• Smart Structures and Systems
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• v.30 no.2
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• pp.135-143
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• 2022

The object of this paper is to investigate the free vibration behavior under the effect of carbon nanotube distribution in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) by using higher-order shear deformation theories. In this work, we present a novel distribution method for carbon nanotubes in the polymer matrix by using a new exponential power law distribution of carbon nanotube volume fraction. It is assumed that the SWCNTs are aligned along the beam axial direction and the distribution of the SWCNTs may vary through the thickness of the beam with different patterns of reinforcement. The rule of mixtures is used in order to obtain material properties of the CNTRC beams. Hamilton's principle is used in deriving the equations of motion. The validity of the free Vibration results is examined by comparing them with those of the known data in the literature. The results that obtained indicate that the carbon nanotube volume fraction distribution play a very important role on the free vibrations characteristics of the CNTRC beam.

• Computers and Concrete
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• v.32 no.2
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• pp.207-215
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• 2023

This paper investigates wave propagation in functionally graded carbon nano-reinforced composite (FG-CNTRC) plates under the influence of temperature based on Reddy' plate model. The material properties of Carbon Nanotubes (CNTs) are size-dependent, and the volume fraction of CNTs varies only along the thickness direction of the plate for different CNTs reinforcement modes. In addition, the material properties of CNTs can vary for different temperature parameters. By solving the eigenvalue problem, analytical dispersion relations can be derived for CNTRC plates. The partial differential equations for the system are derived from Lagrange's principle and higher order shear deformation theory is used to obtain the wave equations for the CNTRC plate. Numerical analyses show that the wave propagation properties in the CNTRC plate are related to the volume fraction parameters of the CNTRC plate and the distribution pattern of the CNTs in the polymer matrix. The effects of different volume fractions of CNTs and the distribution pattern of carbon nanotubes along the cross section (UD-O-X plate) are discussed in detail.

• Computers and Concrete
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• v.34 no.3
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• pp.297-305
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• 2024

This study investigates the buckling behavior of CNTRC beams on a Winkler-Pasternak elastic foundation, considering their stiffness. To achieve the highest accuracy, the shear stiffness is taken into account based on the Higher-order Shear Deformation Theory (HSDT). A novel exponential power-law distribution of the CNT volume fraction across the beam thickness is employed to model CNTRC beams. Various reinforcement patterns are incorporated into the polymer matrix, featuring single-walled carbon nanotubes (SWCNT) that are both aligned and distributed. The effective mechanical properties of the CNTRC beam are predicted using the rule of mixtures. Hamilton's principle is applied to derive the differential equations of motion. This theoretical framework enables the validation of the approach by comparing numerical simulation results with previous studies. The impact of the exponent order (n), CNT volume fraction, geometrical ratio, and Winkler-Pasternak parameters on buckling analysis is thoroughly presented and discussed. The results indicate that, among the different types of analyzed CNTRC beams, the X-Beam pattern demonstrates the highest buckling load capacity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.2
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• pp.340-348
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• 2002

Deformation analysis of injection molded articles whose geometry is considered as the assembly of thin flat plates has been conducted. For the in-mold analysis, thermo-viscoelastic stress calculation of thermo-rheologically simple amorphous polymer and in-mold deformation calculation considering the in-plane mold constraint have been done. Free volume theory has been used to represent the non-equilibrium density state during the fast cooling. At ejection, instantaneous deformation takes place due to the redistribution of in-mold residual stress. During out-of-mold cooling after ejection, thermoelastic model based on the effective temperature has been adopted for the calculation of out-of-mold deformation. In this study, emphasis is also made on the treatment with regard to lateral constraint types during molding process. Two typical mold geometries are used to test the numerical simulation modeling developed in this study.

• Steel and Composite Structures
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• v.27 no.3
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• pp.311-325
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• 2018

This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as non-uniform foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

• Transactions of Materials Processing
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• v.18 no.6
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• pp.500-507
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• 2009

Tensile deformation behavior with different strain rate was investigated. $Zr_{56.2}Ti_{13.8}Nb_{5.0}Cu_{6.9}Ni_{5.6}Be_{12.5}$(bulk metallic glass alloy possessed crystal phase which was called $\beta$-phase of dendrite shape, mean size of $20{\sim}30{\mu}m$ and occupied 25% of the total volume) was used in this study. Maximum tensile strength was obtained as 1.74GPa at strain rate $10^2s^{-1}$ and minimum strength was found to be 1.6GPa at $10^{-1}s^{-1}$. And then, maximum plastic deformation occurred at the strain rate of $5{\times}10^{-2}s^{-1}$ and represented 1.75%, though minimum plastic deformation showed 0%. In the specific range of strain rate, relatively higher plastic deformation and lower ultimate tensile strength were found with lots of shear bands. The fractographical observation after tensile test indicated that vein like pattern on the fracture surface was well developed especially in the above range of strain rate.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.05a
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• pp.353-354
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• 2009

Tensile deformation behavior with different strain rate was investigated. $Zr_{56.2}Ti_{13.8}Nb_{5.0}Cu_{6.9}Ni_{5.6}Be_{12.5}$ (bulk metallic glass alloy possessed crystal phase which was called $\beta$-phase of dendrite shape, mean size of $20{\sim}30{\mu}m$ and occupied 25% of the total volume) was used in this study. Maximum tensile strength was obtained as 1.74Gpa at strain rate of $10^2/s$ and minimum strength was found to be 1.6GPa at $10^{-1}/s$. And then, maximum plastic deformation occurred at the strain rate of $5{\times}10^{-2}/s$ and represented 1.75%, though minimum plastic deformation showed 0%. In the specific range of strain rate, relatively higher plastic deformation and lower ultimate tensile strength were found with lots of shear bands. The fractographical observation after tensile test indicated that vein like pattern on the fracture surface was well developed especially in the above range of strain rate.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.1 s.94
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• pp.227-237
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• 1999

As the interface bonding phenomenon between the matrix and the reinforcements has a large effect on the mechanical properties of MMCs, a sugestion of the strength analysis technique considering the residual stress and the interface bonding phenomenon is very important for the design of pans and the estimation of fatigue behavior. In this paper the three dimensional finite element anaysis is performed during the elasto-plastic deformation of the particulate reinforced metal matrix composites. It was analyzed with the volume fractions in view of microscale. Bonding strength. interface separation and matrix void growth between the matrix and the reinforcements will be predicted on deformation under tensile loading. An interface seperation is estimated by the fracture criterion which is a critical value of generalized plastic work per unit volume. The shape of the reinforcement is assumed to be a perfect sphere. And the type of the reinforcement distribution is assumed as FCC array. The thermal residual stress in MMCs is induced by the heat treatment. It is included at the simulation as an initial residual stress. The element birth and death method of the ANSYS program is used for the estimation of the interface bonding strength, void generation and propagation. It is assumed that the fracture in the matrix region begin to occur under the external loading when the plastic work per unit volume is equal to the critical value. The fracture strain will be defined. The experimental data of the extruded $SiC_p$>/606l Al composites are compared with the theoretical results.

• Korean Journal of Materials Research
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• v.5 no.7
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• pp.765-774
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• 1995

The hot deformation behaviour of particulate reinforced aluminium 6061 Al composite were investigated by hot compression tests in the temperature range from 623K to 823K with strain rate of 10$^{-3}$ ~5.0 S$^{-1}$ . The effect of reinforced particulate volume fraction, mean diameter on the high temperature flow stress has also been studied. Experimental results showed that the increase in the volume fraction of reinforcement contributed to the rising of yield stress, but the stress above the yield point appeared to be steady state at all volume fractions. The apparent activation energy for deformation was 290KJ/mo1 for unreinforced 6061 Al, 327KJ/mo1 for 6061 Al-20vo1.% SiC composite and 531KJ/mo1 for 6061 Al-20vo1.%A1$_2$O$_3$composite. It appeared that $Al_2$O$_3$reinforced composites was more difficult to hot deform.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.237-248
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• 2022

Nowadays, more and more subway tunnels were planed and constructed underneath the ground of urban cities to relieve the congested traffic. Potential damage may occur in existing tunnel if the new tunnel is constructed too close. So far, previous studies mainly focused on the tunnel-tunnel interactions with circular shape. The difference between circular and horseshoe shaped tunnel in terms of deformation mechanism is not fully investigated. In this study, three-dimensional numerical parametric studies were carried out to explore the effect of different tunnel shapes on the complicated tunnel-tunnel interaction problem. Parameters considered include volume loss, tunnel stiffness and relative density. It is found that the value of volume loss play the most important role in the multi-tunnel interactions. For a typical condition in this study, the maximum invert settlement and gradient along longitudinal direction of horseshoe shaped tunnel was 50% and 96% larger than those in circular case, respectively. This is because of the larger vertical soil displacement underneath existing tunnel. Due to the discontinuous hoop axial stress in horseshoe shaped tunnel, significant shear stress was mobilized around the axillary angles. This resulted in substantial bending moment at the bottom plate and side walls of horseshoe shaped tunnel. Consequently, vertical elongation and horizontal compression in circular existing tunnel were 45% and 33% smaller than those in horseshoe case (at monitored section X/D = 0), which in latter case was mainly attributed to the bending induced deflection. The radial deformation stiffness of circular tunnel is more sensitive to the Young's modulus compared with horseshoe shaped tunnel. This is because of that circular tunnel resisted the radial deformation mainly by its hoop axial stress while horseshoe shaped tunnel do so mainly by its flexural rigidity. In addition, the reduction of soil stiffness beneath the circular tunnel was larger than that in horseshoe shaped tunnel at each level of relative density, indicating that large portion of tunneling effect were undertaken by the ground itself in circular tunnel case.