horrocks and Johnson, 1967). When bending wide sheets to a small radius, the constrained anticlastic curvature causes a biaxial stress state on the tension side of the sheet (Gerard, 1946).…”

Section: Introductionmentioning

confidence: 99%