• 자원환경지질
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• 제33권1호
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• pp.31-40
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• 2000

Sorption characteristics of Pb, Cu, Cd, and Zn onto Ca- and Na-bentonites were investigated by the batch experiments in the condition of various pHs and concentrations of groundwater major anions (${So_4}^{2-}$ and ($HCO_3$), which can form a complex with heavy metals. The sorption removal of heavy metals steadily increases as pH increases. The sorption capability about heavy metals of both Ca-bentonite and Na-bentonite is in the order of Pb>Cu>Zn>Cd. The effect of pH and selectivity of heavy metals of bentonites were explained by the change of surface charge of bentonite and the speciation of heavy metals. Na-bentonite has a little higher sorption ability about heavy metals than that of Ca-bentonite. A high sorption removal of Pb in 0.1M sulfate solution may be attributed to the precipitation of $PbSo_4$(anglesite). However, sulfate has a slight effect on the sorption of CU, Cd and Zn. More than 99% of heavy metals were removed from the 0.1 M bicarbonate solution. However, the efficiency of sorption removal of heavy metals highly decreases in the bicarbonate solution of $10^{-2}$M to $10^{-4}$M. The speciation and saturation index calculated by the WATEQ4F program indicate that the sorption of anionic complexes such as ${Pb(CO_3)_2}^{2-}$, ${Cd(CO_3)_2}^{2-}$, ${Zn(CO_3)_2}^{2-}$, ${Cu(CO_3)_2}^{2-}$ and the precipitation of the solid phases such as $PbCO_3$(cerrusite), $ZnCO_3$(smithsonite), $CdCO_3$(obtavite) are involved in sorption removal of heavy metals in bicarbonate solution. The sorption capability about heavy metals of bentonites in the presence of anions shows the following order: Pb>Cu Cd>Zn.

• Smart Structures and Systems
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• 제25권4호
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• pp.409-422
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• 2020

This article deals with the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables. In this theory, the undetermined integral terms are used and the number of variables is reduced to four, instead of five or more in other higher-order theories. The boundary conditions on the top and the bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided. The principle of virtual work is used to obtain governing equations and boundary conditions. Navier solution for simply supported plates is used to derive analytical solutions. For the validation of the present theory, numerical results for displacements and stresses are compared with those of classical, first-order, higher-order and trigonometric shear theories reported in the literature.

• International Journal of Aeronautical and Space Sciences
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• 제18권2호
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

• Steel and Composite Structures
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• 제24권5호
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• pp.603-613
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• 2017

In this research, the free vibration response of laminated composite plates is investigated using a novel and simple higher order shear deformation plate theory. The model considers a non-linear distribution of the transverse shear strains, and verifies the zero traction boundary conditions on the surfaces of the plate without introducing shear correction coefficient. The developed kinematic uses undetermined integral terms with only four unknowns. Equations of motion are obtained from the Hamilton's principle and the Navier method is used to determine the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical examples studied using the present formulation is compared with three-dimensional elasticity solutions and those calculated using the first-order and the other higher-order theories. It can be concluded that the present model is not only accurate but also efficient and simple in studying the free vibration response of laminated composite plates.

• Bulletin of the Korean Chemical Society
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• 제35권8호
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• pp.2471-2476
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• 2014

The aim of the present study is to explore the possibility of utilizing loess for the adsorption of total phosphorous (T-P) and total nitrogen (T-N) in water. Batch adsorption studies were performed to evaluate the influences of various factors like initial concentration, contact time and temperature on the adsorption of T-P and T-N. The adsorption data showed that loess is not effective for the adsorption of T-N. However, loess exhibited much higher adsorption capacity for T-P. At concentration of $1.0mgL^{-1}$, approximately 97% of T-P adsorption was achieved by loess. The equilibrium data were fitted well to the Langmuir isotherm model. The pseudo-second-order kinetic model appeared to be the better-fitting model because it has higher $R^2$ compared with the pseudo-first-order and intra-particle kinetic model. The theoretical adsorption equilibrium $q_{e,cal}$ from pseudo-second-order kinetic model was relatively similar to the experimental adsorption equilibrium $q_{e,exp}$. The thermodynamic parameters such as free energy ${\Delta}G$, the enthalpy ${\Delta}H$ and the entropy ${\Delta}S$ were also calculated.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.157-174
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• 2020

In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

• 한국분말재료학회지
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• 제11권4호
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• pp.314-321
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• 2004

The elastic moduli of simulated dry process fuels with varying composition and density were measured in order to analyze the mechanical properties of a dry process fuel pellet. Resonant ultrasound spectroscopy(RUS) which can determine all elastic moduli with one set of measurements for a rectangular parallelepiped sample was used to measure the elastic moduli of UO$_{2}$ and simulated dry process fuel. The simulated dry process fuel showed a higher value of Young's modulus than UO$_2$ due to the presence of metallic precipitates and solid solution elements in the UO$_{2}$ matrix. The correlation between Young's modulus and porosity(P) of simulated dry process fuel was found to be 231.4-651.8 P (GPa) at room temperature. Dry process fuel with a higher burnup showed higher Young's modulus because total content of fission product element was increased.

• 대한수학회보
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• 제44권3호
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.1-12
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• 2020

In this paper, we solve the difference equation $x_{n+1}={\frac{x_nx_{n-2}}{ax_n-bx_{n-2}}}$, n = 0, 1, …, where a and b are positive real numbers and the initial values x_-2, x_-1 and x₀ are real numbers. We also find invariant sets and discuss the global behavior of the solutions of aforementioned equation.

• 대한수학회지
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• 제37권6호
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• pp.1031-1042
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• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.