• Steel and Composite Structures
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• v.46 no.3
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• pp.367-383
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• 2023

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.

• Geomechanics and Engineering
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• v.31 no.1
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• pp.99-112
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• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.233-252
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.253-261
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Journal of the Korea institute for structural maintenance and inspection
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• v.23 no.7
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• pp.9-15
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• 2019

The purpose of present study is to assess the maximum width of the surface cracks using the histogram analysis of image processing techniques in concrete structures. For this purpose, the concrete crack image is acquired by the camera. The image is Grayscale coded and Binary coded. After Binary coded image is Dilate and Erode coded, the image is then recognized as separated objects by applying Labeling techniques. Over time, dust and stains may occur naturally on the surface of concrete. The crack image of concrete may include shadows and reflections by lighting depending on a surrounding conditions. In general, concrete cracks occur in a continuous pattern and noise of image appears in the form of shot noises. Bilateral Blurring and Adaptive Threshold apply to the Grayscale image to eliminate these effects. The remaining noises are removed by the object area ratio to the Labeled area. The maximum numbers of pixels and its positions in the crack objects without noises are calculated in x-direction and y-direction by Histogram analysis. The widths of the crack are estimated by trigonometric ratio at the positions of the pixels maximum numbers for the Labeled objects. Finally, the maximum crack width estimated by the proposed method is compared to the crack width measured with the crack gauge. The proposed method by the present study may increase the reliability for the estimation of maximum crack width using image processing techniques in concrete surface images.

• The Journal of the Petrological Society of Korea
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• v.26 no.3
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• pp.297-309
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• 2017

Jurassic granite from Geochang was analysed with respect to the characteristics of the rock cleavage. The comprehensive evaluation for rock cleavages was performed through the combination of the 16 parameters derived from the enlarged photomicrographs of the thin section and the spacing-cumulative frequency diagrams. The results of analysis for the representative values of these spacing parameters with respect to the rock cleavage are summarized as follows. First, the above parameters can be classified into group I (spacing frequency (N), total spacing ($1m{\geq}$), constant (a), exponent (${\lambda}$), slope of exponential straight line (${\theta}$), length of line (oa') and trigonometric ratios ($sin{\theta}$, $tan{\theta}$) and group II (mean spacing (Sm), difference value between mean spacing and median spacing (Sm-Sme), density (${\rho}$), lengths of lines (oa and aa'), area of a right-angled triangle (${\Delta}oaa^{\prime}$) and trigonometric ratio($cos{\theta}$). The values of the 8 parameters belonging to group I show an order of H(hardway, H1+H2)

• Journal of Astronomy and Space Sciences
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• v.21 no.4
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• pp.275-282
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• 2004

We completed the light curves of the contact binary CK Boo for 13 nights from June to July in 2004 using the 1-m reflector and BVR filters at Mt. Lemmon Optical Astronomy Observatory, and determined four new times of minimum light (three timings for primary eclipse, one for secondary). With contact mode of the 1998-version Wilson-Devinney binary model, we analyzed our BVR light curves and Rucinski & Lu (1999)'s radial-velocity ones. As a result, we found CK boo to be A-type over-contact binary ($f=84\%$) with the low mass ratio (q=0.11) and orbital inclination ($i=65^{\circ}$). Absolute dimensions of the system are determined from our new solution; $M_1=1.42Me{\odot},\;M_2=0.15M{\odot},\;R_1=1.47R{\odot},\;R_2=0.59M{\odot}$ and the distance to it is derived as about 129pc. Our distance is well consistent with that ($157{\pm}33pc$) from the Hipparcos trigonometric parallax within the limit of the error yielded by the latter.

• Computers and Concrete
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• v.31 no.3
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• pp.267-276
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• 2023

The main purpose of the current research is to develop an efficient two variables trigonometric shear deformation beam theory to investigate the buckling behavior of symmetric and non-symmetric functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beam resting on an elastic foundation with various boundary conditions. The proposed theory obviates the use to shear correction factors as it satisfies the parabolic variation of through-thickness shear stress distribution. The composite beam is made of a polymeric matrix reinforced by aligned and distributed single-walled carbon nanotubes (SWCNTs) with different patterns of reinforcement. The material properties of the FG-CNTRC beam are estimated by using the rule of mixture. The governing equilibrium equations are solved by using new analytical solutions based on the Galerkin method. The robustness and accuracy of the proposed analytical model are demonstrated by comparing its results with those available by other researchers in the existing literature. Moreover, a comprehensive parametric study is presented and discussed in detail to show the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, length-to-thickness ratio, and spring constant factors on the buckling response of FG-CNTRC beam. Some new referential results are reported for the first time, which will serve as a benchmark for future research.