• 한국산학기술학회논문지
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• 제22권4호
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• pp.594-600
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• 2021

곡선 보는 철교 그리고 자동차와 갈은 구조물의 구성으로 널리 사용되어왔다. 많은 연구자들의 관심분야인 이러한 구조물의 안정성 거동 해석분야는 괄목할 만한 성과가 있어 왔다. 곡선 보 구조물의 기하학적 구조 및 물성치가 탄성 및 강성에 미치는 영향을 분석하기 위하여 정역학적 동역학적 해석이 필요하다. 그러나 구조물의 복잡성 때문에 어떠한 경계조건에서도 엄밀해를 얻기가 매우 어렵다. 전통적으로 미분방정식의 해법은 유한차분법 혹은 유한요소법으로 해결해왔으나 이러한 방법들은 때론 복잡한 비선형 구조물에는 과도한 컴퓨터 용량사용과 복잡한 알고리즘 프로그램을 요구한다. 이러한 어려움을 해결하기 위해 미분구적법(DQM)이 여러 분야에 사용되어왔다. 본 연구에서는 복잡한 편미분 방정식의 해를 구하기 위하여 미분구적법이 사용되었다. 중면 신장을 고려한 등분포 하중 하에서 선형으로 변하는 비대칭 곡선 보의 내평면 신장 좌굴의 지배방정식을 유도하였고, DQM을 이용하여 지배방정식의 해를 구하였다. 다양한 열림 각, 경계 조건, 그리고 파라미터에 의한 임계하중을 계산하였다. DQM 결과는 비교 가능한 엄밀해와 비교하였고 DQM은 적은 격자점을 사용하고도 정확성을 보여주었다. 예를 들어 열림 각이 180°인 비 신장 고정단 곡선 보의 경우, 엄밀해의 임계하중 값은 8.0이고 DQM의 임계하중 값은 7.98로, 오차가 0.3% 미만 이었다. 곡선 보의 내평면 비 신장 임계하중도 계산하였고, 두 이론을 상호 비교 분석하였다. 아크축의 중면 신장을 고려한 연구는 곡선 보의 임계하중에 중대한 영향을 미치는 것을 보여준다.

• Smart Structures and Systems
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• 제22권3호
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• pp.327-334
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• 2018

In this paper, dynamic buckling of the smart subjected to blast load subjected to electric field is studied. The sandwich structure is rested on Pasternak foundation with springs and shear elements. Applying piezoelasticity theory and hyperbolic shear deformation beam theory (HSDBT), the motion equations are derived by energy method. For calculating the dynamic instability region (DIR) of the sandwich structure, differential quadrature method (DQM) along with Bolotin method is used. The aim of this study is to investigate the effects of applied voltage, geometrical parameters of structure and boundary conditions on the DIR of the structure. The results show that applying negative voltage, the DIR will be happened at higher excitation frequencies. In addition, the clamped-clamped beam leads to higher excitation frequency with respect to simply supported boundary condition.

• Steel and Composite Structures
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• 제43권1호
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• pp.129-137
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• 2022

Dynamic response of a laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the sinusoidal shear deformation theory (SSDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Geomechanics and Engineering
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• 제36권4호
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• pp.407-416
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• 2024

Dynamic response of a rock tunnels by laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the exponential shear deformation theory (ESDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Earthquakes and Structures
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• 제15권3호
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• pp.285-294
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• 2018

In this study, nonlinear dynamic response of a concrete plate retrofit with Aluminium oxide ($Al_2O_3$) under seismic load and magnetic field is investigated. The plate is a composite reinforced by Aluminium oxide with characteristics of the equivalent composite being determined using Mori-Tanka model considering agglomeration effect. The plate is simulated with higher order shear deformation plate model. Employing nonlinear strains-displacements, stress-strain, the energy equations of column was obtained and using Hamilton's principal, the governing equations were derived. Differential quadrature method (DQM) in conjunction with Newark method is applied for obtaining the dynamic response of structure. The influences of magnetic field, volume percent of nanoparticles, geometrical parameters of column, agglomeration and boundary conditions on the dynamic response were investigated. Results showed that with increasing volume percent of nanoparticles, the dynamic deflection decreases.

• Computers and Concrete
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• 제19권3호
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• pp.333-338
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• 2017

In this paper, nonlinear vibration of embedded nanocomposite concrete is investigated based on Timoshenko beam model. The beam is reinforced by with agglomerated silicon dioxide (SiO2) nanoparticles. Mori-Tanaka model is used for considering agglomeration effects and calculating the equivalent characteristics of the structure. The surrounding foundation is simulated with Pasternak medium. Energy method and Hamilton's principal are used for deriving the motion equations. Differential quadrature method (DQM) is applied in order to obtain the frequency of structure. The effects of different parameters such as volume percent of SiO2 nanoparticles, nanoparticles agglomeration, elastic medium, boundary conditions and geometrical parameters of beam are shown on the frequency of system. Numerical results indicate that with increasing the SiO2 nanoparticles, the frequency of structure increases. In addition, considering agglomeration effects leads to decrease in frequency of system.

• Wind and Structures
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• 제25권4호
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• pp.381-395
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• 2017

Nonlinear vibration and instability of cylindrical shell conveying fluid-nanoparticles mixture flow are studied in this article. The surrounding elastic medium is modeled by Pasternak foundation. Mixture rule is used for obtaining the effective viscosity and density of the fluid-nanoparticles mixture flow. The material properties of the elastic medium and cylindrical shell are assumed temperature-dependent. Employing first order shear deformation theory (FSDT), the motion equations are derived using energy method and Hamilton's principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The effects of different parameters such as volume percent of nanoparticles, boundary conditions, geometrical parameters of cylindrical shell, temperature change, elastic foundation and fluid velocity are shown on the frequency and critical fluid velocity of the structure. Results show that with increasing volume percent of nanoparticles in the fluid, the frequency and critical fluid velocity will be increases.

• Wind and Structures
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• 제24권1호
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• pp.43-57
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• 2017

The use of nanotechnology materials and applications in the construction industry should be considered for enhancing material properties. However, the nonlinear buckling of an embedded straight concrete columns reinforced with silicon dioxide ($SiO_2$) nanoparticles is investigated in the present study. The column is simulated mathematically with Euler-Bernoulli and Timoshenko beam models. Agglomeration effects and the characteristics of the equivalent composite are determined using Mori-Tanaka approach. The foundation around the column is simulated with spring and shear layer. The governing equations are derived using energy method and Hamilton's principal. Differential quadrature method (DQM) is used in order to obtain the buckling load of structure. The influences of volume percent of $SiO_2$ nanoparticles, geometrical parameters and agglomeration on the buckling of column are investigated. Numerical results indicate that considering agglomeration effects leads to decrease in buckling load of structure.

• Geomechanics and Engineering
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• 제12권2호
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• pp.327-346
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• 2017

Laminated plates have many applications in different industrials. Buckling analysis of these structures with the nano-scale reinforcement has not investigated yet. However, buckling analysis of embedded laminated plates with nanocomposite layers is studied in this paper. Considering the single-walled carbon nanotubes (SWCNTs) as reinforcement of layers, SWCNTs agglomeration effects and nonlinear analysis using numerical method are the main contributions of this paper. Mori-Tanaka model is applied for obtaining the equivalent material properties of structure and considering agglomeration effects. The elastic medium is simulated by spring and shear constants. Based on first order shear deformation theory (FSDT), the governing equations are derived based on energy method and Hamilton's principle. Differential quadrature method (DQM) is used for calculating the buckling load of system. The effects of different parameters such as the volume percent of SWCNTs, SWCNTs agglomeration, number of layers, orientation angle of layers, elastic medium, boundary conditions and axial mode number of plate on the buckling of the structure are shown. Results indicate that increasing volume percent of SWCNTs increases the buckling load of the plate. Furthermore, considering agglomeration effects decreases the buckling load of system. In addition, it is found that the present results have good agreement with other works.

• Steel and Composite Structures
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• 제34권1호
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.