• Steel and Composite Structures
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• 제49권3호
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• pp.281-291
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• 2023

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

• Structural Engineering and Mechanics
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• 제88권4호
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• 한국지하수토양환경학회지:지하수토양환경
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• 제8권4호
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• pp.53-63
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• 2003

연구의 목적은 옥동천 유역 토양의 중금속의 존재형태와 존재형태에 따른 중금속의 오염지수를 산정하는데 있다. 토양채취는 경작지 토양을 대상으로 하였고 토양은 물리적 특성과 이화학적 특성을 분석하였다. 그 결과 경작지 토양의 pH는 5.2에서 7.6을, 총질소 함량과 loss on ignition은 각각 0.6∼2.5%, 1.9∼12.9%를 나타냈다. 경작지 토양의 중금속 농도는 폐광된 탄광지역의 논토양에서 높게 나타났으며, 총 중금속의 농도는 Zn > Pb > Ni > Cu > Cd 순으로 나타났다. 이러한 결과는 토양환경기준치와 비오염 경작지 토양의 중금속 농도 보다 높게 나타나는 경향을 보였으며, 총 중금속 중 일부분이 이동 가능성이 있는 부분으로 나타났다. 토양오염 평가지수(SPAI)는 조사지 토양에서 Non polluted와 Moderately polluted를 나타냈으며, 이러한 결과는 비 이동성 형태보다는 이동성 형태의 값이 났게 나타났다. 경작지 토양에서 중금속 존재형태와 SPAI 값은 중금속에 의한 오염과 식물체에 미치는 잠재적인 유해한 결과를 얻을수 있다. 따라서 결과에서 보여진 폐탄광지역의 토양을 복원하기 위해서 신속한 대책이 필요하다.

• Journal of Theoretical and Applied Mechanics
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• 제1권1호
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• pp.69-88
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• 1995

The paper attempts to estimate the incubation time of a cavity in the interface between a power law creep particle and an elastic matrix subjected to a uniaxial stress. Since the power law creep particle is time dependent, the stresses in the interface relax. Through previous stress analysis related to the present physical model, the relaxation time is defined by ${\alpha}$2 which satisfies the equation $\Gamma$0 ｜1+${\alpha}$2k｜m=1-${\alpha}$2 [19]. $\Gamma$0=2(1/√3)1+m($\sigma$$\infty$/2${\mu}$)m($\sigma$0/$\sigma$$\infty$tm) where $\sigma$$\infty$ is an applied stress, ${\mu}$ is a shear modulus of a matrix, $\sigma$$\infty$ is a material constant of a power law particle, $\sigma$=$\sigma$0 $\varepsilon$ and t elapsed time. the volume free energy associated with Helmholtz free energy includes strain energies associated with Helmholtz free energy includes strain energies caused by applied stress anddislocations piled up in interface (DPI). The energy due to DPI is found by modifying the results of Dundurs and Mura[20]. The volume free energies caused by both applied stress and DPI are a function of the cavity size(${\gamma}$) and elapsed time(t) and arise from stress relaxation in the interface. Critical radius ${\gamma}$ and incubation time t to maximize Helmholtz free energy is found in present analysis. Also, kinetics of cavity fourmation are investigated using the results obtained by Riede[16]. The incubation time is defied in the analysis as the time required to satisfy both the thermodynamic and kinetic conditions. Through the analysis it is found that [1] strain energy caused by the applied stress does not contribute significantly to the thermodynamic and kinetic conditions of a cavity formation, 2) in order to satisfy both thermodynamic and kinetic conditions, critical radius ${\gamma}$ decreases or holds constant with increase of time until the kinetic condition(eq.40) is satisfied. Therefore the cavity may not grow right after it is formed, as postulated by Harris[11], and Ishida and Mclean[12], 3) the effects of strain rate exponent (m), material constant $\sigma$0, volume fraction of the particle to matrix(f) and particle size on the incubation time are estimated using material constants of the copper as matrix.

• 천문학회지
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• 제43권2호
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• pp.25-39
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• 2010

We perform kinetic simulations of diffusive shock acceleration (DSA) in Type Ia supernova remnants (SNRs) expanding into a uniform interstellar medium (ISM). Bohm-like diffusion due to self-excited $Alfv\acute{e}n$ waves is assumed, and simple models for $Alfv\acute{e}nic$ drift and dissipation are adopted. Phenomenological models for thermal leakage injection are considered as well. We find that the preshock gas temperature is the primary parameter that governs the cosmic ray (CR) acceleration efficiency and energy spectrum, while the CR injection rate is a secondary parameter. For SNRs in the warm ISM of $T_0\lesssim10^5K$, if the injection fraction is $\xi\gtrsim10^{-4}K$, the DSA is efficient enough to convert more than 20% of the SN explosion energy into CRs and the accelerated CR spectrum exhibits a concave curvature flattening to $E^{-1.6}$, which is characteristic of CR modified shocks. Such a flat source spectrum near the knee energy, however, may not be reconciled with the CR spectrum observed at Earth. On the other hand, SNRs in the hot ISM of$T_{0}\approx10^{6}K$ with a small injection fraction, $\xi$<$10^{-4}$, are inefficient accelerators with less than 10% of the explosion energy getting converted to CRs. Also the shock structure is almost test-particle like and the ensuing CR spectrum can be steeper than $E^{-2}$. With amplified magnetic field strength of order of $30{\mu}G$ $Alfv\acute{e}n$ waves generated by the streaming instability may drift upstream fast enough to make the modified test-particle power-law as steep as $E^{-2.3}$, which is more consistent with the observed CR spectrum.

• Wind and Structures
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• 제22권4호
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• pp.429-454
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• 2016

In this paper, a shear deformation plate theory based on neutral surface position is developed for free vibration analysis of functionally graded material (FGM) plates. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. During manufacture, defects such as porosities can appear. It is therefore necessary to consider the vibration behavior of FG plates having porosities in this investigation. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The equation of motion for FG rectangular plates is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Numerical results are presented and the influences of the volume fraction index and porosity volume fraction on frequencies of FGM plates are clearly discussed.

• Steel and Composite Structures
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• 제25권6호
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• pp.717-726
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• 2017

In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier's procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Steel and Composite Structures
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• 제43권5호
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• pp.581-601
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• 2022

The main objective of this research work is to investigate the free vibration behavior of annular sandwich plates resting on the Kerr foundation at thermal conditions. This sandwich configuration is composed of two FGM face sheets as coating layer and a porous GPLRC (GPL reinforced composite) core. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the core thickness direction. To model closed-cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme is used, while the Poisson's ratio and density are computed by the rule of mixtures. Besides, the material properties of two FGM face sheets change continuously through the thickness according to the power-law distribution. To capture fundamental frequencies of the annular sandwich plate resting on the Kerr foundation in a thermal environment, the analysis procedure is with the aid of Reddy's shear-deformation plate theory based high-order shear deformation plate theory (HSDT) to derive and solve the equations of motion and boundary conditions. The governing equations together with related boundary conditions are discretized using the generalized differential quadrature (GDQ) method in the spatial domain. Numerical results are compared with those published in the literature to examine the accuracy and validity of the present approach. A parametric solution for temperature variation across the thickness of the sandwich plate is employed taking into account the thermal conductivity, the inhomogeneity parameter, and the sandwich schemes. The numerical results indicate the influence of volume fraction index, GPLs volume fraction, porosity coefficient, three independent coefficients of Kerr elastic foundation, and temperature difference on the free vibration behavior of annular sandwich plate. This study provides essential information to engineers seeking innovative ways to promote composite structures in a practical way.

• Smart Structures and Systems
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• 제20권3호
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• pp.369-383
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• 2017

In this work, the effects of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is studied by proposing a novel simple trigonometric shear deformation theory. The main advantage of this theory is that, in addition to including the shear deformation influence, the displacement field is modeled with only 2 unknowns as the case of the classical beam theory (CBT) and which is even less than the Timoshenko beam theory (TBT). Three types of environmental condition namely uniform, linear, and sinusoidal hygrothermal loading are studied. Material properties of FG beams are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from Hamilton's principle. Numerical examples are presented to show the validity and accuracy of present shear deformation theories. The effects of hygro-thermal environments, power law index, nonlocality and elastic foundation on the free vibration responses of FG beams under hygro-thermal effect are investigated.

• Wind and Structures
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• 제27권4호
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• pp.269-282
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• 2018

In this paper, a new displacement field based on quasi-3D hybrid-type higher order shear deformation theory is developed to analyze the static and dynamic response of exponential (E), power-law (P) and sigmoïd (S) functionally graded beams. Novelty of this theory is that involve just three unknowns with including stretching effect, as opposed to four or even greater numbers in other shear and normal deformation theories. It also accounts for a parabolic distribution of the transverse shear stresses across the thickness, and satisfies the zero traction boundary conditions at beams surfaces without introducing a shear correction factor. The beam governing equations and boundary conditions are determined by employing the Hamilton's principle. Navier-type analytical solutions of bending and free vibration analysis are provided for simply supported beams subjected to uniform distribution loads. The effect of the sigmoid, exponent and power-law volume fraction, the thickness stretching and the material length scale parameter on the deflection, stresses and natural frequencies are discussed in tabular and graphical forms. The obtained results are compared with previously published results to verify the performance of this theory. It was clearly shown that this theory is not only accurate and efficient but almost comparable to other higher order shear deformation theories that contain more number of unknowns.