• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1143-1149
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• 2020

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

• East Asian mathematical journal
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• v.34 no.5
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• pp.549-570
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• 2018

We establish existence and bifurcation of global positive solutions for parametrized nonhomogeneous elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms. The main approach to the problem is the variational method.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.259-269
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• 1997

Bayesian inference for a record value statistics(RVS) model of nonhomogeneous Poisson process is considered. We seal with Bayesian inference for double exponential, Gamma, Rayleigh, Gumble RVS models using Gibbs sampling and Metropolis algorithm and also explore Bayesian computation and model selection.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.7-13
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• 1987

This paper is a study of the oscillatory and asymptotic behaviour of solutions of the second order nonhomogeneous linear differential equation y"+P(x)y=f(x), and the associated homogeneous equation. Conditions are determined, under which the nonhomogeneous equation is oscillatory if and only if the homogeneous equation is oscillatory.

• East Asian mathematical journal
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• v.30 no.3
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• pp.335-353
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• 2014

We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.

• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.

• Geomechanics and Engineering
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• v.13 no.5
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• pp.825-844
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• 2017

This study aimed to find out the pullout capacity of inclined strip anchor plate embedded in anisotropic and nonhomogeneous fully saturated cohesive soil in undrained condition. The ultimate pullout load has been found out by using numerical lower bound finite element analysis with linear programming. The undrained pullout capacity of anchor plate of width B is determined for different embedment ratios (H/B) varying from 3 to 7 and various inclination of anchor plates ranging from $0^{\circ}$ to $90^{\circ}$ with an interval of $15^{\circ}$. In case of anisotropic fully saturated clay the variation of cohesion with direction has been considered by varying the ratio of the cohesion along vertical direction ($c_v$) to the cohesion along horizontal direction ($c_h$). In case of nonhomogeneous clay the cohesion of the undrained clay has been considered to be increased with depth below ground surface keeping $c_v/c_h=1$. The results are presented in terms of pullout capacity factor ($F_{c0}=p_u/c_H$) where $p_u$ is the ultimate pullout stress along the anchor plate at failure and $c_H$ is the cohesion in horizontal direction at the level of the middle point of the anchor plate. It is observed that the pullout capacity factor increases with an increase in anisotropic cohesion ratio ($c_v/c_h$) whereas the pullout capacity factor decreases with an increase in undrained cohesion of the soil with depth.

• Journal of computational fluids engineering
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• v.18 no.4
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• pp.25-34
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• 2013

A numerical study of a laminar natural convection of the CuO-water nanofluid in a square cavity using the Buongiorno's nonhomogeneous model is presented. All the governing equations including the volume fraction equation are discretized on a cell-centered, non-uniform grid employing the finite-volume method with a primitive variable formulation. Calculations are performed over a range of Rayleigh numbers and volume fractions of the nanopartile. From the computed results, it is shown that both the homogeneous and nonhomogeneous models predict the deterioration of the natural convection heat transfer well with an increase of the volume fraction of nanoparticle at the same Rayleigh number, which was observed in the previous experimental studies. It is also shown that the differences in the computed results of the average Nusselt number at the wall between the homogeneous and nonhomogeneous models are very small, and this indicates that the slip mechanism of the Brown diffusion and thermophoresis effects are negligible in the laminar natural convection of the nanofluid. The degradation of the heat transfer with an increase of the volume fraction of the nanoparticle in the natural convection of nanofluid is due to the increase of the viscosity and the decrease of the thermal expansion coefficient and the specific heat. It is clarified in the present study that the previous controversies between the numerical and experimental studies are owing to the different definitions of the Nusselt number.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.329-343
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• 2002

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.406-413
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• 1998

The distinct element method is improved to consider the charateristics of stress wave propagation in media involving the discontinuous faces. The distinct element method has many advantages to analyse the characteristics of the reflection, refraction and deflection of the waves in nonhomogeneous media. The double-suing connection system is adopted instead of the single-spring connection system because the distinct element cannot be used for analysing the contact behavior between the different materials by only one contact spring. For the verification of the improved code, the results of the numerical analysis are compared with that of the photoelastic experiments which are one or two dimensional wave propagation problem of the nonhomogeneous media including the different accoustic impendence material or voids. It is shown that the characteristics of the stress wave propagation in nonhomogeneous media can be simulated appropriately using the improved distinct element method.