• Composites Research
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• v.12 no.4
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• pp.1-7
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• 1999

Fatigue life prediction of matrix dominated composite laminates, which have a nonlinear stress/strain response, was studied analytically and experimentally. A stress function describing the relation of initial fatigue modulus and elastic modulus was used in order to consider the material nonlinearty. New modified fatigue life prediction equation was suggested based on the fatigue modulus and reference modulus concept as a function of applied stress. The prediction was verified by torsional fatigue test using crossply carbon/epoxy laminate tubes. It was shown that the proposed equation has wide applicability and good agreement with experimental data.

• Steel and Composite Structures
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• v.23 no.6
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• pp.657-668
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• 2017

In the most of previous studies, researchers have restricted their own studies to consider the effect of single walled carbon nanotubes as a reinforcement on the vibrational behavior of structures. In the present work, free vibration characteristics of functionally graded annular plates reinforced by multi-walled carbon nanotubes resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of the multi-walled carbon nanotube/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the multi-walled carbon nanotubes wt% range considered. The 2-D generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the plates are investigated. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of annular plates.

• Proceedings of the Korea Concrete Institute Conference
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• 1996.10a
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• pp.239-244
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• 1996

The aim of this study is to present the elastic modulus equation that suits to a domestic situation to coincide the improved mechanical properties of high-strength concrete. For this purpose, this study collected the laboratory data more than 400 connected with the modulus of elasticity that performed in this country and also compared with the existing equations compressive strength of investigated concrete ranged from 400 to 1, 400kg/$\textrm{cm}^2$. As a result, it could confirm that the existing equations which were proposed by the ACI 363R. CEB-FIP, NS 3473, and New-RC have a tendency to the overestimation in general.

• Tunnel and Underground Space
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• v.9 no.3
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• pp.221-229
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• 1999

Parameters of failure criteria, compressive strength and elastic modulus are most important for design and stability analysis of rock structure using numerical analysis. In this study, it suggests that the application of input data for numerical analysis by the literature study and the result of the 150 sets of triaxial compressive test. There was much different between parameters of failure criterion suggested by Hoek-Brown and parameters resulted from the analysis using 150 sets of triaxial compressive test. But the converting equations of compressive strength have had an interrelation with RMR. However, the converting of elastic of elastic modulus were different as chosen of equation, and the equation by Nicholson et at was more useful than others.

• Structural Engineering and Mechanics
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• v.12 no.6
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• pp.657-668
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• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.295-318
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• 2018

This research studies thermo-elastic behavior of rotating micro discs that are employed in various micro devices such as micro gas turbines. It is assumed that material is functionally graded with a variable profile thickness, density, shear modulus and thermal expansion in terms of radius of micro disc and as a power law function. Boundary condition is considered fixed-free with uniform thermal loading and elastic field is symmetric. Using incompressible material's constitutive equation, we extract governing differential equation of four orders; to solution this equation, we utilize general differential quadrature (GDQ) method and the results are schematically pictured. The obtained result in a particular case is compared with another work and coincidence of results is shown. We will find out that surface effect tends to split micro disc's area to compressive and tensile while nonlocal parameter tries to converge different behaviors with each other; this convergence feature make FGIMs capable to resist in high temperature and so in terms of thermo-elastic behavior we can suggest, using FGIMs in micro devices such as micro turbines (under glass transition temperature).

• Journal of Industrial Technology
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• v.33 no.A
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• pp.109-116
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• 2013

In this study the compressive strength data were collected from ready­mix concrete plants, and the analysis result showed that when using A­D test the concrete of 24MPa is suitable than that of 21MPa for normal distribution. The prediction formula for average compressive strength were proposed to $f_{cu}=f_{ck}+4(MPa)$. When comparing the proposed equations and existing relationship, the estimation variations of elastic modulus and creep modulus were not significant. The proposed equation confirmed that there was no effect to the influence function for modulus of elasticity and creep. Therefore, it was concluded that the proposed equation could replace the exiting interaction formula.

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.657-668
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• 2021

In this study, a relationship between the resonance frequency ratio and Poisson's ratio was proposed that can be used to directly determine the elastic constants. Using this relationship, the frequency ratio between the 1st bending mode and 2nd bending mode for any rectangular Timoshenko beam can be directly estimated and used to determine the elastic constants efficiently. The exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The highest percent difference for the frequency ratio between the theoretical values and the estimated values for all the beam dimensions studied was less than 0.02%. The proposed equations were used to obtain the elastic constants of beams with different material properties and dimensions using the first two measured transverse bending frequencies. Results show that using the equations proposed in this study, the Young's modulus and Poisson's ratio of rectangular Timoshenko beams can be determined more efficiently and accurately than those obtained from industry standards such as ASTM E1876-15 without the need to test the torsional vibration.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1081-1089
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• 2018

The deformation and strength of brittle rocks are significantly influenced by the crack closure behavior. The relationship between the strength and deformation of rocks under uniaxial loading is the foundation for design and assessment of such scenarios. The concept of relative crack closure strain was proposed to describe the influence of the crack closure behavior on the deformation and strength of rocks. Considering the crack compaction effect, a new damage constitutive model was developed based on accumulated AE counts. First, a damage variable based on the accumulated AE counts was introduced, and the damage evolution equations for the four types of brittle rocks were then derived. Second, a compaction coefficient was proposed to describe the compaction degree and a correction factor was proposed to correct the error in the effective elastic modulus instead of the elastic modulus of the rock without new damage. Finally, the compaction coefficient and correction factor were used to modify the damage constitutive model obtained using the Lemaitre strain equivalence hypothesis. The fitted results of the models were then compared with the experimental data. The results showed that the uniaxial compressive strength and effective elastic modulus decrease with an increase in the relative crack closure strain. The values of the damage variables increase exponentially with strains. The modified damage constitutive equation can be used to more accurately describe the compressive deformation (particularly the compaction stage) of the four types of brittle rocks, with a coefficient of determination greater than 0.9.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.12
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• pp.98-106
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• 2016

Measurements of the elastic modulus and hardness using a nano indentation machine rely on the equation for the fitted contact area, which is valid for only sink-in materials. For most soft engineering materials that involve pile-up behavior rather than sink-in, the contact area equation underestimates the contact area and thus overestimates the elastic modulus and hardness. This study proposes a correction method to amend erroneous hardness measurements in pile-up situations. The method is a supplemental derivation to the original hardness measurement with the known value of the elastic modulus. The method was examined for soft engineering metals, Al 6061 T6 and C 12200, via tensile tests, nano indentation tests, impression observations, and finite element analysis. The proposed technique shows reasonable agreement with the analytical results accounting for strain gradient plasticity from a previous study.