• Structural Engineering and Mechanics
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• 제67권5호
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• pp.527-544
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• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.

• Geomechanics and Engineering
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• 제14권6호
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• Steel and Composite Structures
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• 제19권1호
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• pp.93-110
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• 2015

The thermomechanical bending response of anti-symmetric cross-ply composite plates is investigated by the use of the simple four variable sinusoidal plate theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. The validity of the present theory is demonstrated by comparison with solutions available in the literature. Numerical results are presented to demonstrate the behavior of the system. The influences of aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response are studied. The present study is relevant to aerospace, chemical process and nuclear engineering structures which may be subjected to intense thermal loads.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.922-927
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• 2004

The bending moment and settlement of the slab track can be reduced by the installation of small numbers of micro piles beneath the track. This paper presents the effect of micro pile installation on the reduction of bending moment and settlement of slab track, estimated by a numerical method. The slab track is modeled as a plate based on the Mindlin's plate theory, and soil and piles are modeled as Winkler and coupled springs, respectively. The stiffness of piles is obtained by the approximate analytical method proposed by Randolph and Wroth. and the modulus of subgrade reaction is adopted to evaluate Winkler spring constant. From the analysis results, the effect of the micro pile installation is significant to considerably reduce the settlement of slab track. However, for the proper reduction of bending moments in a slab track, the pile arrangement should be reasonably taken into account to prevent the stress concentration at pile location.

• 한국구조물진단유지관리공학회 논문집
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• 제1권1호
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• pp.65-73
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• 1997

In this paper, It is the effect of using fiber sheet (Carbon Fiber Sheet & Aramid Fiber Sheet) and Steel Plate for reinforced concrete beam. 25 specimens are tested, 16 specimens are for bending capacity and the other are for shear capacity. In the case of bending testing, the kind and quantity of the reinforcement materials, the bondage and the existence of crack were selected as experimental variables. In the case of shear testing, It is testified the effect of reinforcement with the variables of the method of reinforcement (side type and U type). As a result, Using the reinforcing materials can increase the capacity of bending and shear stress.

• 한국항공우주학회지
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• 제31권1호
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• pp.34-41
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• 2003

경사기능재료 판에 대한 열탄성 변형과 응력 해석을 위해 Green 함수 방법이 채택되었다. 3차원 정상 온도분포에 대한 해는 적층판 이론에 의해 얻어진다. 열탄성 문제에 대한 기본 방정식은 각각 평면의(out-plane) 변형과 평면내(in-plane) 힘에 의해 유도되었다. 굽힙과 평면내 힘으로 인한 열탄성 변형과 응력분포는 Galerkin 방법에 근거한 Green 함수를 이용하여 해석되었다. 열탄성 변형과 응력분포 해석을 위한 Galerkin Green 함수의 특성함수들은 사각판의 제차 경계조건을 만족시키는 허용함수들의 급수 형태로 근사화 되었다. 수치예제가 수행되었으며, 경사기능재료의 물성치가 판의 열탄성 거동에 미치는 영향이 검토되었다.

• 대한기계학회논문집A
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• 제41권8호
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• pp.703-709
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• 2017

본 논문에서는 재분배된 크리프 응력을 근사적으로 접근하기 위해 크리프 해석에 비해 비교적 간단한 탄성 및 탄성-소성 해석법을 사용하여 그 결과와 비교하였다. 탄성해석 결과를 이용하여 $M_{\alpha}-tangent$ method의 Primary Stress와 ASME 코드의 $P_L+P_b/K_t$를 구하였고 탄성-소성 해석 결과를 이용하여 R5 코드의 ${\sigma}^R_{ref}$ 를 구하였다. 용접 형상이 있는 십자 모양의 판 형상에 굽힘 하중, 단축인장 및 이축인장이 작용하는 경우와 r/t가 5, 20인 곡관에 굽힘 하중 및 내압이 작용하는 경우 등 여러 형상에 대한 해석을 수행하였다. 요소 민감도 확인을 위해서는 판 형상에 굽힘 하중이 가해 지는 경우 여러 요소 크기에 대한 해석을 수행하였다. 간략 해석 결과는 크리프 응력과 큰 차이를 보이지 않았지만, $M_{\alpha}-tangent$ method의 경우 요소 크기에 민감하고 ASME코드와 R5코드의 결과는 요소 크기에 민감하지 않았다.

• 한국구조물진단유지관리공학회 논문집
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• 제18권6호
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• pp.50-59
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• 2014

본 논문에서는 경북 구미시 봉곡천에 최근 건설된 다기능어도를 대상으로 SAP2000으로 구조 해석하기 위한 변수를 R/C Slab, R/C+S/C Slab 및 지하이동통로 규격(가로${\times}$세로)을 $1m{\times}0.2m$, $1m{\times}0.4m$, $1m{\times}0.6m$와 유속 0.8m/s, 1.2m/s, 1.6m/s으로 구분하여 해석한 결과와 봉곡천 설계식을 비교하여 안정성을 검토하였다. 봉곡천의 설계식 보다 R/C+S/C Slab 타입이 지하이동통로 출구부는 휨모멘트와 최대응력은 각각 28~54%, 26~50%, 측벽은 24~47%, 17~31%, 상부슬래브인 경우도 10~27%, 4~20% 적게 나타났다. 따라서 최대응력과 휨모멘트가 R/C+S/C Slab 타입이 구조 안정성이 확보되는 것으로 나타났기 때문에 지하통로는 휨모멘트와 최대 응력이 27%, 25%, 측벽은 24%, 15% 상부슬래브는 14%, 10%의 보완이 요구되는 것으로 판단된다. 이러한 결과는 지하이동통로 규격이 봉곡천 규격과 동일한 $1m{\times}0.4m$일 때가 $1m{\times}0.2m$, $1m{\times}0.6m$ 보다 안정성이 가장 유리한 것으로 확인되었다. 또한 해석 및 분석 결과를 근거로 다기능어도 시공 시 기본 자료로 활용이 기대된다.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• 대한기계학회논문집A
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• 제27권2호
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• pp.302-309
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• 2003

Hybrid-Trefftz plate bending elements are known to be robust and free of shear locking in the thin limit because of Internal displacements fields and linked boundary displacements. Also, their finite element approximation is very simple regardless to boundary shape since all element matrices can be calculated using only boundary integrals. In this study, new hybrid-Trefftz variational formulation based on the total potential energy principle of internal displacements and displacement consistency conditions at the boundary is derived. And flat shell elements are derived by combining hybrid-Trefftz bending stiffness and plane stress stiffness with drilling dofs.