• Steel and Composite Structures
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• v.49 no.3
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• pp.293-306
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• 2023

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as a higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

• Advances in nano research
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• v.10 no.5
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• pp.493-507
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• 2021

This article focused on studying the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity based on first shear deformation and higher-order theory of tube. The nano-scale tube is simulated based on the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. The parametric study is performed to study the effects of different parameters such as axial and radial FG power indexes, porosity parameter, nonlocal gradient strain parameters on the buckling behavior of di-dimensional functionally graded porous tube.

• Asian-Australasian Journal of Animal Sciences
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• v.14 no.1
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• pp.21-29
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• 2001

An experiment was conducted with twenty crossbred male lambs to assess the effect of cotton (Gossypium) seed meal (CSM) on blood constituents and immunity. Lambs were randomly assigned to a reference diet (30% deoiled peanut meal, DPNM) and four test diets containing 40% of either raw, 45 minutes cooked, 1% $Ca(OH)_2$ and iron (1 free gossy-pol, FG : 0.3 Fe) treated CSM (replacing approximately 50%, reference concentrate mixture). These isonitrogenous and isocaloric concentrate mixtures were fed to meet 80% of protein requirements (NRC, 1985) along with ad lib maize hay for 180 days. Blood was collected at 60, 120 and 180 days post feeding. The lambs were sensitized with Brucella abortus S99 antigen after 140 days and were subjected to ELISA and delayed type hypersensitivity. Blood haemoglobin, erythrocyte count, leucocyte count, total protein, total albumin, total globulin, urea, creatinine concentration and aspartate aminotransferase activity in lambs fed on raw or processed CSM were comparable to the values of reference lambs. The higher (p<0.01) blood glucose levels observed in CSM fed lambs at 60 days of feeding was latter reduced to the levels comparable with those on reference diet at 120 and 180 days of feeding. The alanine amino transferase activity was lower in lambs fed raw and cooked CSM containing diets at 120 and 180 days of feeding. A marginal increase in serum iron and alkaline posphatase activity was observed in iron treated group and raw CSM fed lambs, respectively. The humoral immune response and DTH reactivity was lower (p<0.05) in lambs fed raw CSM (consuming 302.83 mg FG/day). Cooking, $Ca(OH)_2$ and iron treatment of raw CSM showed a positive response in alleviating the suppression of immune response owing to the reduced consumption of FG by 40.19, 17.40% and 26.73%, respectively in these diets. The present study thus indicated that consumption of 40% raw CSM (302.83 mg FG/day) though did not affect majority of the haematological and blood biochemical parameters, but markedly suppressed the immune mechanism of lambs.

• Steel and Composite Structures
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• v.42 no.5
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• pp.599-615
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• 2022

In the present paper, the numerical dynamic analysis of a functionally graded nano-scale nonuniform tube was investigated according to the high-order beam theory coupled with the nonlocal gradient strain theory. The supposed cross-section is changed along the pipe length, and the material distribution, which combines both metal and ceramics, is smoothly changed in the pipe length direction, which is called axially functionally graded (AFG) pipe. Moreover, the porosity voids are dispersed in the cross-section and the radial pattern that the existence of both material distribution along the tube length and porosity voids make a two-dimensional functionally graded (2D-FG) truncated conical pipe. On the basis of the Hamilton principle, the governing equations and the associated boundary conditions equations are derived, and then a numerical approach is applied to solve the obtained equations.

• Geomechanics and Engineering
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• v.35 no.4
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• pp.367-383
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• 2023

The present paper examines the natural frequency responses of the bi-directional (n_x-n_y, n_y-n_z and n_z-n_x) and multidirectional (n_x-n_y-n_z) functionally graded (FG) plate and curved structures with and without porosity. The even and uneven kind of porosity pattern are considered to observe the influence of porosity type and porosity index. The numerical findings have been obtained using a higher order shear deformation theory (HSDT) based isometric finite element (FE) approach generated in a MATLAB platform. According to the convergence and validation investigation, the proposed HSDT based FE model is adequate to predict free vibrational responses of multidirectional porous FG plates and curved structures. Further a parametric analysis is carried out by taking various design parameters into account. The free vibrational behavior of bidirectional (2D) and multidirectional (3D) perfect-imperfect FGM structure is examined against various power law index, support conditions, aspect, and thickness ratio, and for the curvature of curved structures. The results indicate that the maximum non-dimensional fundamental frequency (NFF) value is observed in perfect FGM plates and curved structures compared to porous FGM plates and curved structures and it is maximum for FGM plates and curved structures with uneven kind of porosity than even porosity.

• Advances in materials Research
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• v.12 no.2
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• pp.161-177
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• 2023

This paper proposes an analytical method to investigate the free vibration behaviour of new functionally graded (FG) carbon nanotubes reinforced composite beams based on a higher-order shear deformation theory. Cosine functions represent the material gradation and material properties via the thickness. The kinematic relations of the beam are proposed according to trigonometric functions. The equilibrium equations are obtained using the virtual work principle and solved using Navier's method. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure-scale, material distribution and geometry.

• Steel and Composite Structures
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• v.38 no.5
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• pp.477-496
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• 2021

The main objective of this paper is to study vibration of sandwich open cylindrical panel with damaged core and FG face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions. It is seen that for the large amount of power-law index "P", increasing this parameter does not have significant effect on the non-dimensional natural frequency parameters of the FG sandwich curved panel. Results indicate that by increasing the value of isotropic damage parameter "D" up to the unity (fully damaged core) the frequency would tend to become zero. One can dictate the fiber variation profile through the radial direction of the sandwich panel via the amount of "P", "b" and "c" parameters. It should be noticed that with increase of volume fraction of fibers, the frequency parameter of the panels does not increase necessarily, so by considering suitable amounts of power-law index "P" and the parameters "b" and "c", one can get dynamic characteristics similar or better than the isotropic limit case for laminated FG curved panels.

• Computers and Concrete
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• v.31 no.2
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• pp.139-149
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• 2023

This article investigates the statically analysis regarding the thermal buckling behavior of a nonuniform small-scale nanobeam made of functionally graded material based on classic beam theories along with the nonlocal Eringen elasticity. The material distribution of functionally graded structures is composed of temperature-dependent ceramic and metal phases in axial and thickness directions, called two-dimensional functionally graded (2D-FG). The partial differential (PD) formulations and end conditions are extracted by using to the conservation energy method. The porosity voids are assumed in the nonuniform functionally graded (FG) structure. The thermal loads are in the axial direction of the beam. The extracted nonlocal PD equations are also solved by employing generalized differential quadrature method (GDQM). Last but not least, the information acquired is used to produce miniature sensors, providing a unique perspective on the growth of nanoelectromechanical systems (NEMS).

• Geomechanics and Engineering
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• v.14 no.6
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• Asian-Australasian Journal of Animal Sciences
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• v.26 no.6
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• pp.845-855
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• 2013

Requirements of dietary chloride (dCl) and chloride salts were determined by using $4{\times}2$ factorial arrangement under four phase feeding program. Four levels (0.31, 0.45, 0.59 and 0.73%) and two sources ($NH_4Cl$ and $CaCl_2$) of the dCl were allocated to 1,472 chicks in eight dietary treatments in which each treatment was replicated four times with 46 birds per replicate. The four phase feeding program was comprised of four dietary phases: Prestarter (d 1 to 10), Starter (d 11 to 20), Grower (d 21 to 33) and Finisher (d 34 to 42); and diets were separately prepared for each phase. The cations, anions, pH, dissolved oxygen (DO), temperature, electrical conductivity (EC), total dissolved solids (TDS) and salinity were analyzed in drinking water and were not affected by dietary treatments. BW gain (BWG; $p{\leq}0.009$) and feed:gain (FG; $p{\leq}0.03$) were improved in $CaCl_2$ supplemented diets during d 1 to 10. The maximum response of BWG and FG was observed at 0.38% and 0.42% dCl, respectively, for d 34 to 42. However, the level of dCl for BWG during d 21 to 33 ($p{\leq}0.04$) and d 34 to 42 ($p{\leq}0.009$) was optimized at 0.60% and 0.42%, respectively. The level of dCl for optimized feed intake (FI; $p{\leq}0.006$), FG ($p{\leq}0.007$) and litter moisture (LM; $p{\leq}0.001$) was observed at 0.60%, 0.38% and 0.73%, respectively, for d 1 to 42. Water intake (DWI) was not affected by increasing dCl supplementation (p>0.05); however, the ratio between DWI and FI (DWI:FI) was found highest at 0.73% dCl during d 1 to 10 ($p{\leq}0.05$) and d 21 to 33 ($p{\leq}0.009$). Except for d 34 to 42 ($p{\leq}0.006$), the increasing level of dCl did not result in a significant difference in mortality during any phase. Blood pH and glucose, and breast and thigh weights (percentage of dressed weight) were improved while dressing percentage (DP) and gastrointestinal health were exacerbated with $NH_4Cl$ as compared to $CaCl_2$ supplemented diets ($p{\leq}0.001$). Higher plasma $Na^+$ and $HCO_3{^-}$ and lower $Cl^-$ and $Ca^{{+}{+}}$ were observed in $NH_4Cl$ supplemented diets ($p{\leq}0.001$). Increasing supplementation of dCl increased plasma $Cl^-$ ($p{\leq}0.04$; quadratically) and linearly reduced plasma $K^+$ ($p{\leq}0.001$), $Ca^{{+}{+}}$ ($p{\leq}0.003$), $HCO_3{^-}$ ($p{\leq}0.001$), and $Na^+$ ($p{\leq}0.001$; quadratically). Consequently, higher requirements of dietary chloride are suggested for feed intake; nevertheless, lower levels of dietary chloride are sufficient to support optimal BWG and FG with increasing age. The $NH_4Cl$ supplemented diets ameliorate breast and thigh meat yield along with overall energy balance (glucose).