Size-dependent free flexural vibration behavior of functionally graded nanoplates

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. (c) 2012 Elsevier B.V. All rights reserved.

Ballistic Studies on TiB2-Ti Functionally Graded Armor Ceramics

The objective of this paper is to discuss the results of the ballistic testing of spark plasma sintered TiB2-Ti based functionally graded materials (FGMs) with an aim to assess their performance in defeating small-calibre armor piercing projectiles. We studied the efficacy of FGM design and compared its ballistic properties with those of TiB2-based composites as well as other competing ceramic armors. The ballistic properties are critically analyzed in terms of depth of penetration, ballistic efficiency, fractographs of fractured surfaces as well as quantification of the shattered ceramic fragments. It was found that all the investigated ceramic compositions exhibit ballistic efficiency (eta) of 5.1 -5.9. We also found that by increasing the thickness of FGM from 5 mm to 7.8 mm, the ballistic property of the composite degraded. Also, the strength of the ceramic compositions studied is sufficient to completely fracture the nose of the pointed projectile used. Analysis of the ceramic fragments (2 mu m-10 mm) showed that harder the ceramic, coarser were the fragments formed. On comparing the results with available armor systems, it has been concluded that TiB2 based composites can show better ballistic properties, except B4C. SEM analysis of the fragments obtained after testing with FGM showed formation of cleavage steps as well as presence of intergranular cracks, indicating that the FGM fractured by mixed mode of failure. It can be concluded that the FGM developed has lower ballistic properties compared to its monolith TiB2-20 wt.% Ti.

Compositionally Graded Microstructure for Ag-Fe Nanoparticles

Ag-Fe nanoparticles with a highly Ag rich average composition were synthesized by the sonochemical route. Silver-iron system exhibits a wide miscibility gap in the bulk materials. Interestingly, a graded compositional profile along the nanoparticle radius was observed. Regions at and near the surface of the nanoparticle contained both Ag and Fe atoms. The composition got relatively deficient Fe towards the center of the particle with particle core made up of pure Ag. Alloying of Ag and Fe is confirmed by the absence of diffraction signal corresponding to pure Fe phase and presence of a paramagnetic phase in nanoparticles containing a diamagnetic (Ag) and ferromagnetic (Fe) elements.

Electrochemical Determination of Gibbs Energy of Formation of LaCrO3 Using a Composition-Graded Bielectrolyte

Presented are new measurements of the standard Gibbs free energy of formation of rhombohedral LaCrO3 from component oxides La2O3 and Cr2O3 in the temperature range from 875 to 1175K, using a bielectrolyte solid-state cell incorporating single crystal CaF2 and composition-graded solid electrolyte (LaF3)(y)(CaF2)(1-y) (y=0-0.32). The results can be represented analytically as Delta G(f(ox))(o) (+/- 2270)/Jmol(-1)=-72329+4.932 (T/K). The measurements were undertaken to resolve serious discrepancies in the data reported in the literature. A critical analysis of previous electrochemical measurements indicates several deficiencies that have been rectified in this study. The enthalpy of formation obtained in this study is consistent with calorimetric data. The standard enthalpy of formation of orthorhombic LaCrO3 from elements at 298.15K computed from the results of this study is Delta H-f(298.15)(o)/kJmol(-1)=-1536.2 (+/- 7). The standard entropy of orthorhombic LaCrO3 at 298.15K is estimated as 99.0 (+/- 4.5)J(molK)(-1).

Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition. (C) 2013 Elsevier Masson SAS. All rights reserved.

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a `footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by similar to 50% in generator potentials, to similar to 3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Use of Composition-Graded Bi-Electrolyte Cells for Thermodynamic Studies on Lanthanum Aluminates

Innovative bi-electrolyte solid-state cells incorporating single crystal CaF2 and composition-graded solid electrolyte (LaF3) y (CaF2) 1-y (y = 0 to 0.32) were used for measurement of the standard Gibbs energy of formation of hexagonal La0.885Al11.782O19 and cubic LaAlO3 from component binary oxides La2O3 and alpha-Al2O3 in the temperature range from 875 to 1175 K. The cells were designed based on experimentally verified relevant phase relations in the systems La2O3-Al2O3LaF3 and CaF2-LaF3. The results can be summarized as: 5.891 alpha-Al2O3 + 0.4425 La2O3 (A-rare earth)-> La0.885Al11.782O19 (hex), Delta G(f(ox))(degrees)(+/- 2005)/Jmol(-1) = -80982 + 7.313(T/K); 1/2 La2O3 (A-rare earth) + 1/2 a-Al2O3 -> LaAlO3 (cubic), Delta G(f(ox))(degrees)(+/- 2100)/Jmol(-1) = -59810 + 4.51(T/K). Electron probe microanalysis was used to ascertain the non-stoichiometric range of the hexaaluminate phase. The results are critically analyzed in the light of earlier electrochemical measurements. Several imperfections in the electrochemical cells used by former investigators are identified. Data obtained in the study for LaAlO3 are consistent with calorimetric enthalpy of formation and entropy derived from heat capacity data. Estimated are the standard entropy and the standard enthalpy of formation from elements of hexagonal La0.885Al11.782O19 and rhombohedral LaAlO3 at 298.15 K. c 2014 The Electrochemical Society. All rights reserved.

Graded IR Filters: Distinguishing Between Single and Multipoint NO2 center dot center dot center dot I Halogen Bonded Supramolecular Synthons (P, Q, and R Synthons)

The NO2 center dot center dot center dot I supramolecular synthon is a halogen bonded recognition pattern that is present in the crystal structures of many compounds that contain these functional groups. These synthons have been previously distinguished as P, Q, and R types using topological and geometrical criteria. A five step IR spectroscopic sequence is proposed here to distinguish between these synthon types in solid samples. Sets of known compounds that contain the P, Q, and R synthons are first taken to develop IR spectroscopic identifiers for them. The identifiers are then used to create graded IR filters that sieve the synthons. These filters contain signatures of the individual NO2 center dot center dot center dot I synthons and may be applied to distinguish between P, Q, and R synthon varieties. They are also useful to identify synthons that are of a borderline character, synthons in disordered structures wherein the crystal structure in itself is not sufficient to distinguish synthon types, and in the identification of the NO2 center dot center dot center dot I synthons in compounds with unknown crystal structures. This study establishes clear differences for the three different geometries P, Q, and Rand in the chemical differences in the intermolecular interactions contained in the synthons. Our IR method can be conveniently employed when single crystals are not readily available also in high throughput analysis. It is possible that such identification may also be adopted as an input for crystal structure prediction analysis of compounds with unknown crystal structures.

Compressive and Flexural Properties of Functionally Graded Fly Ash Cenosphere-Epoxy Resin Syntactic Foams

The present study focuses on developing functionally graded syntactic foams (FGSFs) based on a layered co-curing technique. The FGSFs were characterized for compressive and flexural properties and compared with plain syntactic foams. The results showed that the specific compressive modulus was 3-67% higher in FGSFs compared to plain syntactic foams. FGSF exhibited 5-34% and 34-87% higher specific modulus and strength, respectively in flexural mode. The microscopic examinations of comparative responses of the filler and matrix to deformation suggest that the failure is dominated by the matrix. The gradient in the composition of syntactic foams helps in effectively distributing the stress throughout the microstructure and results in improved mechanical performance of syntactic foams. From the microscopy studies, it is evident that, the failure mechanism in the FGSF under flexural loading is governed by a crack that initiated on the tensile side of the specimen and propagated through the thickness to cause complete fracture. The microscopic observations further clearly demonstrate the existence of seamless interfaces between the layers and a clear difference in the cenosphere concentration across the interface, affirming the gradation in the prepared samples. The results show that appropriate compositions of FGSFs can be selected to develop materials with improved mechanical performance. POLYM. COMPOS., 36:685-693, 2015. (c) 2014 Society of Plastics Engineers

Activation of InsP(3) receptors is sufficient for inducing graded intrinsic plasticity in rat hippocampal pyramidal neurons

The synaptic plasticity literature has focused on establishing necessity and sufficiency as two essential and distinct features in causally relating a signaling molecule to plasticity induction, an approach that has been surprisingly lacking in the intrinsic plasticity literature. In this study, we complemented the recently established necessity of inositol trisphosphate (InsP(3)) receptors (InsP(3)R) in a form of intrinsic plasticity by asking if InsP(3)R activation was sufficient to induce intrinsic plasticity in hippocampal neurons. Specifically, incorporation of D-myo-InsP(3) in the recording pipette reduced input resistance, maximal impedance amplitude, and temporal summation but increased resonance frequency, resonance strength, sag ratio, and impedance phase lead. Strikingly, the magnitude of plasticity in all these measurements was dependent on InsP 3 concentration, emphasizing the graded dependence of such plasticity on InsP(3)R activation. Mechanistically, we found that this InsP(3)-induced plasticity depended on hyperpolarization-activated cyclic nucleotide-gated channels. Moreover, this calcium-dependent form of plasticity was critically reliant on the release of calcium through InsP(3)Rs, the influx of calcium through N-methyl-D-aspartate receptors and voltage-gated calcium channels, and on the protein kinase A pathway. Our results delineate a causal role for InsP(3)Rs in graded adaptation of neuronal response dynamics, revealing novel regulatory roles for the endoplasmic reticulum in neural coding and homeostasis.

SOME INFINITE SUMS IDENTITIES

We find the sum of series of the form Sigma(infinity)(i=1) f(i)/i(r) for some special functions f. The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mezo's paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of pi.

FEM Simulations and Optimization about Residual Stresses in Coating Structures with Functionally Graded Materials Layer

An elasto-plastic finite element method is developed to predict the residual stresses of thermal spraying coatings with functionally graded material layer. In numerical simulations, temperature sensitivity of various material constants is included and mix

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.