• Title/Summary/Keyword: analytical solutions

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COMPARISON OF HENYEY-GREENSTEIN WITH DRAINE SCATTERNING PHASE FUNCTIONS (DRAINE 과 HENYEY-GREENSTEIN 산란 위상 함수 비교)

  • Seon, Kwang-Il
    • Publications of The Korean Astronomical Society
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    • v.23 no.2
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    • pp.25-29
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    • 2008
  • Scattering of incident light by the interstellar dust is usually approximated by Henyey-Greenstein scattering phase function. Recently, Draine (2003) proposed a new analytic phase function with two parameters. We describe an algorithm to generate random numbers distributed according to the Draine’s function, and compare two phase functions. It is also derived exact solutions of two parameters for given values ${\langle}cos{\theta}{\rangle}$ and ${\langle}cos^2{\theta}{\rangle}$. It is found that Henyey-Greenstein function with g = ${\langle}cos{\theta}{\rangle}$ provides a good approximation for ${\lambda}\;>\;2000{\AA}$. At shorter wavelengths, more realistic phase function may be needed for radiative transfer models.

The analytical solution for buckling of curved sandwich beams with a transversely flexible core subjected to uniform load

  • Poortabib, A.;Maghsoudi, M.
    • Structural Engineering and Mechanics
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    • v.52 no.2
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    • pp.323-349
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    • 2014
  • In this paper, linear buckling analysis of a curved sandwich beam with a flexible core is investigated. Derivation of equations for face sheets is accomplished via the classical theory of curved beam, whereas for the flexible core, the elasticity equations in polar coordinates are implemented. Employing the von-Karman type geometrical non-linearity in strain-displacement relations, nonlinear governing equations are resulted. Linear pre-buckling analysis is performed neglecting the rotation effects in pre-buckling state. Stability equations are concluded based on the adjacent equilibrium criterion. Considering the movable simply supported type of boundary conditions, suitable trigonometric solutions are adopted which satisfy the assumed edge conditions. The critical uniform load of the beam is obtained as a closed-form expression. Numerical results cover the effects of various parameters on the critical buckling load of the curved beam. It is shown that, face thickness, core thickness, core module, fiber angle of faces, stacking sequence of faces and openin angle of the beam all affect greatly on the buckling pressure of the beam and its buckled shape.

Numerical Computation of Dynamic Stress Intensity Factors Based on the Equations of Motion in Convolution Integral (시간적분형 운동방정식을 바탕으로 한 동적 응력확대계수의 계산)

  • Sim, U-Jin;Lee, Seong-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.5
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    • pp.904-913
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    • 2002
  • In this paper, the dynamic stress intensity factors of fracture mechanics are numerically computed in time domain using the FEM. For which the finite element formulations are derived applying the Galerkin method to the equations of motion in convolution integral as has been presented in the previous paper. To assure the strain fields of r$^{-1}$ 2/ singularity near the crack tip, the triangular quarter-point singular elements are imbedded in the finite element mesh discretized by the isoparametric quadratic quadrilateral elements. Two-dimensional problems of the elastodynamic fracture mechanics under the impact load are solved and compared with the existing numerical and analytical solutions, being shown that numerical results of good accuracy are obtained by the presented method.

ADI Finite Difference Method of Linear Shallow Water Wave Equation (선형 천수방탁식의 ADI 유한차분법)

  • 이종찬;서승남
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.4 no.2
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    • pp.108-120
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    • 1992
  • An ADI model for linearized shallow water equation is modified using the method of factorization. In order to show its validity. the computational results are compared both with the analytical solution and with those from existing models, for a rectangualr domain with constant and varying amplitudes at the open boundary. It is shown the accuracy of numerical solutions depends on the size of time step. depth and bottom friction. The modified ADI model is shown to be superior to the existing models such as Leendertse (1971). Butler (1980) and Sheng (1983).

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Preparation and Characterization of Chemically Stable PVDF-HFP Asymmetric Microfiltration (MF) Membranes

  • Lee, Yeon-Ee;JeGal, Jong-Geon
    • Membrane Journal
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    • v.22 no.2
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    • pp.104-112
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    • 2012
  • Chemically stable Polyvinylidene fluoride-hexa-fluoropropane (PVDF-HFP) copolymer asymmetric membranes were prepared by the conventional phase inversion process, using Dimethyacetamide (DMAc) as a solvent and water as a non-solvent. To control the pore size and porosity of the PVDF-HFP membranes, tetra-ethoxysilane (TEOS) was used as a pore-forming agent. The prepared membranes were characterized, using several analytical methods such as Fourier Transform Infrared spectroscopy (FTIR), Thermo-gravimetric analyzer (TGA), Field Emission Scanning Electronic Microscopy (FESEM). TEOS turned out to increase porosity and make homogeneous pores on the membranes. Depending on the composition of the dope solutions, the pore size was ranged from 0.1 to 1.0 ${\mu}m$. The flux of the PVDF-HFP membranes prepared by using TEOS as a pore forming agent was increased substantially without much decrease in the rejection. When 15 wt% PVDF-HFP solution was blended with 13 wt% TEOS solution at composition ratio of 70/30 in wt%, the water flux at 2 bars was about 2 $m^3/m^2day$.

On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams

  • Bayat, Mahmoud;Pakar, Iman;Bayat, Mahdi
    • Steel and Composite Structures
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    • v.14 no.1
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    • pp.73-83
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    • 2013
  • In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin's method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering.

Free-edge effect in cross-ply laminated plates under a uniform extension

  • Sheng, Hongyu;Ye, Jianqiao
    • Structural Engineering and Mechanics
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    • v.18 no.3
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    • pp.377-388
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    • 2004
  • Based on the basic equations of elasticity, free-edge effects on stresses in cross-ply laminated plates are found by using the state space method. The laminates are subjected to uniaxial-uniform extension plate, which is a typical example of general plane strain problem. The study takes into account material constants of all individual material layers and the state equation of a laminate is solved analytically in the through thickness direction. By this approach, a composite plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The solution provides a continuous displacement and inter-laminar stress fields across all material interfaces and an approxiamte prediction to the singularity of stresses occurring in the boundary layer region of a free-edge. Numerical solutions are obtained and compared with the results obtained from an alternative numerical method.

CURVED BOUNDARY TREATMENT OF THE LATTICE BOLTZMANN METHOD FOR SLIP FLOW SIMULATIONS (Slip flow 해석을 위한 격자볼츠만 방법의 곡면처리기법)

  • Jeong, Namgyun
    • Journal of computational fluids engineering
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    • v.19 no.3
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    • pp.77-84
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    • 2014
  • The lattice Boltzmann (LB) method has been used to simulate rarefied gas flows in a micro-system as an alternative tool. However, previous results were mainly focused on a simple geometry with flat walls because the LB method is modeled on uniform Cartesian lattices. When previous boundary conditions for the microflows are applied to curved walls, the use of them requires approximation of the curved boundary by a series of stair steps, and introduces additional errors. For macroflows, no-slip curved wall boundary treatments have been developed remarkably in order to overcome these limits. However, the investigations for the slip curved wall boundary have rarely been performed for microflows. In this work, a curved boundary treatment of the LB method for a slip flow has been introduced. The results of the LB method for 2D microchannel and 3D microtube flows are in excellent agreement with the analytical solutions.

A Research on Mobile Malware Model propagated Update Attacks (변조 업데이트를 통해 전파되는 모바일 악성어플리케이션 모델 연구)

  • Ju, Seunghwan;Seo, Heesuk
    • Journal of Korea Society of Digital Industry and Information Management
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    • v.11 no.2
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    • pp.47-54
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    • 2015
  • The popularity and adoption of smart-phones has greatly stimulated the spread of mobile malware, especially on the popular platforms such as Android. The fluidity of application markets complicate smart-phone security. There is a pressing need to develop effective solutions. Although recent efforts have shed light on particular security issues, there remains little insight into broader security characteristics of smart-phone application. Now, the analytical methods used mainly are the reverse engineering-based analysis and the sandbox-based analysis. Such methods are can be analyzed in detail. but, they take a lot of time and have a one-time payout. In this study, we develop a system to monitor that mobile application permissions at application update. We had to overcome a one-time analysis. This study is a service-based malware analysis, It will be based will be based on the mobile security study.

Vibration Analysis of Trapezoidally Corrugated Plates (사다리꼴 주름판의 진동해석)

  • Kim, Young-Wann
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.23 no.10
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    • pp.928-934
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    • 2013
  • In this paper, the vibration characteristics of the trapezoidally corrugated plate are investigated by the analytical method. The corrugated plate is widely used as the structural elements because of its high stiffness and light weight. Because the corrugated plate is flexible in the corrugation direction and stiff in the transverse direction, it is treated as an equivalent orthotropic plate to analyze the corrugated plate simply. This equivalent plate must include both extensional and flexural effect to obtain the precise solution. The effective extensional and flexural stiffness of the equivalent plate are derived to consider these effects in the analysis. To demonstrate the validity of the proposed approach, the comparison is made with the previously published results and ANSYS solutions. Some numerical results are presented to check the effect of the geometric properties.