• Steel and Composite Structures
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• 제45권3호
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• pp.305-330
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• 2022

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

• Steel and Composite Structures
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• 제44권5호
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Geomechanics and Engineering
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• 제35권4호
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• pp.367-383
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• 2023

The present paper examines the natural frequency responses of the bi-directional (n_x-n_y, n_y-n_z and n_z-n_x) and multidirectional (n_x-n_y-n_z) functionally graded (FG) plate and curved structures with and without porosity. The even and uneven kind of porosity pattern are considered to observe the influence of porosity type and porosity index. The numerical findings have been obtained using a higher order shear deformation theory (HSDT) based isometric finite element (FE) approach generated in a MATLAB platform. According to the convergence and validation investigation, the proposed HSDT based FE model is adequate to predict free vibrational responses of multidirectional porous FG plates and curved structures. Further a parametric analysis is carried out by taking various design parameters into account. The free vibrational behavior of bidirectional (2D) and multidirectional (3D) perfect-imperfect FGM structure is examined against various power law index, support conditions, aspect, and thickness ratio, and for the curvature of curved structures. The results indicate that the maximum non-dimensional fundamental frequency (NFF) value is observed in perfect FGM plates and curved structures compared to porous FGM plates and curved structures and it is maximum for FGM plates and curved structures with uneven kind of porosity than even porosity.

• Steel and Composite Structures
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• 제49권5호
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• pp.587-602
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• 2023

This article presents the numerical modelling of transient heat transfer in highly heterogeneous composite materials where the thermal conductivity, specific heat and density are assumed to be directional-dependent. This article uses a coupled finite element-finite difference scheme to perform the transient heat transfer analysis of unidirectional (1D) and multidirectional (2D/3D) functionally graded composite panels. Here, 1D/2D/3D functionally graded structures are subjected to nonuniform heat source and inhomogeneous boundary conditions. Here, the multidirectional functionally graded materials are modelled by varying material properties in individual or in-combination of spatial directions. Here, fully spatial-dependent material properties are evaluated using Voigt's micromechanics scheme via multivariable power-law functions. The weak form is obtained through the Galerkin method and solved further via the element-space and time-step discretisation through the 2D-isoparametric finite element and the implicit backward finite difference schemes, respectively. The present model is verified by comparing it with the previously reported results and the commercially available finite element tool. The numerous illustrations confirm the significance of boundary conditions and material heterogeneity on the transient temperature responses of 1D/2D/3D functionally graded panels.

• Structural Engineering and Mechanics
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• 제90권1호
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• pp.1-18
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• 2024

The present study conducts a thorough analysis of thermal vibrations in functionally graded porous nanocomposite beams within a thermal setting. Investigating the temperature-dependent material properties of these beams, which continuously vary across their thickness in accordance with a power-law function, a finite element approach is developed. This approach utilizes a nonlocal strain gradient theory and accounts for a linear temperature rise. The analysis employs four different patterns of porosity distribution to characterize the functionally graded porous materials. A novel two-variable shear deformation beam nonlocal strain gradient theory, based on trigonometric functions, is introduced to examine the combined effects of nonlocal stress and strain gradient on these beams. The derived governing equations are solved through a 3-nodes beam element. A comprehensive parametric study delves into the influence of structural parameters, such as thicknessratio, beam length, nonlocal scale parameter, and strain gradient parameter. Furthermore, the study explores the impact of thermal effects, porosity distribution forms, and material distribution profiles on the free vibration of temperature-dependent FG nanobeams. The results reveal the substantial influence of these effects on the vibration behavior of functionally graded nanobeams under thermal conditions. This research presents a finite element approach to examine the thermo-mechanical behavior of nonlocal temperature-dependent FG nanobeams, filling the gap where analytical results are unavailable.

• Advances in nano research
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• 제16권3호
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• pp.313-324
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• 2024

The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.

• 한국재료학회지
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• 제3권6호
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• pp.614-623
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• 1993

높은 알칼리량을 함유하는 LiF-$Li_{2}O-B_{2}O_{3}-P_{2}O_5$계 유리의 전기적 특성을 분석하였다. $Li_{+}$ 이온은 모두 전기전도에 기여하지 않으나 조성에 따른 전기전도도의 변동은 약전해질 모델을 따르지 않았다. 또한 이동이온의 농도를 구하는데 사용되는 승법칙(power law)의 적용이 가능하지 않았다. 이들 계에서 조성에 따른 전기전도도의 변동은 유리내에서의 이동 가능한 $Li^{+}$이온의 농도변화만으로 또는 이동도의 변화만으로는 설명할 수 없었다. 전도도의 향상은 $(B-O-P)^{o}$ 보다 $Li^{+}$이온의 확산에 부가적인 자리를 제공하는$(B-O-P)^-,di^-$, 및 metaborate가 형성된 것과 관련이 있었다. 전기전도성이 가장 좋은 조성의 $150^{\circ}C$에서의 전기전도도는 $2.43 \times 10^{-4}$S/cm였고 분해포텐샬은 5.94V, emf는 3.14V였고 에너지 밀도는 22Wh/Kg이었다.

• 대한토목학회논문집
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• 제34권4호
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• pp.1227-1240
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• 2014

휴 폐광산지역은 복합지질재해지역으로 집중호우에 의해 토사재해와 산성광산배수를 발생시킨다. 본 연구는 폐석적치장 전반에 걸쳐 토사재해가 관측된 임기광산에 대해 지반공학적 유변학적 시험을 수행하고 얻어진 시험결과를 토대로 1-D 토석류 수치해석을 수행함으로써 토석류의 확산성을 조사하였다. 모래와 자갈로 구성된 광산폐석 시료의 유변학적 특성을 조사하기 위해 베인관입형 레오미터(Vane-penetrated rheometer)를 사용하였으며, 전단응력 제어를 통한 전단응력(${\tau}$)-전단속도(${\dot{\gamma}}$)와 점도(${\eta}$)-전단속도(${\dot{\gamma}}$) 간의 상관관계를 얻었다. 또한 광산폐석 시료에 대해 잘 알려진 유변학적 모델들(Bingham, Herschel-Bulkley, Power-law, bilinear 및 Papanastasiou 모델)을 적용함으로써 수치해석에 필요한 유변학적 매개변수(항복응력과 소성점도)를 결정하였다. 실험결과에 따르면, 체적농도에 무관하게 전형적인 전단담화(shear thinning) 거동이 관측되었으며, 함수비가 증가할수록 Bingham 유체처럼 거동하는 것으로 나타났다. 또한 사용된 모든 유변학적 모델들은 파괴 후 거동에 적합한 모델들로 밝혀졌다. 토석류 흐름특성을 조사하기 위해 실험결과를 토대로 토석류 크기(5 m, 10 m 및 15 m)와 항복응력(100 Pa, 200 Pa, 300 Pa 및 500 Pa)을 선정하여 1-D BING을 통해 수치해석을 수행하였다. 그 결과, 토석류 이동거리와 이동속도는 항복응력의 크기에 반비례한 것으로 나타났으며, 토석류 항복응력이 500 Pa 이하인 경우 대부분의 토사는 계곡부까지 흘러갈 수 있는 것으로 나타났다. 따라서 집중호우 기간에 산악지역에 방치된 광산폐석은 토사재해에 취약하고 2차적으로 인근 수계로 유입되어 환경적 문제를 야기시킬 수 있는 것으로 나타났다.

• 한국식품영양과학회지
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• 제38권9호
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• pp.1253-1257
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• 2009

7종류의 상업용 검(xanthan gum, guar gum, pectin, gum arabic, gellan, locust bean gum, sodium alginate)을 국내산 고구마전분에 대해 0%, 0.3%, 0.6% 농도로 첨가한 전분-검혼합 페이스트(5%, w/w)의 유동특성과 항복응력을 측정하였다. 고구마전분-검 혼합물은 대부분 검 농도가 0.3%에서 0.6%로 증가할 때 팽윤력이 증가하였다. 또한 유동특성은 power law 모델식으로부터 결정되었고, 항복응력 측정을 위해 vane 방법이 사용되었다. 고구마전분-검 혼합물은 $25^{\circ}C$에서 shear-thinning 거동특성을 보여주었고, 겉보기 점도(${\eta}_{a,100}$)와 점조도 지수(K)는 pectin과 sodium alginate를 제외한 모든 시료에서 검의 농도가 증가함에 따라 증가하는 경향을 나타내었다. Pectin은 다른 검에 비해 매우 낮은 항복 응력 값을 나타내었고, gellan은 매우 높은 항복응력 값을 나타내었다. 고구마전분-검 혼합물은 pectin, gum arabic 그리고 sodium alginate를 제외한 다른 검 첨가에서 탄성적상승효과를 나타냈다. 일반적으로 고구마전분의 유동특성과 vane 항복응력은 검 첨가에 의해 크게 영향을 받으며, 검 종류와 농도에 의존함을 알 수 있었다.

• 한국수자원학회논문집
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• 제52권2호
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• pp.149-161
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• 2019

본 연구에서는 3차원 이산 균열망 수치모형을 이용하여 균열망을 구성하는 균열요소의 길이분포가 유체 흐름 특성이 미치는 영향에 대해 수치적으로 분석하였다. 균열요소의 길이분포의 생성을 위해 절단멱분포법칙을 적용하였으며, 지수 ${\beta}_l$을 1.0에서부터 6.0까지 변화시키면서 유체 흐름 모의를 수행하였다. 모의결과 지수 ${\beta}_l$이 증가함에 따라 균열요소들의 길이분포는 점차적으로 작아지며, 이로 인해 균열망의 투수성에 영향을 미치는 균열요소들 간의 연결성은 취약해지는 것으로 나타났다. 각각의 지수 ${\beta}_l$에 대해 균열요소 각각에서 계산된 유량분포를 분석하였을 때 ${\beta}_l=1.0$에서의 평균유량이 ${\beta}_l=6.0$에 비해 약 447배 크게 산정되었으며, 균열망의 유출경계에서 계산된 유량의 경우 ${\beta}_l=1.0$일 때가 6.0에 비해 약 6,440배 크게 산정되었다.