• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Steel and Composite Structures
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• v.32 no.3
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• pp.361-372
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• 2019

Tubular joints are used in the construction of offshore structures and other land-based structures because of its ease of fabrication. These joints are subjected to different environmental loadings in their lifetime. At the time of fabrication or modification of an existing offshore platform, tubular joints are usually strengthened to withstand the environmental loads. Currently, various strengthening techniques such as ring stiffeners, gusset plates are employed to strengthen new and existing tubular joints. Due to some limitations with the present practices, some new techniques need to be addressed. Many researchers used Fibre Reinforced Polymer (FRP) to strengthen tubular joints. Some of the studies were focused on axial compression of Glass Fibre Reinforced Polymer (GFRP) strengthened tubular joints and found that it was an efficient technique. Earlier, the authors had performed studies on Carbon Fibre Reinforced Polymer (CFRP) strengthened tubular joint subjected to axial compression. The study steered to the conclusion that FRP composites is an alternative strengthening technique for tubular joints. In this work, the study was focused on axial compression of Y-joint and in plane and out of plane bending of T-joints. Experimental investigations were performed on these joints, fabricated from ASTM A106 Gr. B steel. Two sets of joints were fabricated for testing, one is a reference joint and the other is a joint strengthened with CFRP. After performing the set of experiments, test results were then compared with the numerical solution in ANSYS Parametric Design Language (APDL). It was observed that the joints strengthened with CFRP were having improved strength, lesser surface displacement and ovalization when compared to the reference joint.

• Structural Engineering and Mechanics
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• v.71 no.6
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• pp.627-641
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• 2019

The paper focuses on bending analysis of the functionally graded (FG) plates with arbitrary shapes and boundary conditions. The material property of FG plates is modelled by using the power law distribution. Based on the first order shear deformation plate theory (FSDT), the governing equations as well as boundary conditions are formulated and obtained by using the principle of virtual work. The coupled Boundary Element-Radial Basis Function (BE-RBF) method is established to solve the complex FG plates. The proposed methodology is developed by applying the concept of the analog equation method (AEM). According to the AEM, the original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. Then, the fictitious sources are established by the application of a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential problem. Therefore, the kernels of the boundary integral equations are conveniently evaluated and readily determined, so that the complex FG plates can be easily computed. The reliability of the proposed method is evaluated by comparing the present results with those from analytical solutions. The effects of the power index, the length to thickness ratio and the modulus ratio on the bending responses are investigated. Finally, many interesting features and results obtained from the analysis of the FG plates with arbitrary shapes and boundary conditions are demonstrated.

• Steel and Composite Structures
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• v.39 no.5
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• pp.631-643
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• 2021

The aim of this work is to study the hygro-thermo-mechanical bending responses of simply supported FG plate resting on a Winkler-Pasternak elastic foundation. The effect transverse shear strains is taken into account in which the zero transverse shear stress condition on the top and bottom surfaces of the plate is ensured without using any shear correction factors. The developed model contains only four unknowns variable which is reduced compared to other HSDTs models. The material properties of FG-plate are supposed to vary across the thickness of the plate according to power-law mixture. The differential governing equations are derived based on the virtual working principle. Numerical outcomes of bending analysis of FG plates under hygro-thermo-mechanical loads are performed and compared with those available in the literature. The effects of the temperature, moisture concentration, elastic foundation parameters, shear deformation, geometrical parameters, and power-law-index on the dimensionless deflections, axial and transverse shear stresses of the FG-plate are presented and discussed.

• Advances in nano research
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• v.14 no.3
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• pp.211-224
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• 2023

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

• Structural Engineering and Mechanics
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• v.81 no.2
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.103-119
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• 2024

The present research investigates the thermodynamically bending behavior of FG sandwich plates, laying on the Winkler/Pasternak/Kerr foundation with various boundary conditions, subjected to harmonic thermal load varying through thickness. The supposed FG sandwich plate has three layers with a ceramic core. The constituents' volume fractions of the lower and upper faces vary gradually in the direction of the FG sandwich plate thickness. This variation is performed according to various models: a Power law, Trigonometric, Viola-Tornabene, and the Exponential model, while the core is constantly homogeneous. The displacement field considered in the current work contains integral terms and fewer unknowns than other theories in the literature. The corresponding equations of motion are derived based on Hamilton's principle. The impact of the distribution model, scheme, aspect ratio, side-to-thickness ratio, boundary conditions, and elastic foundations on thermodynamic bending are examined in this study. The deflections obtained for the sandwich plate without elastic foundations have the lowest values for all boundary conditions. In addition, the minimum deflection values are obtained for the exponential volume fraction law model. The sandwich plate's non-dimensional deflection increases as the aspect ratio increases for all distribution models.

• Advances in nano research
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• v.16 no.3
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• pp.289-301
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• 2024

In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.

• Journal of the Korean Society for Nondestructive Testing
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• v.25 no.5
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• pp.339-342
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• 2005

In long-period fiber grating (LPFG) to be made up optical fiber sensors, resonance coupling occurs between the forward-propagating core mode and cladding modes at the wavelength that satisfy the Phase matching condition. The resonance wavelength and the coupling strength depends strongly on the external environment like temperature, strain, and ambient index. These characteristics can be utilized for various applications as optical fiber sensors. fabrication of optical fiber gratings is typically based on the photosensitivity effect, i.e. the permanent change of the refractive index upon irradiation of the UV beam, and therefore, fabrication of the optical fiber with high phososensitivity is an important part of the research on optical fiber gratings. In this work, we measured the effort of to-doping of boron on the index difference between the core and cladding of the optical fiber and the sensitivity of the LPFC to the temperature and bending changes. We observed that the index difference between the core and the cladding decreased by $(1.69{\times}10^{-4}/SCCM)$ and the temperature sensitivity of the resonance wavelength shirt decreased by $(0.01145nm/^{\circ}C/SCCM)$. The dependence or the bending-induced changes or the transmission characteristics of LPFG on the tore-cladding index difference was investigated experimentally. The measurement results indicate that the bending sensitivity increases as the index difference decreases.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.08a
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• pp.176-176
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• 2010

One of the critical issues for applications of flexible organic thin film transistors (OTFTs) for flexible electronic systems is the electrical stabilities of the OTFT devices, including variation of the current on/off ratio (Ion/Ioff), leakage current, threshold voltage, and hysteresis under repetitive mechanical deformation. In particular, repetitive mechanical deformation accelerates the degradation of device performance at the ambient environment. In this work, electrical stability of the pentacene organic thin film transistors (OTFTs) employing multi-stack hybrid encapsulation layers was investigated under mechanical cyclic bending. Flexible bottom-gated pentacene-based OTFTs fabricated on flexible polyimide substrate with poly-4-vinyl phenol (PVP) dielectric as a gate dielectric were encapsulated by the plasma-deposited organic layer and atomic-layer-deposited inorganic layer. For cyclic bending experiment of flexible OTFTs, the devices were cyclically bent up to 105 times with 5mm bending radius. In the most of the devices after 105 times of bending cycles, the off-current of the OTFT with no encapsulation layers was quickly increased due to increases in the conductivity of the pentacene caused by doping effects from $O_2$ and $H_2O$ in the atmosphere, which leads to decrease in the Ion/Ioff and increase in the hysteresis. With encapsulation layers, however, the electrical stabilities of the OTFTs were improved significantly. In particular, the OTFTs with multi-stack hybrid encapsulation layer showed the best electrical stabilities up to the bending cycles of $10^5$ times compared to the devices with single organic encapsulation layer. Changes in electrical properties of cyclically bent OTFTs with encapsulation layers will be discussed in detail.