• 제목/요약/키워드: equilibrium equation

검색결과 843건 처리시간 0.022초

Phase Equilibrium of Binary Mixture for the (Carbon Dioxide + 1-Phenyl-2-Pyrrolidone) System at High Pressure

  • Lee, Ho;Jeong, Jong-Dae;Byun, Hun-Soo
    • Korean Chemical Engineering Research
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    • 제56권5호
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    • pp.732-737
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    • 2018
  • Experimental data of phase equilibria are reported for the binary mixture of 1-phenyl-2-pyrrolidone in supercritical carbon dioxide. Phase behavior data was measured in a synthetic method at a temperature ranging from 333.2 to 393.2 K and at pressures up to 97.14 MPa. The solubility of 1-phenyl-2-pyrrolidone in the carbon dioxide + 1-phenyl-2-pyrrolidone system increased as temperature increased at a constant pressure and it exhibited the type-I phase behavior. The experimental data for the binary mixture were correlated with the Peng-Robinson equation of state using mixing rule and the critical properties of 1-phenyl-2-pyrrolidone were predicted with the Joback and Lyderson method.

Simplified Algorithm of the Novel Steel-concrete Mixed Structure under Lateral Load

  • Li, Liang;Li, Guo-qiang;Liu, Yu-shu
    • 국제초고층학회논문집
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    • 제1권4호
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    • pp.247-254
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    • 2012
  • In order to improve the seismic behaviors of traditional steel-concrete mixed structure, a novel steel concrete mixed structure consisting of steel frames braced with buckling restrained braces (BRBs) and a concrete tube is proposed. Based on several assumptions, the simplified mechanical model of the novel mixed structure is established, and the shear and bending stiffness formulas of the steel frames, BRBs and concrete tube are respectively introduced. The equilibrium differential equation of the novel mixed structure under horizontal load is developed based on the structural elastic theory. The simplified algorithms to determine the lateral displacement and internal forces of the novel mixed structure under the inverted-triangle distributed load, uniformly load and top-concentrated load are then obtained considering several boundary conditions and compatible deformation conditions. The effectiveness of the simplified algorithms is verified by FEM comparison.

On an improved numerical method to solve the equilibrium problems of solids with bounded tensile strength that are subjected to thermal strain

  • Pimpinelli, Giovanni
    • Structural Engineering and Mechanics
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    • 제15권4호
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    • pp.395-414
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    • 2003
  • In this paper we recall briefly the constitutive equations for solids subjected to thermal strain taking in account the bounded tensile stress of the material. In view to solve the equilibrium problem via the finite element method using the Newton Raphson procedure, we show that the tangent elasticity tensor is semi-definite positive. Therefore, in order to obtain a convergent numerical method, the constitutive equation needs to be modified. Specifically, the dependency of the stress by the anelastic deformation is made explicit by means of a parameter ${\delta}$, varying from 0 to 1, that factorizes the elastic tensor. This parameterization, for ${\delta}$ near to 0, assures the positiveness of the tangent elasticity tensor and enforces the convergence of the numerical method. Some numerical examples are illustrated.

Weak forms of generalized governing equations in theory of elasticity

  • Shi, G.;Tang, L.
    • Interaction and multiscale mechanics
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    • 제1권3호
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    • pp.329-337
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    • 2008
  • This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

초산과 n-heptane 이성분계의 회합성에 대한 화학적 이론을 이용한 연구 (A study for an association of acetic acid with n-heptane based on the chemical theory)

  • 홍승호;이진엽;이태종
    • 한국가스학회지
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    • 제3권3호
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    • pp.34-38
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    • 1999
  • 초산의 회합성을 설명할 수 있는 모델식을 비교 제안하기 위해 298.15K와 318.15K의 실험치 자료를 화학적 이론이 고려된 전개식과 일반적인 기액 평형식에 Margules, Wilson, NRTL식을 각각 적용하여 계산한 값들을 서로 비교하였다. 회합성이 고려된 모델식을 적용하여 계산한 값이 실험치와 잘 일치하였다.

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자동볼평형장치가 부착된 광디스크 드라이브의 동특성해석 (Dynamic Analysis of an Optical Disk Drive with an Automatic Ball Balancer)

  • 김강성;정진태
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2001년도 추계학술대회논문집 II
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    • pp.983-988
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    • 2001
  • Dynamic behaviors and stability of an optical disk drive coupled with an automatic ball balancer(ABB) are analyzed by a theoretical approach. The feeding system is modeled a rigid body with six degree-of-freedom. Using Lagrange's equation, we derive the nonlinear equations of motion for a non-autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of the equilibrium positions, the monodromy matrix technique is applied to the perturbed equations. On the other hand, time responses are computed by the Runge-Kutta method. We also investigate the effects of the damping coefficient and the position of ABB on the dynamic behaviors of the system.

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자동 볼 평형장치를 이용한 광 디스크 드라이브의 진동 저감 (Vibration Reduction of an Optical Disk Drive Using an Automatic Ball Balancer)

  • 이동진;정진태;노대성
    • 소음진동
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    • 제9권2호
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    • pp.355-362
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    • 1999
  • Vibration reduction of an optical disk drive is achieved by an automatic ball balancer and dynamic behaviors of the drive are studied by theoretical approaches. Using Lagrange's equation, we derive nonlinear equations of motion for a non-autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of equilibrium positions, the Floquet theory is applied to the perturbed equations. On the other hand, time responses are computed by an explicit time integration method. We also investigate the effects of mass center and the position of the ABB on the dynamic behaviors of the system.

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Viscosity and Thermodynamic Properties of Liquid Sulfur

  • Chang, Man-Chai;Jhon, Mu-Shik
    • Bulletin of the Korean Chemical Society
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    • 제3권4호
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    • pp.133-139
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    • 1982
  • It has been presumed that the molten sulfur above $159^{\circ}C$ consists of an equilibrium mixture of $S_8$ rings and $S_x$ polymers where the number average degree of polymerization, P, is large. But it is known that admixture of halogens with liquid sulfur greatly reduce the viscosity. Constructing a new equilibrium equation, it is possible to evaluate the viscosity when halogens are added to liquid sulfur. Calculated viscosity is in good agreement with experimental values. Using the proposed model, the thermodynamic properties of liquid sulfur are also calculated over a wide range of temperature which the sulfur exists as the polymer.

Nonlinear analysis of reinforced concrete beam elements subject to cyclical combined actions of torsion, biaxial flexure and axial forces

  • Cocchi, Gian Michele;Tiriaca, Paolo
    • Structural Engineering and Mechanics
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    • 제17권6호
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    • pp.829-862
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    • 2004
  • This paper presents a method for the nonlinear analysis of beam elements subjected to the cyclical combined actions of torsion, biaxial flexure and axial forces based on an extension of the disturbed compression field (DSFM). The theoretical model is based on a hybrid formulation between the full rotation of the cracks model and the fixed direction of the cracking model. The described formulation, which treats cracked concrete as an orthotropic material, includes a new approach for the evaluation of the re-orientation of both the compression field and the deformation field by removing the restriction of their coincidence. A new equation of congruence permits evaluating the deformation of the middle line. The problem consists in the solution of coupled nonlinear simultaneous equations expressing equilibrium, congruence and the constitutive laws. The proposed method makes it possible to determine the deformations of the beam element according to the external stresses applied.

Dust Radiative Transfer Model of Spectral Energy Distributions in Clumpy, Galactic Environments

  • 선광일
    • 천문학회보
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    • 제43권2호
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    • pp.52.2-52.2
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    • 2018
  • The shape of a galaxy's spectral energy distribution ranging from ultraviolet (UV) to infrared (IR) wavelengths provides crucial information about the underlying stellar populations, metal contents, and star-formation history. Therefore, analysis of the SED is the main means through which astronomers study distant galaxies. However, interstellar dust absorbs and scatters UV and optical light, re-emitting the absorbed energy in the mid-IR and Far-IR. I present the updated 3D Monte-Carlo radaitive transfer code MoCafe to compute the radiative transfer of stellar, dust emission through a dusty medium. The code calculates the emission expected from dust not only in pure thermal equilibrium state but also in non-thermal equilibrium state. The stochastic heating of very small dust grains and/or PAHs is calculated by solving the transition probability matrix equation between different vibrational, internal energy states. The calculation of stochastic heating is computationally expensive. A pilot study of radiative transfer models of SEDs in clumpy (turbulent), galactic environments, which has been successfully used to understand the Calzetti attenuation curves in Seon & Draine (2016), is also presented.

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