• Earthquakes and Structures
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• v.16 no.5
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• pp.547-561
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• 2019

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

• Advances in nano research
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• v.10 no.3
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• pp.281-293
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• 2021

This paper presents a new nonlocal Hyperbolic Shear Deformation Beam Theory (HSDBT) for the free vibration of porous Functionally Graded (FG) nanobeams. A new displacement field containing integrals is proposed which involves only three variables. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect and its account for shear deformation by a hyperbolic variation of all displacements through the thickness without using the shear correction factor. It has been observed that during the manufacture of Functionally Graded Materials (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the free vibration analysis of FG beams taking into account the influence of these imperfections is established. Four different porosity types are considered for FG nanobeam. Material characteristics of the FG beam are supposed to vary continuously within thickness direction according to a power-law scheme which is modified to approximate material characteristics for considering the influence of porosities. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio, and the porosity types on the dynamic responses of the nanobeam are discussed.

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.477-490
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• 2022

This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved first-order shear deformation shell theory (IFSDST) and von Karman's type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton's principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

• Structural Engineering and Mechanics
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• v.91 no.5
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• pp.527-538
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• 2024

The standard numerical approximation of structural displacement field leads to the thickness-wise transverse shear stress distributions which are quite different from the exact ones. To overcome this inherent problem, an effective and reliable post-processing method is presented based on the strain recovery and the stress equilibrium, particularly for functionally graded cylindrical and conical elastic panels. The present method is developed in the framework of locking-free 2-D natural element method. Through the recovery of displacement component-wise derivatives, the element-wise discontinuous in-plane strain distributions are enhanced to be globally continuous and smoothened. And, using the continuous in-plane strains, the troublesome poor transverse shear stress distributions are enhanced through the thickness-wise integration of static equilibrium equations. The validity of present post-processing method is verified through the comparison with the reference solutions. In addition, the comparative experiments are also performed to investigate the difference between the present method and other available post-processing methods. The numerical results confirm that the present method provides the accurate transverse shear stress distributions which are consistent with the reference solutions and much better than other available methods.

• Advances in materials Research
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• v.13 no.5
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• pp.335-353
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• 2024

In the present paper, a simple quasi-3D integral higher-order beam theory (HBT) is presented, in which both shear deformation and thickness stretching effects are included for mechanical analysis of advanced composite beams with simply supported boundary conditions, handling mainly bending, buckling, and free vibration problems. The kinematics is based on a novel displacement field which includes the undetermined integral terms and the parabolic function is used in terms of thickness coordinate to represent the effect of transverse shear deformation. The governing equilibrium equations are drawn from the dynamic version of the principle of virtual work; whereas the solution of the problem is obtained by assuming a Navier technique for simply supported advanced composite beams subjected to sinusoidally and uniformly distributed loads. The correctness of the present computational method is checked by comparing the obtained numerical results with quasi-3D solutions found in the literature and with those provided by other shear deformation beam theories. It can be confirmed that the proposed model, which does not involve any shear correction factor, is not only accurate but also simple and useful in solving the static and dynamic response of advanced composite beams.

• Advances in Computational Design
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• v.9 no.3
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• pp.151-165
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• 2024

In this paper, the evaluation of the elastic lateral stiffness factor (ELSF) of steel frames for different lateral load-resisting systems (LLRSs) is presented. First, 720 steel structural frame models have been analyzed and designed using the equivalent lateral force method. Then by using pushover analysis method, all models have been analyzed, compared and evaluated. Finally, the effects of a number of influenced parameters such as different types of LLRSs, span length, number of stories, number of spans as well as story height of the buildings on the lateral stiffness are assessed and by applying regression analysis some useful equations were submitted. Based on the results obtained for steel frames having different LLRSs, compared to ordinary moment-resisting frames (OMRFs) as a base (having ELSF of 1), the normalized average ELSFs of K-eccentrically braced-frames (K-EBFs), V-, Z-, inverted V-, X-braced-frames, shear walls with thickness of 25 cm (SW25) and shear walls with thickness of 30 cm (SW30) are about 2.2, 6, 7, 9, 11, 95, 155, respectively. Among the braced-frames, X-braced-frames have the maximum ELSF, about 10 times more than OMRF, while OMRFs provide the minimum ELSFs among all LLRSs, and the frames supported by shear walls have ELSFs about 100 to 150 times more than OMRFs.

• Steel and Composite Structures
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• v.52 no.6
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• pp.657-662
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• 2024

In the present analysis, the buckling behavior of smart beams integrated into racket frames for enhancing player control was examined by numerical solutions and sinusoidal shear deformation theory. The smart beam under consideration is subjected to an external voltage in the thickness direction. The integration of this smart material into the structure of the racket should optimize performance, improving the racket's stability and responsiveness during play. In this, an accurate representation of complex shear effects is made by using a sinusoidal shear deformation theory, while the solution of the resulting governing equations is made by numerical methods. The critical buckling loads and the characteristics of deformation obtained through the analysis provide insight into some design parameters controlling and influencing stability. Obtained results are validated with other published works. The length and thickness of the beam, elastic medium, boundary condition, and influence of external voltages have been represented for buckling load in the structure. These results will help in designing smart racket frames using smart beams to provide more precision and control for the players in an intelligent way.

• Wind and Structures
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• v.27 no.4
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• pp.269-282
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• 2018

In this paper, a new displacement field based on quasi-3D hybrid-type higher order shear deformation theory is developed to analyze the static and dynamic response of exponential (E), power-law (P) and sigmoïd (S) functionally graded beams. Novelty of this theory is that involve just three unknowns with including stretching effect, as opposed to four or even greater numbers in other shear and normal deformation theories. It also accounts for a parabolic distribution of the transverse shear stresses across the thickness, and satisfies the zero traction boundary conditions at beams surfaces without introducing a shear correction factor. The beam governing equations and boundary conditions are determined by employing the Hamilton's principle. Navier-type analytical solutions of bending and free vibration analysis are provided for simply supported beams subjected to uniform distribution loads. The effect of the sigmoid, exponent and power-law volume fraction, the thickness stretching and the material length scale parameter on the deflection, stresses and natural frequencies are discussed in tabular and graphical forms. The obtained results are compared with previously published results to verify the performance of this theory. It was clearly shown that this theory is not only accurate and efficient but almost comparable to other higher order shear deformation theories that contain more number of unknowns.

• Journal of the Microelectronics and Packaging Society
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• v.12 no.1 s.34
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• pp.87-93
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• 2005

Interfacial reactions between 48Sn-52In solder and $0.1{\mu}m$ Ti/3 ${\mu}m$ Cu/Au under bump metallurgies(UBM) with various Au thickness of $0.1{\~}0.7{\mu}m$ have been investigated after solder reflow at $150^{\circ}C,\;200^{\circ}C$, and $250^{\circ}C$ for 1 minute. Ball shear strength and shear energy of the Sn-52In solder bump on each UBM was also evaluated. With reflowing at $150^{\circ}C$ and $200^{\circ}C$, $Cu_6(Sn,In)_5$ and $AuIn_2$ intermetallic compounds were formed at UBW solder interface. However, UBM was consumed almost completely with reflowing at $250^{\circ}C$. While ball shear strength was not consistent with UBM/solder reactions, ball shear energy matched well with UBM/solder reactions.

• Journal of Korean Society of Steel Construction
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• v.27 no.5
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• pp.435-445
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• 2015

Concrete filled steel tube(CFT), which has superior ductility and strength, is used for building column, bridge piers of ocean structure. Shear design equations of CFT existing in structural design provisions are excessively conservative. It has an effect on constructability and the economics of CFT. However, to suggest the reasonable shear design equation, experimental studies on the shear capacity of CFT have been rarely conducted. This study is analytical research to suggest improved shear design equations of large-diameter concrete-filled steel tubes. This analytical research was conducted to apply finite element analysis model of CFT based on the prior research. It was verified by comparison with prior test results. The verified model was used for parameter studies to estimate the influence of overhang length, concrete compressive strength and diameter-thickness ratio on shear strength.