• Title/Summary/Keyword: parametric equations

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Finding an Intersection Point between Cutter Swept Surface with a Z-Direction Vector (공구 이동 궤적면과 Z-direction 벡터의 교차점 계산)

  • Park, Pae-Yong;Ahn, Jeong-Ho
    • Proceedings of the KSME Conference
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    • 2001.06c
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    • pp.235-239
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    • 2001
  • Finding intersection point between a surface and a line is one of major problem in CAD/CAM. The intersection point could be found in an exact form or with numerical method. In this paper, the exact solution of the intersection point between a ruled surface which is generated by the movement of an endmill and the z-direction vector is presented. The cutter swept surface which is a ruled surface and the Z-direction vector are represented with parametric equations. With the nature of parametric equations, the geometric properties at the intersection point are easily acquired.

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A Parametric Study on Inlet Duct Treatment for Improving the Operational Stability of a Centrifugal Compressor (운전안정성 향상을 위한 원심 압축기의 유입부 형상변화에 관한 연구)

  • Seo, Tae-Wan;Heo, Man-Woong;Kim, Kwang-Yong
    • The KSFM Journal of Fluid Machinery
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    • v.19 no.5
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    • pp.12-19
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    • 2016
  • In present study, a parametric study of a centrifugal compressor with inlet treatment has been performed numerically using three-dimensional Reynolds-averaged Navier-Stokes equations. The shear stress transport turbulence model was used for analysis of turbulence. The finite volume method and unstructured grid system were used for the numerical solution. Tested parameters were related to the geometry of the inlet duct. It was found that the application of circumferentially distributed holes in the inlet duct improves operational stability of the compressor compared to that with conventional inlet duct.

POSITION VECTOR OF SPACELIKE SLANT HELICES IN MINKOWSKI 3-SPACE

  • Ali, Ahmad T.;Mahmoud, S.R.
    • Honam Mathematical Journal
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    • v.36 no.2
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    • pp.233-251
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    • 2014
  • In this paper, position vector of a spacelike slant helix with respect to standard frame are deduced in Minkowski space $E^3_1$. Some new characterizations of a spacelike slant helices are presented. Also, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike curve. In terms of solution, we determine the parametric representation of the spacelike slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of some special spacelike slant helices such as: Salkowski and anti-Salkowski curves.

EFFECTS OF FLUIDIC OSCILLATOR GEOMETRY ON PERFORMANCE (유체진동기의 형상 변화가 성능에 미치는 영향)

  • Jeong, Han-Sol;Kim, Kwang-Yong
    • Journal of computational fluids engineering
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    • v.21 no.3
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    • pp.77-88
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    • 2016
  • A parametric study on a fluidic oscillator was performed numerically in this work. Three-dimensional unsteady Reynolds-averaged Navier-Stokes equations were solved to analyze the flow in the fluidic oscillator. As turbulence closure, $k-{\varepsilon}$ model was employed. Validation of the numerical results was performed by comparing numerical results with experimental data for frequency of the oscillation. The parametric study was performed using five geometric parameters. Performance of the fluidic oscillator was evaluated in terms of velocity ratio and pressure drop. The results show that the inlet channel width and the distance between splitters are important factors in determining the performance of the fludic oscillator.

A Parametric Investigation Into the Aeroelasticity of Composite Helicopter Rotor Blades in Forward Flight (전진비행시 복합재료 헬리콥터 회전익의 공탄성에 대한 파라미터 연구)

  • 정성남;김경남;김승조
    • Journal of KSNVE
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    • v.7 no.5
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    • pp.819-826
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    • 1997
  • The finite element analyses of a composite hingeless rotor blade in forward flight have been performed to investigate the influence of blade design parameters on the blade stability. The blade structure is represented by a single cell composite box-beam and its nonclassical effects such as transverse shear and torsion-related warping are considered. The nonlinear periodic differential equations of motion are obtained by moderate deflection beam theory and finite element method based on Hamilton principle. Aerodynamic forces are calculated using the quasi-steady strip theiry with compressibility and reverse flow effects. The coupling effects between the rotor blade and the fuselage are included in a free flight propulsive trim analysis. Damping values are calculated by using the Floquet transition matrix theory from the linearized equations perturbed at equilibrium position of the blade. The aeroelastic results were compared with an alternative analytic approch, and they showed good correlation with each other. Some parametric investigations for the helicopter design variables, such as pretwist and precone angles are carried out to know the aeroelastic behavior of the rotor.

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Effects of Geometry of a Boot-Shaped Rib on Heat Transfer and Pressure Drop (신발형 리브의 형상변화가 열전달 및 압력 강하에 미치는 영향)

  • Seo, Jae-Won;Kim, Jun-Hee;Kim, Kwang-Yong
    • The KSFM Journal of Fluid Machinery
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    • v.18 no.3
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    • pp.66-73
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    • 2015
  • This paper deals with a parametric study on boot-shaped ribs in a rectangular cooling channel. Numerical analysis of the flow and heat transfer was performed using three-dimensional Reynolds averaged Navier-Stokes equations with the Speziale, Sarkar and Gatski turbulence model. The parametric study was performed for the parameters, tip width-to rib width, tip height-to-rib height, rib height-to-channel height, and rib height-to-width ratios. To assess the cooling performance and friction loss, Numsselt number and friction factor were defined as the performance parameter, respectively. The results showed that the cooling performance and friction loss were seriously affected by the four geometric parameters.

A study on the dynamic instabilities of a smart embedded micro-shell induced by a pulsating flow: A nonlocal piezoelastic approach

  • Atabakhshian, Vahid;Shooshtaria, Alireza
    • Advances in nano research
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    • v.9 no.3
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    • pp.133-145
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    • 2020
  • In this study, nonlinear vibrations and dynamic instabilities of a smart embedded micro shell conveying varied fluid flow and subjected to the combined electro-thermo-mechanical loadings are investigated. With the aim of designing new hydraulic sensors and actuators, the piezoelectric materials are employed for the body and the effects of applying electric field on the stability of the system as well as the induced voltage due to the dynamic behavior of the system are studied. The nonlocal piezoelasticity theory and the nonlinear cylindrical shell model in conjunction with the energy approach are utilized to mathematically modeling of the structure. The fluid flow is assumed to be isentropic, incompressible and fully develop, and for more generality of the problem both steady and time dependent flow regimes are considered. The mathematical modeling of fluid flow is also carried out based on a scalar potential function, time mean Navier-Stokes equations and the theory of slip boundary condition. Employing the modified Lagrange equations for open systems, the nonlinear coupled governing equations of motion are achieved and solved via the state space problem; forth order numerical integration and Bolotin's method. In the numerical results, a comprehensive discussion is made on the dynamical instabilities of the system (such as divergence, flutter and parametric resonance). We found that applying positive electric potential field will improve the stability of the system as an actuator or vibration amplitude controller in the micro electro mechanical systems.

Finite element and design code assessment of reinforced concrete haunched beams

  • Gulsan, Mehmet Eren;Albegmprli, Hasan M.;Cevik, Abdulkadir
    • Structural Engineering and Mechanics
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    • v.66 no.4
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    • pp.423-438
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    • 2018
  • This pioneer study focuses on finite element modeling and numerical modeling of three types of Reinforced Concrete Haunched Beams (RCHBs). Firstly, twenty RCHBs, consisting of three types, and four prismatic beams which had been tested experimentally were modeled via a nonlinear finite element method (NFEM) based software named as, ATENA. The modeling results were compared with experimental results including load capacity, deflection, crack pattern and mode of failure. The comparison showed a good agreement between the results and thus the model used can be effectively used for further studies of RCHB with high accuracy. Afterwards, new mechanism modes and design code equations were proposed to improve the shear design equation of ACI-318 and to predict the critical effective depth. These equations are the first comprehensive formulas in the literature involving all types of RCHBs. The statistical analysis showed the superiority of the proposed equation to their predecessors where the correlation coefficient, $R^2$ was found to be 0.89 for the proposed equation. Moreover, the new equation was validated using parametric and reliability analyses. The parametric analysis of both experimental and predicted results shows that the inclination angle and the compressive strength were the most influential parameters on the shear strength. The reliability analysis indicates that the accuracy of the new formulation is significantly higher as compared to available design equations and its reliability index is within acceptable limits.

Elastic stiffness of perfobond connections in composite structures

  • Qin, Xi;Yang, Guotao
    • Steel and Composite Structures
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    • v.42 no.2
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    • pp.221-241
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    • 2022
  • Perfobond rib connectors are widely used in composite structures to achieve the composite action between the steel and the concrete, and empirical expressions for their strength and secant stiffness have been obtained by numerical simulations or push-out tests. Since perfobond connections are generally in an elastic state in the service process and the structural analysis are always based on the elastic properties of the members, the secant stiffness is not applicable for the normal structural analysis. However, the tangent stiffness of perfobond connections has not been introduced in previous studies. Moreover, the perfobond connections are bearing tension and shear force simultaneously when the composite beams subjected to torque or local loads, but the current studies fail to arrive at the elastic stiffness considering the combined effects. To resolve these discrepancies, this paper investigates the initial elastic stiffness of perfobond connections under combined forces. The calculation method for the elastic stiffness of perfobond connections is analyzed, and the contributions of the perfobond rib, the perforating rebar and the concrete dowel are investigated. A finite element method was verified with a high value of correlation for the test results. Afterwards, parametric studies are carried out using the reliable finite element analysis to explore the trends of several factors. Empirical equations for predicting the initial elastic stiffness of perfobond connections are proposed by the numerical regression of the data extracted by parametric studies. The equations agree well with finite element analysis and test results, which indicates that the proposed empirical equations reflect a high accuracy for predicting the initial elastic stiffness of perfobond connections.

Static strengths of preloaded circular hollow section stub columns strengthened with carbon fiber reinforced polymer

  • Chen Wei;Yongbo Shao;Mostafa Fahmi Hassanein;Chuannan Xiong;Hongmei Zhu
    • Steel and Composite Structures
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    • v.47 no.4
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    • pp.455-466
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    • 2023
  • To investigate the load bearing capacity of axially preloaded circular hollow section (CHS) stub columns strengthened by carbon fiber reinforced polymer (CFRP), theoretical analysis is carried out. The yield strength and the ultimate strength of a CFRP strengthened preloaded CHS stub column are determined at the yielding of the CHS tube and at the CFRP fracture, respectively. Theoretical models are proposed and corresponding equations for calculating the static strengths, including the yield strength and the ultimate strength, are presented. Through comparison with reported experimental results, the theoretical predictions on the static strengths are proved to be accurate. Through finite element (FE) analyses, parametric studies for 258 models of CFRP strengthened preloaded CHS stub columns are conducted by considering different values of tube diameter, tube thickness, CFRP layer and preloading level. The static strengths of the 258 models predicted from presented equations are proved to be in good agreement with FE simulations when the diameter-to-thickness ratio is less than 90ε2. The parametric study indicates that the diameter and the thickness of the steel tube have great effects on CFRP strengthening efficiency, and the recommended ranges of the diameter and the thickness are proposed.