• Structural Engineering and Mechanics
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• 제63권2호
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Geomechanics and Engineering
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• 제19권3호
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• pp.201-215
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• 2019

A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

• 대한용접접합학회:학술대회논문집
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• 대한용접접합학회 2000년도 특별강연 및 춘계학술발표대회 개요집
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• pp.228-231
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• 2000

Based on the principle of complementary energy an analytical method is developed for determining thermal stress distribution in an thermal barrier coating. This method gives the stress distributions which satisfy the stress-free boundary conditions at the edge. Numerical examples are given in order to verify the method and to investigate the thickness effects of the ZrO$_2$-8wt％Y$_2$O$_3$ top coat on the integrity of thermal barrier coating consisted of IN738LC substrate and MCrAlY bond coat.

• Structural Engineering and Mechanics
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• 제3권2호
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• pp.193-199
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• 1995

Two kinds of special 3-dimensional 12-node finite elements-each one contains a traction-free planar surface-have been developed based on Hellinger-Reissner principle by assumed stress hybrid method. Example solutions have demonstrated the advantage of using these special elements for analyzing plates and solids with rectangular holes.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 1997년도 가을 학술발표회 논문집
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• pp.307-314
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• 1997

• 한국농공학회지
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• 제40권1호
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• pp.106-117
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• 1998

The nature of stress-path dependency, the principle that governs deformations in granular soil, and the use of Lade's double work-hardening model for predicting soil response for a variety of stress-paths have been investigated, and are examined The test results and the analyses presented show that under some conditions granular soils exhibit stress-path dependent behavior. For stress-paths involving unloading or reloading, the stress-path with the higher average stress level produces the larger strains, whereas all stress-paths having the same intial states of stress, and involving only primary loading conditions, produce strains of similar magnitudes. Experimental evidence indicates that the stress- path dependent response obtained from the double work-hardening model is also observed for real soils. It is concluded that the influence of stress history on the friction angle is negligible and the strains increment direction is uniquely determined from the state of stress but is not perpendicular to the yield surface. The strains calculated from Lade's double work-hardening model are in reasonable agreement with those measured.

• 한국전산구조공학회논문집
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• 제29권3호
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• pp.229-235
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• 2016

본 논문에서는 기존에 개발된 생브낭의 원리를 이용한 응력개선방법에 부가적인 면외 워핑함수를 도입하여 후처리함으로써 기계 및 열응력을 개선할 수 있는 방법을 소개하였다. 열응력 예측이 중요한 문제로 다루어지고 있으며, 이에 따라 수많은 보이론들이 개발되어왔다. 일반적으로 고차이론들이 열응력 예측에 유용하다고 알려져 있지만, 자유도가 많아 계산과정이 복잡하다는 단점이 존재한다. 이러한 단점들을 보완하기 위해, 본 연구에서는 계산이 비교적 간단한 고전 보이론의 변위장에 면외 워핑함수를 부가적으로 도입하고 합응력 등가를 통해 후처리함으로써 보 구조물의 열응력을 정확하게 예측할 수 있는 방법을 제시하였다. 그리고 다양한 경계조건을 가지는 수치예제들을 통해 탄성해와 비교함으로써 그 정확도를 검증하고, 면외 워핑함수가 응력개선에 미치는 영향에 대해 분석하였다.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.403-411
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• 2017

In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for EulerBernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.

• 한국도로학회논문집
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• 제14권5호
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• pp.75-83
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• 2012

PURPOSES: Suggestion of asphalt binder constitutive model based on time-temperature superposition principle and overstress concept in order to describe behavior of asphalt binders. METHODS: A series of temperature sweep tests and multiple stress creep and recovery(MSCR) tests are performed to verify the applicability of time-temperature superposition principle(t-Ts) and to develop viscoelastoplastic constitutive equation based on overstress concept. For the tests, temperature sweep tests at various high temperature and various frequency and MSCR test at $58^{\circ}C$, $64^{\circ}C$ $70^{\circ}C$, $76^{\circ}C$, and $82^{\circ}C$ are performed. From the temperature sweep tests, dynamic shear modulus mastercurve and time-temperature shift function are built and the shift function and MSCR at $58^{\circ}C$ are utilized to determine model coefficients of VBO model. RESULTS: It is observed that the time-temperature shift function built at low strain level of 0.1% is applicable not only to 1.0% strain level temperature sweep test but also maximum 500,00% strain level of MSCR test. As well, the modified VBO model shows perfect prediction on MSCR measured strain at the other temperatures. CONCLUSIONS: The Time-temperature superposition principle stands hold from very low strain level to very high strain level and that the modified VBO model can be applicable for various range of strain and temperature region to predict elastic, viscoelastic, and viscoplastic strain of asphalt binders.

• Journal of the Korean Wood Science and Technology
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• 제37권2호
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• pp.128-136
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• 2009

Curved glued laminated timber (glulam) is rapidly coming into the domestic modern timber frame buildings and predominant in building construction. The radial stress is frequently occurred in curved beams and is a critical design parameter in curved glulam. Three models, Wilson equation, Exact solution and Approximation equation were introduced to determine the radial stress of curved glulam under pure bending condition. It is obvious that radial stress distribution between small radius and large radius was different due to slight change of neutral plane location to center line. If the beam design with extremely small radius, it should be considered to determine the exact location of maximum radial stress. The current standard KSF 3021 was reviewed and would be considered some adjustment determining the optimum radius in curved glulam. Current design principle is that the stress factor is given by the curvature term only in constant depth of the beam, but like tapered or small radius of beams, the stress factor by Wilson equation was underestimated. So current design formula should be considered to improvement for characterizing the radial stress factor under pure bending condition.