• Smart Structures and Systems
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• v.19 no.1
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• pp.33-38
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• 2017

This research tries to present a nonlinear thermo-elastic solution for a functionally graded spherical shell subjected to mechanical and thermal loads. Geometric nonlinearity is considered using the Lagrange or finite strain tensor. Non-homogeneous material properties are considered based on a power function. Adomian's decomposition method is used for calculation of nonlinear results. Nonlinear results such as displacement can be evaluated for sphere in terms of different indexes of non-homogeneity. A comprehensive comparison between linear and nonlinear results and evaluation of the percentage of difference between them can be performed in this paper. The obtained results indicate that the improvement of the results due to usage of nonlinear analysis is depending on the non-homogeneous index.

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.259-265
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• 1992

Cyclic voltammetric behavior of symmetric (dimethyl, diheptyl, dioctyl, dibenzyl) and asymmetric (methyloctyl, methyldodecyl, methylbenzyl) viologens was investigated in homogeneous aqueous solution and sodium dodecyl sulfate (SDS) micellar media. In SDS-free 0.1 M NaCl solutions, the reduction potential is less negative as the chain length of alkyl substituent is longer. This is due to the stabilization of the reduced cationic radical and neutral form of viologen by adsorption on electrode surface. The adsorbed species show the "aging-effect". With the exceptions of methyldodecyl viologen and methylbenzyl viologen, the viologens show strong tendency of conproportionation reaction between viologen dications and neutral forms. In cases of methyldodecyl viologen and methylbenzyl viologen, the conproportionation reaction is kinetically disfavored, though it is thermodynamically favorable. SDS micelles dissolve the adsorbed species and the viologens exhibit two reversible redox processes in SDS micellar solutions. The reduction potentials of viologens in SDS micellar solutions depend little on the length of alkyl chain. Benzyl-substituted viologens are more easily reduced than the alkyl substituted viologens, presumably due to electron-withdrawing character of benzyl group.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.513-532
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• 2022

This paper deals with the stability of solutions to 𝜓-Hilfer fractional differential systems. We derive the fundamental solution for the system by using the generalized Laplace transform and the Mittag-Leffler function with two parameters. In addition, we obtained some necessary conditions on the stability of the solutions to linear fractional differential systems for homogeneous, non-homogeneous and non-autonomous cases. Numerical examples are also given to illustrate the behavior of solutions.

• Geomechanics and Engineering
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• v.32 no.5
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• pp.475-482
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• 2023

This paper studies the effect of the relaxation time on a two-dimensional thermoelastic medium which has a doubly porous structure in the presence of diffusion and gravity. The normal mode analysis is used to obtain the analytic expressions of the physical quantities, which we take the solution form in the exponential image. We have discussed a homogeneous thermoelastic half-space with double porosity with the effect of diffusion and gravity. The equations of generalized thermoelastic material with double porosity structure with one relaxation time have been developed. Moreover, the expressions of many physical quantities are explained. The general solutions, under specific boundary conditions of the problem, were found in some detail. In addition, numerical results are computed.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Structural Engineering and Mechanics
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• v.28 no.1
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• pp.19-38
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• 2008

A general solution to the field equations of homogeneous isotropic generalized thermoelastic diffusion with two relaxation times (Green and Lindsay theory) has been obtained using the Fourier transform. Assuming the disturbances to be harmonically time.dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed loads have been considered to show the utility of the solution obtained. The transformed components of displacement, stress, temperature distribution and chemical potential distribution are inverted numerically, using a numerical inversion technique. Effect of diffusion on the resulting expressions have been depicted graphically for Green and Lindsay (G-L) and coupled (C-T) theories of thermoelasticity.

• East Asian mathematical journal
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• v.34 no.5
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• pp.623-632
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• 2018

In [7, 8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.

• Journal of Powder Materials
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• v.10 no.5
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• pp.310-317
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• 2003

Two-component ceramic (alumina-zirconia) composites were fabricated by a soft-solution process in which polyethylene glycol (PEG) was used as a polymeric carrier. Metal salts and PEG were dissolved in ethyl alcohol without any precipitation in 1:1 volume ratio of alumina and zirconia. In the non-aqueous system, the flammable solvent made explosive, exothermic reaction during drying process. The reaction resulted in formation of volume expanded, porous precursor powders by a vigorous decomposition of organic components in the precursor sol. The PEG content affected the grain size of sintered composites as well as the morphology of precursor powders. The difference of microstructure in sintered composite was attribute to the solubility and homogeneity of metal cations in precursor sol. At the optimum amount of the PEG polymer, the metal ions were dispersed effectively in solution and a homogeneous polymeric network was formed. It made less agglomerated particles in the precursor sol and affected on uniform grain size in sintered composite.

• Journal of Powder Materials
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• v.18 no.1
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• pp.35-40
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• 2011

LAS-system ceramic powder, spodumene ($Li_2O{\cdot}Al_2O_3{\cdot}4SiO_2$), was successfully synthesized by a chemical solution technique employing PVA(polyvinyl alcohol) as an organic carrier. The PVA content affected the microstructure of porous precursor gels and the crystalline development. The optimum PVA content contributed to homogeneous distribution of metal ions in the precursor gel and it resulted in the synthesis of glass free $\beta$-spodumene powder having a specific surface area of $7.57\;m^2/g$. The agglomerated $\beta$-spodumene powders were also enough soft to grind to fine powders by a simple ball milling process. The microstructures of the densified powder compacts were strongly dependant on the minor phases of spodumene solid solution and amount of liquid phase, which were formed from the inhomogeneous precursors.

• Journal of Powder Materials
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• v.9 no.5
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• pp.346-351
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• 2002

Pure and fine, two-component titanate powders (barium titanate, calcium titanate etc.) were synthesized by an ethylene glycol method. Titanium isopropoxide and other metal ionic salts were dissolved in liquid-type ethylene glycol without any precipitation. In non-aqueous system, the amount of ethylene glycol affected the solubility and homogeneity of metal cation sources in the solution. At the optimum amount of the polymer, the metal ions were dispersed effectively in solution and a homogeneous polymeric network was formed. Most of the synthesized powders had sub-micron or nano-size primary particles after calcination and the agglomerated calcined powders were easily ground by ball milling process. All synthesized titanate powders had stable crystallization behavior at low temperature and high specific surface area after ball milling. The crystallization behavior and the microstructures of the calcined powders were affected on the ethylene glycol content.