• 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.

• Advances in nano research
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• v.10 no.2
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• pp.151-163
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• 2021

The main target of this study is to investigate nonlinear transient responses of moving polymer nano-size plates fortified by means of Graphene Platelets (GPLs) and resting on a Winkler-Pasternak foundation under a transverse pressure force and a temperature variation. Two graphene spreading forms dispersed through the plate thickness are studied, and the Halpin-Tsai micro-mechanics model is used to obtain the effective Young's modulus. Furthermore, the rule of mixture is employed to calculate the effective mass density and Poisson's ratio. In accordance with the first order shear deformation and von Karman theory for nonlinear systems, the kinematic equations are derived, and then nonlocal strain gradient scheme is used to reflect the effects of nonlocal and strain gradient parameters on small-size objects. Afterwards, a combined approach, kinetic dynamic relaxation method accompanied by Newmark technique, is hired for solving the time-varying equation sets, and Fortran program is developed to generate the numerical results. The accuracy of the current model is verified by comparative studies with available results in the literature. Finally, a parametric study is carried out to explore the effects of GPL's weight fractions and dispersion patterns, edge conditions, softening and hardening factors, the temperature change, the velocity of moving nanoplate and elastic foundation stiffness on the dynamic response of the structure. The result illustrates that the effects of nonlocality and strain gradient parameters are more remarkable in the higher magnitudes of the nanoplate speed.

• Structural Engineering and Mechanics
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• v.87 no.6
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• pp.529-540
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• 2023

A novel laminated-hybrid-composite-beam (LHCB) of glass-epoxy infused with flyash and graphene is constructed for this study. The conventional mixture-rule and constitutive-relationship are modified to incorporate filler and lamina orientation. Eringen's non-local-theory is used to include the filler effect. Hamilton's principle based on fifth-order-layer-wise-shear-deformation-theory is applied to formulate the equation of motion. The analogous shear-spring-models for LHCB with multiple-cracks are employed in finite-element-analysis (FEA). Modal-experimentations are conducted (B&K-analyser) and the findings are compared with theoretical and FEA results. In terms of dimensionless relative-natural-frequencies (RNF), the dynamic-response in cantilevered support is investigated for various relative-crack-severities (RCSs) and relative-crack-positions (RCPs). The increase of RCS increases local-flexibility in LHCB thus reductions in RNFs are observed. RCP is found to play an important role, cracks present near the end-support cause an abrupt drop in RNFs. Further, multiple cracks are observed to enhance the nonlinearity of LHCB strength. Introduction of the first to third crack in an intact LHCB results drop of RNFs by 8%, 10%, and 11.5% correspondingly. Also, it is demonstrated that the RNF varies because of the lamina-orientation, and filler addition. For 0° lamina-orientation the RNF is maximum. Similarly, it is studied that the addition of graphene reduces weight and increases the stiffness of LHCB in contrast to the addition of flyash. Additionally, the response of LHCB to moving mass is accessed by appropriately modifying the numerical programs, and it is noted that the successive introduction of the first to ninth crack results in an approximately 40% to 120% increase in the dynamic-amplitude-ratio.

• Journal of the Korean Wood Science and Technology
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• v.11 no.3
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• pp.3-13
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• 1983

Fiber mats were made at five density levels, using fibers from kraft pulp screening rejects, rice straw and a 50/50 mixture of the two. They were soaked in the sulfur compounds. Specimens cut from the composite panels were tested in flexure at time intervals for one year to study the effect of aging. Modulus of elasticity (MOE) and modulus of rupture (MOR) were determined. Under optimum conditions of fiber mat preparation and saturation with molten sulfur and modified sulfur, composites were produced which exhibited mechanical properties comparable to conventional fiberglass in some properties and superior to conventional wood-based composition boards, For example. the moduli of elasticity of the reinforced composites made from pulp screening rejects, with a density of 0.35 gm/$cm^3$, were greater than 1,000,000 psi as compared 800.000 psi for high-density hardboard (1.28 gm/$cm^3$). Modulus of rupture of the best reinforced composites was about 7,000 psi, comparable to 6,000 psi of high-density hardboard.

• Journal of the Korean institute of surface engineering
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• v.45 no.6
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• pp.257-263
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• 2012

CrN/AlN multilayer coatings with various bilayer periods in the range of 1.8 to 7.4 nm were synthesized using a closed-field unbalanced magnetron sputtering method. Their crystalline structure, chemical compositions and mechanical properties have been investigated with Auger electron spectroscopy, X-ray diffractometry, atomic force microscopy, nanoindentation, scratch tests. The properties of the multilayer coatings varied strongly depending upon the magnitude of the bilayer period. The multilayer coating with a bilayer period of 1.8 nm showed the maximum hardness and an elastic modulus of approximately 37.6 and 417 GPa, respectively, which was 1.54 times higher than the hardness predicted by the rule of mixture from the CrN and AlN coatings. The hardness of the multilayer coating increased as the bilayer period decreased, i.e. as the rotation speed increased. The Hall-Petch type relationship, hardness being related to (1/periodicity)$^{-1/2}$, suggested by Lehoczky was confirmed for the CrN/AlN multilayer coatings with bilayer period close to the 5-10 nm range. With decreasing bilayer period, the surface morphology of the films became rougher and the critical load of films for adhesion strength gradually decreased.

• Computers and Concrete
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• v.27 no.2
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• pp.111-130
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• 2021

In the present work, an extensive study for predicting efficiency parameters (��i) of various simulated nanocomposites including Polymethyl methacrylate (PMMA) as matrix and different structures including various sizes of graphene platelets (GPLs), single, double, and multi-walled carbon nanotubes (SWCNTs-DWCNTs-MWCNTs), and single and double-walled boron nitride nanotubes (SWBNNTs-DWBNNTs) are investigated. It should be stated that GPLs, carbon and boron nitride nanotubes (CNTs, BNNT) with different chiralities (5, 0), (5, 5), (10, 0), and (10, 10) as reinforcements are considered. In this research, molecular dynamics (MDs) method with Materials studio software is applied to examine the mechanical properties (Young's modulus) of simulated nanocomposite boxes and calculate η1 of each nanocomposite boxes. Then, it is noteworthy that by changing length (6.252, 10.584, and 21.173 nm) and width (7.137, 10.515, and 19.936) of GPLs, ��1, ��2, and ��3 approximately becomes (0.101, 0.114, and 0.124), (1.15, 1.22, and 1.26), (1.04, 1.05, and 1.07) respectively. After that efficiency parameters of SWCNTs, DWCNTs, and MWCNTs are calculated and discussed separately. Finally efficiency parameters of SWBNNTs and DWBNNTs with different chiralities by PMMA as matrix are determined by MD and discussed separately. It is known that the accurate efficiency parameters helps a lot to calculate the properties of nanocomposite analytically. In particular, the obtained results from this research can be used for analytical work based on the extended rule of mixture (ERM) in bending, buckling and vibration analysis of structure in future study.

• Transactions of Materials Processing
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• v.20 no.3
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• pp.257-264
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• 2011

Multilayer(clad) sheets, composed of two or more materials with different properties, are fabricated using the roll-bonding process. A good formability is an essential property for a multilayered sheet in order to manufacture parts by plastic deformation. In this study, the influences of temperature and strain rate on the plastic properties of stainless steel-aluminum-magnesium multilayered(STS-Al-Mg) sheets were investigated. Tensile tests were performed at various temperatures and strain rates on the multilayered sheet and on each separate layer. Fracture of the multilayered sheet was observed to be temperature-dependent. At the base temperature of $200^{\circ}C$, all materials fractured simultaneously. At lower temperatures, the Mg alloy sheet fractured earlier than the other materials. Conversely, the other materials fractured earlier than the Mg alloy sheet at higher temperatures. The uniform and total elongations of the multilayered sheet were observed to be higher than that of each material at a temperature of $250^{\circ}C$. Larger uniform elongations were obtained for higher strain rates at constant temperature. The same trend was observed for the Mg alloy sheet, which exhibited the lowest elongation among the three materials. The tensile strengths and elongations of the single layer sheets were compared to those of the multilayer material. The strength of the multilayered sheet was successfully calculated by the rule of mixture from the values of each single layer. However, no simple correlation between the elongation of each layer and that of the multilayer was obtained.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.3
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• pp.192-203
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• 2004

The AA5182/polypropylene/AA5182 (AA/PP/AA) sandwich sheets have been developed for the application for automotive body panels in the future light weight vehicles with significant weight reduction. It has been reported that the 5182 aluminum sheet shows Luders band because of dissolved Mg atoms that causes fabrication process problem, especially surface roughness. The examination of serration behavior has been made after the tensile deformation of the AA/PP/AA sandwich sheets as well as that of the 5182 aluminum skin at room and elevated temperatures. All sandwich sheets and the 5182 aluminum skin showed serration phenomena on their flow curves. However, the magnitude of the serration was significantly diminished in the sandwich sheet with the high volume fraction of the polypropylene core. According to the results of the surface roughness analysis after the tensile test, the sandwich sheet evidently showed lower Luders band depth than the 5182 aluminum skin. Strain rate sensitivity, m-value, of the 5182 aluminum skin was -0.006. By attaching this skin with polypropylene core which has relatively large positive value, 0.050, m-value of the sandwich sheets was changed to the positive value. The serration reduction of the sandwich sheets was quantitatively investigated in the point of the effect on the polypropylene core thickness variation, that on the strain rate sensitivity. It was found that the serration reduction degree from the experimental results of the sandwich sheet was higher than that from the calculated values by the rule of mixture based on volume fraction of the skins and the core.

• Earthquakes and Structures
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• v.13 no.3
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Composites Research
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• v.34 no.2
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• pp.129-135
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• 2021

In this paper, in order to examine the effect of fiber volume fraction non-uniformity in thickness direction on the buckling load of cylindrical composite lattice structures, we modified the equation of buckling load of the cylindrical composite lattice structures proposed by Vasiliev. The thickness of each layer of the rib was varied by fiber volume fraction, and material properties were applied differently by using the rule of mixture. Also, we performed linear buckling analysis by varying the structure size, thickness, and average value of the fiber volume fraction of finite element model. Finally, by comparing the calculation results of the buckling load of the equivalent model using the modified buckling load equation and the results of the finite element analysis, we found that the fiber volume fraction non-uniformity in thickness direction can reduce the buckling load of the cylindrical composite lattice structure.