• Steel and Composite Structures
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• 제39권5호
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• pp.599-614
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• 2021

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young's and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

• Coupled systems mechanics
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• 제11권1호
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• pp.15-32
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• 2022

The comprehensive understanding of the fiber reinforced polymer behavior requires the use of advanced non-destructive testing methods due to its heterogeneous microstructure and anisotropic mechanical proprieties. In addition, the material response under load is strongly associated with manufacturing defects (e.g., voids, inclusions, fiber misalignment, debonds, improper cure and delamination). Such imperfections and microstructures induce various damage mechanisms arising at different scales before macrocracks are formed. The origin of damage phenomena can only be fully understood with the access to underlying microstructural features. This makes X-ray Computed Tomography an appropriate imaging tool to capture changes in the bulk of fibrous materials. Moreover, Digital Volume Correlation (DVC) can be used to measure kinematic fields induced by various loading histories. The correlation technique relies on image contrast induced by microstructures. Fibrous composites can be reinforced by different fiber architectures that may lead to poor natural contrast. Hence, a priori analyses need to be performed to assess the corresponding DVC measurement uncertainties. This study aimed to evaluate measurement resolutions of global and regularized DVC for glass fiber reinforced polymers with different fiber architectures. The measurement uncertainties were evaluated with respect to element size and regularization lengths. Even though FE-based DVC could not reach the recommended displacement uncertainty with low spatial resolution, regularized DVC enabled for the use of fine meshes when applying appropriate regularization.

• Steel and Composite Structures
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• 제41권6호
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• pp.805-820
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• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Earthquakes and Structures
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• 제22권3호
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• pp.219-230
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• 2022

Knowing that the variability of soil properties is an important source of uncertainty in geotechnical analyses, we will study in this paper the effect of this variability on the seismic response of a structure within the framework of Soil Structure Interaction (SSI). We use the proposed and developed model (N2-ISS, Mekki et al., 2014). This approach is based on an extension of the N2 method by determining the capacity curve of the fixed base system oscillating mainly in the first mode, then modified to obtain the capacity curve of the system on a flexible basis using the concept of the equivalent nonlinear oscillator. The properties of the soil that we are interested in this paper will be the shear wave velocity and the soil damping. These parameters will be modeled at first, as independent random fields, then, the two parameters will be correlated. The results obtained showed the importance of the use of random field in the study of SSI systems. The variability of soil damping and shear wave velocity introduces significant uncertainty not only in the evaluation of the damping of the soil-structure system but also in the estimation of the displacement of the structure and the base-shear force.

• Earthquakes and Structures
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• 제24권2호
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• pp.127-140
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• 2023

The vibration of microtubule in human cells is the source of electrical field around it and inside cell structure. The induction of electrical field is a direct result of the existence of dipoles on the surface of the microtubules. Measuring the electrical fields could be performed using nano-scale sensors and the data could be transformed to other computers using internet of things (IoT) technology. Processing these data is feasible by artificial intelligence-based methods. However, the first step in analyzing the vibrational behavior is to study the mechanics of microtubules. In this regard, the vibrational behavior of the microtubules is investigated in the present study. A shell model is utilized to represent the microtubules' structure. The displacement field is assumed to obey first order shear deformation theory and classical theory of elasticity for anisotropic homogenous materials is utilized. The governing equations obtained by Hamilton's principle are further solved using analytical method engaging Navier's solution procedure. The results of the analytical solution are used to train, validate and test of the deep neural network. The results of the present study are validated by comparing to other results in the literature. The results indicate that several geometrical and material factors affect the vibrational behavior of microtubules.

• Advances in nano research
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• 제13권4호
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• pp.393-406
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• 2022

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

• Steel and Composite Structures
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• 제44권4호
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• pp.531-543
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• 2022

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

• Steel and Composite Structures
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• 제49권6호
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• pp.713-728
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• 2023

This paper aims to investigate the free vibration analysis of FG plates, taking into account the effects of even and uneven porosity. The study employs the Hellinger-Reisner functional and obtains the element's bending stress and membrane stress fields from the analytical solution of the governing equations of the thick plate and plane problem, respectively. The displacement field serves as the second independent field. While few articles on free vibration analysis of circular plates exist, this paper investigates the free vibration of both rectangular and circular plates. After validating the proposed element, the paper investigates the effects of porosity distributions on the natural frequency of the FG porous plate. The study calculates the natural frequency of thin and thick bending plates with different aspect ratios and support conditions for various porosity and volume fraction index values. The study uses three types of porosity distributions, X, V, and O, for the uneven porosity distribution case. For O and V porosity distribution modes, porosity has a minor effect on the natural frequency for both circular and rectangular plates. However, in the case of even porosity distribution or X porosity distribution, the effect of porosity on the natural frequency of circular and rectangular plates increases with an increase in the volume fraction index.

• Structural Engineering and Mechanics
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• 제15권4호
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• pp.381-394
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• 2003

While constructing multistorey buildings with reinforced concrete framed structures it is a common practice to provide parking space for vehicles at the ground floor level. This floor will generally consist of open frames without any infilled walls and is called an open-storey. From a post disaster damage survey carried out, it was noticed that during the January 26, 2001 Bhuj (Gujarat, India) earthquake, a large number of reinforced concrete framed buildings with open-storey at ground floor level, suffered extensive damage and in some cases catastrophic collapse. This has brought into sharp focus the need to carry out systematic studies on the seismic vulnerability of such buildings. Determination of vulnerability requires realistic structural response estimations taking into account the stochasticity in the loading and the system parameters. The stochastic finite element method can be effectively used to model the random fields while carrying out such studies. This paper presents the details of stochastic finite element analysis of a five-storey three-bay reinforced concrete framed structure with open-storey subjected to standard seismic excitation. In the present study, only the stochasticity in the system parameters is considered. The stochastic finite element method used for carrying out the analysis is based on perturbation technique. Each random field representing the stochastic geometry/material property is discretised into correlated random variables using spatial averaging technique. The uncertainties in geometry and material properties are modelled using the first two moments of the corresponding parameters. In evaluating the stochastic response, the cross-sectional area and Young' modulus are considered as independent random fields. To study the influence of correlation length of random fields, different correlation lengths are considered for random field discretisation. The spatial expectations and covariances for displacement response at any time instant are obtained as the output. The effect of open-storey is modelled by suitably considering the stiffness of infilled walls in the upper storey using cross bracing. In order to account for changes in soil conditions during strong motion earthquakes, both fixed and hinged supports are considered. The results of the stochastic finite element based seismic analysis of reinforced concrete framed structures reported in this paper demonstrate the importance of considering the effect of open-storey with appropriate support conditions to estimate the realistic response of buildings subjected to earthquakes.

• Journal of Oral Medicine and Pain
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• 제24권1호
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• pp.9-24
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• 1999

Pumping into the upper joint cavity of the TMJ was done on patients who had reducible disc displacement with pain. This article discusses the change in TMJ sounds before and after the Pumping treatment. 20subjects(mean age of $32.1{\pm}10.2yr$)were selected among those who visited the department of Oral Medicine of Yonsei University for the treatment of craniomandibular dysfunctions. Through a thorough history taking, clinical exam and X-ray taking these subjects were diagnosed as reducible disc displacement patients, and they were subdivided into two groups as acute and chronic according to the time the TMJ sound was made. Sonopak was used to measure the TMJ sound before, right after and one-week after the Pumping treatment. VAS was used to measure the degree of subjective TMJ complaints(sounds and pain) before and one-week after the Pumping treatment. Vibration related items included total integral, high integral, low integral, ratio of high integral to low integral, peak amplitude, peak frequency and median frquency. 1. It was not statistically significant between the acute and chronic groups before the treatment. However, total integral, high integral, low integral, peak amplitude, peak frequency, median frequency showed to be greater in the chronic group. 2. In all the subjects, just after the Pumping treatment was done, total integral, high and low integral, peak amplitude and peak frequency significantly decreased (p<0.05). Even after one week, low integral, peak frequency and median frequency significantly decreased (p<0,05), and the TMJ sound diminished accordingly. 3. Comparing the two groups(before and right after the Pumping treatment), there was the following difference ; in the acute group, high integral, high amplitude, high frequency and median frequency significantly decreased(p<0.05). In the chronic group, total integral, high integral, low integral, ratio, peak amplitude and peak frequency significantly decreased(p<0,05). It was not statistically significant between the acute and chronic group. 4. Comparing the two groups(right after and one week after the Pumping treatment), there was the following difference : in the acute group, high integral, high amplitude, high frequency and median frequency significantly decreased(p<0.05), In the chronic group, low integral significantly decreased(p<0.05). However, although it was not statistically significant, after one week, there was an increase in total integral, ratio, peak amplitude and peak frequency compared to right after the treatment group. 5. In the VAS of before and one week after the Pumping treatment of the TMJ pain and sound, the TMJ pain significantly decreased(p<0.05) in both the acute and chronic group. However, it was not statistically significant between the two groups. There was a statistically significant decrease(p<0.05) in the TMJ sound in the acute group after one week of Pumping treatment, but no change was notable in the chronic group and it was not statistically significant between the two groups. From the above results, we can conclude that Pumping into the upper joint cavity of patients having reducible disc displacement is effective in reducing clicking and pain. Therefore, it can be applied in diverse clinical fields.