The Influence of Torsional-Rigidity Bounds for Composite Shafts with Specific Cross-Sections

2011 ◽  
Vol 462-463 ◽  
pp. 674-679
Author(s):  
I Tung Chan ◽  
Tung Yang Chen ◽  
Min Sen Chiu
Keyword(s):  
Shear Modulus ◽  
Cross Sections ◽  
Variational Principles ◽  
Torsional Rigidity ◽  
Lower And Upper Bounds ◽  
Imperfect Interfaces ◽  
Section Shape ◽  
The Matrix ◽  
Rigorous Bounds ◽  
Low Shear

We consider the Saint-Venant torsion problem of composite shafts. Two different kinds of imperfect interfaces are considered. One models a thin interphase of low shear modulus and the other models a thin interphase of high shear modulus. The imperfect interfaces are characterized by parameters given in terms of the thickness and shear modulus of the interphases. Using variational principles, we derive rigorous bounds for the torsional rigidity of composite shafts with cross-sections of arbitrary shapes. The analysis is based on the construction of admissible fields in the inclusions and in the matrix. We obtain the general expression for the bounds and demonstrate the results with some particular examples. Specifically, circular, elliptical and trianglar shafts are considered to exemplify the derived bounds. We incorporate the cross-section shape factor into the bounds and show how the position and size of the inclusion influence the bounds. Under specific conditions, the lower and upper bounds will coincide and agree with the exact torsional rigidity.

scholarly journals Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections

1982 ◽  
Vol 5 (2) ◽  
pp. 393-401
Author(s):  
S. K. Bose ◽  
L. Debnath
Keyword(s):  
Shear Modulus ◽  
Cross Sections ◽  
Graphical Representation ◽  
Coarse Graining ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Axial Shear ◽  
The Matrix ◽  
Fiber Reinforced Material

A study is made of the effective axial shear modulus of a fiber reinforced material with random fiber cross-sections so that the micromechanics is governed by stochastic differential equations. A coarse-graining procedure is adopted to investigate the macroscopic behavior of the material. This analysis leads to the formula for the effective axial shear modulusμ∗=μ1/{1−2c(μ2−μ1)/(μ2+μ1)},whereμ1andμ2are the shear modulus of the matrix and fibers respectively andcis the concentration of the fibers less that0.5. Forc>0.5, the fiber and matrix moduli are to be interchanged andcis to be replaced by1−c. The results of this study are compared with those of the theory of fibre reinforced materials. Finally, a numerical example is presented with graphical representation.

Comparative Isolation of Cilia and Flagella from the Lamellibranch Mollusc, Aequipecten irradians

1973 ◽  
Vol 12 (2) ◽  
pp. 345-367
Author(s):  
R. W. LINCK
Keyword(s):  
Atpase Activity ◽  
Cross Sections ◽  
Basal Body ◽  
Electron Dense Material ◽  
The Matrix ◽  
Fine Structures ◽  
Dynein Arms ◽  
Cilia And Flagella ◽  
Triton X ◽  
Ciliary Ultrastructure

Gill cilia and sperm flagella from the lamellibranch mollusc Aequipecten irradians were compared with respect to their ultrastructures and adenosinetriphosphatase activities. Cilia were isolated from excised gills using 3 different solutions: twice-concentrated seawater, 10 % ethanol-10 mM CaCl2 and 60% glycerol. In each case deciliation occurs by the severance of the cilium at the junction of the transition zone and the basal body, and in each case the ciliary ultrastructure is maintained. Sperm flagella were purified by mechanical decapitation. Cilia and sperm flagella have similar fine structures, except that the matrix of the cilia contains substantially more electron-dense material than that of flagella. The ATPase activity of purified cilia is approximately 0.09,µmol P1/min/mg protein; that of flagella is 0.13. Ciliary and flagellar axonemes were prepared by repeated extraction of the membranes with 1% Triton X-100. Ciliary axonemes maintain their 9 + 2 cylindrical orientation, whereas flagellar axonemes often appear as opened or fragmented arrays of the 9 + 2 structure, due to the partial breakdown of the flagellar nexin fibres. A-subfibre arms which were obvious in whole organelles are rarely seen in axoneme preparations. Again the ciliary matrix is considerably more amorphous than in flagellar axonemes. The ATPase activities of ciliary and flagellar axonemes are 0.13 and 0.12 µmol P1/min/mg protein respectively; however, activities of ciliary axonemes may vary by a factor of 2, depending on the method of isolation. The difficulty in observing A-subfibre arms in cross-sections of ciliary and flagellar axonemes is discussed in terms of random, non-reinforcing arrangements of the dynein arms.

scholarly journals Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
N. Ahmadiniaz ◽  
V. M. Banda Guzmán ◽  
F. Bastianelli ◽  
O. Corradini ◽  
J. P. Edwards ◽  
...  
Keyword(s):  
Cross Sections ◽  
Drop Out ◽  
Matrix Elements ◽  
Fermion Propagator ◽  
Particle Path ◽  
Path Integral Representation ◽  
Fermion Line ◽  
Electron Propagator ◽  
The Matrix ◽  
Standard Linear

Abstract In the first part of this series, we employed the second-order formalism and the “symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N-photon kernel,” where this kernel appears also in “subleading” terms involving only N − 1 of the N photons.In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications.We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for “all +” photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

scholarly journals Normal modes of a "cylindrical valley" of alluvium

1989 ◽  
Vol 22 (2) ◽  
pp. 76-80 ◽  
Author(s):  
W. R. Stephenson
Keyword(s):  
Shear Modulus ◽  
Structural Damage ◽  
Travelling Waves ◽  
Soft Soil ◽  
Normal Modes ◽  
Modes Of Vibration ◽  
Rigid Material ◽  
Cylindrical Volume ◽  
High Bulk ◽  
Low Shear

Some normal modes of vibration are deduced for a cylindrical volume of high bulk modulus, low shear modulus material, embedded in an infinite half space of rigid material. The manner in which they may be excited by travelling waves in the rigid material is examined. The relevance of such processes is discussed with regard to the enhancement of structural damage on soft soil during an earthquake.

STIFFNESS OF REINFORCED CONCRETE STRUCTURES UNDER BENDING WITH TRANSVERSE AND LONGITUDINAL FORCES

2021 ◽  
Vol 98 (6) ◽  
pp. 5-19
Author(s):  
VL.I. KOLCHUNOV ◽  
◽  
O.I. AL-HASHIMI ◽  
M.V. PROTCHENKO ◽  
◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Cross Sections ◽  
Concrete Structures ◽  
Bending Moment ◽  
Reinforced Concrete Structures ◽  
The Matrix ◽  
Local Shear ◽  
The Difference ◽  
Inclined Cracks ◽  
Opening Width

The authors developed a model for single reinforced concrete strips in block wedge and arches between inclined cracks and approximated rectangular cross-sections using small squares in matrix elements. From the analysis of the works of N.I. Karpenko and S.N. Karpenko the "nagel" forces in the longitudinal tensile reinforcement and crack slip , as a function of the opening width and concrete deformations in relation to the cosine of the angle . The experimental " nagel " forces and crack slip dependences for the connection between and in the form of an exponent for the reinforcement deformations and spacing are determined. The forces have been calculated for two to three cross-sections (single composite strips) of reinforced concrete structures. On the bases of accepted hypothesis, a new effect of reinforced concrete and a joint modulus in a strip of composite single local shear zone for the difference of mean relative linear and angular deformations of mutual displacements of concrete (or reinforcement) are developed. The hypothesis allows one to reduce the order of the system of differential equations of Rzhanitsyn and to obtain in each joint the total angular deformations of concrete and the "nagel" effect of reinforcement. The curvature of the composite bars has a relationship from the total bending moment of the bars to the sum of the rigidities. The stiffness physical characteristics of the matrix from the compressed concrete area and the working reinforcement are obtained in a system of equations of equilibrium and deformation, as well as physical equations.

Effect of Phase Fraction Ratio Between Al3Mg2 and Mg2Si on the Oxidation Behavior of Al–Mg–Si Alloys

2021 ◽  
Vol 16 (7) ◽  
pp. 1047-1051
Author(s):  
Seong-Ho Ha ◽  
Abdul Wahid Shah ◽  
Bong-Hwan Kim ◽  
Young-Ok Yoon ◽  
Hyun-Kyu Lim ◽  
...  
Keyword(s):  
Oxidation Resistance ◽  
High Temperatures ◽  
Cross Sections ◽  
Oxidation Behavior ◽  
Eutectic Phase ◽  
Mg Alloy ◽  
Phase Fraction ◽  
The Matrix ◽  
Si Content

The effect of the phase fraction ratio between Al3Mg2 and Mg2Si on the oxidation resistance of Al–Mg–Si alloys at high temperatures was investigated. With addition of 1 mass%Si in Al-6 mass%Mg alloy, the as-cast microstructures showed formation of Mg2Si phase by eutectic reactions. With increasing Si content more than 3 mass%, the Mg2Si and Si are formed as eutectic phases with no β-Al3Mg2 phase. In addition, with an increase in the Si content from 3 mass%, significantly refined as-cast microstructures and distribution of extended eutectic phase areas were observed. The oxidized cross-sections of Al-6 mass%Mg and Al-6 mass%Mg-1 mass%Si alloys showed coarse and dark areas, which are considered as oxide clusters, nonuniformly grown into the matrix. However, Al-6 mass%Mg-3 mass%Si and Al-6 mass%Mg-5 mass%Si alloys had no significantly grown oxide clusters on the surfaces. Based on the results, it was concluded that the reduction of the ratio between β-Al3Mg2 and Mg2Si phases can reduce the rapid oxidation of Mg.

scholarly journals Fragility and an extremely low shear modulus of high porosity silicic magma

2020 ◽  
Vol 392 ◽  
pp. 106760
Author(s):  
Atsuko Namiki ◽  
Yukie Tanaka ◽  
Satoshi Okumura ◽  
Osamu Sasaki ◽  
Kyohei Sano ◽  
...  
Keyword(s):  
Shear Modulus ◽  
Silicic Magma ◽  
High Porosity ◽  
Low Shear

Laboratory Study of Corrosion of an Alumina Refractory by Molten Potassium Salts

2010 ◽  
Vol 70 ◽  
pp. 65-71 ◽  
Author(s):  
Na Li ◽  
Leena Hupa ◽  
Patrik Yrjas ◽  
Mikko Hupa
Keyword(s):  
Cross Sections ◽  
Molar Ratio ◽  
Biomass Combustion ◽  
Silicate Matrix ◽  
Potassium Salts ◽  
Scale Method ◽  
Matrix Layer ◽  
The Matrix ◽  
Alumina Refractory ◽  
Refractory Surface

The increasing use of biomass and waste derived fuels in combustion challenges the chemical durability of refractories. Durability of an alumina refractory was studied in a chemically aggressive environment. A mixture of potassium chloride and carbonate (molar ratio 1:9) was placed on the sample and heated at 700-1000°C in an electric laboratory furnace in air for one week. Cross-sections of the samples were studied by SEM-EDXA to determine penetration of potassium in the refractory. Potassium was found only in the silicate matrix phase of the alumina refractory. Penetration of potassium decreased steeply from the surface to 1 mm, after which the decrease was linear but varied with temperature. At 700 and 800°C the thickness of the matrix layer that had reacted with potassium was 3 mm, while the layer was thinner at 900 and 1000°C. At the higher temperatures a glassy layer consisting of K2O, Na2O, CaO and SiO2 formed on the refractory surface. At 900°C the thickness of the surface layer was of 10μm, while a 200μm layer was measured at 1000°C. The procedure used in this work can be used to develop a laboratory scale method to be used to study corrosion of refractories in biomass combustion devices.

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