• Title/Summary/Keyword: lagrangian analysis

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Level Set Based Shape Optimization of Linear Structures Using Topological Derivatives (Topological Derivative를 이용한 선형 구조물의 레벨셋 기반 형상 최적 설계)

  • Ha Seung-Hyun;Kim Min-Geun;Cho Seon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2006.04a
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    • pp.299-306
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    • 2006
  • Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The 'Hamilton-Jacobi (H-J)' equation and computationally robust numerical technique of 'up-wind scheme' lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H -J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes is not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

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Numerical Simulation on the Response of Moored Semi-submersible Under Ice Load (유빙 하중을 받는 계류된 반잠수식 시추선의 응답해석)

  • Kim, Jeong-Hwan;Kim, Yooil
    • Journal of Ocean Engineering and Technology
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    • v.32 no.3
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    • pp.177-183
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    • 2018
  • This study simulated ice load and the motion response of a moored semi-submersible rig in pack-ice conditions using a finite element method. Ice flows of random size and shape were modeled, and interactions for ice-sea, ice-structure, ice-ice were simulated using a simplified method. Parameters for the simplified method such as drag force coefficient and the pressure-penetration relation were obtained based on the result of detailed analysis using the coupled Eulerian-Lagrangian method. The mooring lines were modeled by spring elements based on their stiffness. As a result of the simulation over 1,400 seconds, the force and motion response of the rig were obtained and validated using discrete elements and compared with the results found by the Krylov State Research Centre.

A geometrically nonlinear thick plate bending element based on mixed formulation and discrete collocation constraints

  • Abdalla, J.A.;Ibrahim, A.K.
    • Structural Engineering and Mechanics
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    • v.26 no.6
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    • pp.725-739
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    • 2007
  • In recent years there are many plate bending elements that emerged for solving both thin and thick plates. The main features of these elements are that they are based on mix formulation interpolation with discrete collocation constraints. These elements passed the patch test for mix formulation and performed well for linear analysis of thin and thick plates. In this paper a member of this family of elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both thin and thick plates with geometric nonlinearity. The Von K$\acute{a}$rm$\acute{a}$n's large displacement plate theory based on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterative-incremental procedure is implemented to solve the nonlinear equations. The element is then tested for plates with simply supported and clamped edges under uniformly distributed transverse loads. The results obtained using the geometrically NDRM element is then compared with the results of available analytical solutions. It has been observed that the NDRM results agreed well with the analytical solutions results. Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and thick plates with geometric non-linearity.

NUMERICAL ANALYSIS ON A SPHERICALLY SYMMETRIC UNDERWATER EXPLOSION USING THE ALE GODUNOV SCHEME FOR TWO-PHASE FLOW (이상유동에 대한 ALE Godunov법을 이용한 구대칭 수중폭발 해석)

  • Shin S.;Kim I.C.;Kim Y.J.
    • Journal of computational fluids engineering
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    • v.11 no.1 s.32
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    • pp.29-35
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    • 2006
  • A code is developed to analyze a spherically symmetric underwater explosion. The arbitrary Lagrangian-Eulerian(ALE) Godunov scheme for two-phase flow is used to calculate numerical fluxes through moving control surfaces. For detonation gas of TNT and liquid water, the Jones-Wilkins-Lee(JWL) equation of states and the isentropic Tait relation are used respectively. It is suggested to use the Godunov variable to estimate the velocity of a material interface. The code is validated through comparisons with other results on the gas-water shock tube problem. It is shown that the code can handle generation of discontinuity and recovering of continuity in the normal velocity near the material interface during shock waves interact with the material interface. The developed code is applied to analyze a spherically symmetric underwater explosion. Repeated transmissions of shock waves are clearly captured. The calculated period and maximum radius of detonation gas bubble show good agreements with experimental and other numerical results.

A Syudy on Applications of Convex Hull Algorithm in the SPH (SPH에서의 Convex Hull 알고리즘 적용연구)

  • Lee, Jin-Sung;Lee, Young-Shin
    • Journal of the Korea Institute of Military Science and Technology
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    • v.14 no.2
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    • pp.313-320
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    • 2011
  • SPH(Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique that is useful as an alternative numerical analysis method used to analyze high deformation problems as well as astrophysical and cosmological problems. In SPH, all points within the support of the kernel are taken as neighbours. The accuracy of the SHP is highly influenced by the method for choosing neighbours from all particle points considered. Typically a linked-list method or tree search method has been used as an effective tool because of its conceptual simplicity, but these methods have some liability in anisotropy situations. In this study, convex hull algorithm is presented as an improved method to eliminate this artifact. A convex hull is the smallest convex set that contains a certain set of points or a polygon. The selected candidate neighbours set are mapped into the new space by an inverse square mapping, and extract a convex hull. The neighbours are selected from the shell of the convex hull. These algorithms are proved by Fortran programs. The programs are expected to use as a searching algorithm in the future SPH program.

A numerical Study on Optimum Ventilation Conditions for the Task of Exchange Catalyst (반응기촉매 교체작업시 최적 환기조건에 대한 수치해석적 연구)

  • Yoon, Jang-ken;Im, Yong-Sun;Shin, Misoo
    • Journal of Korean Society of Occupational and Environmental Hygiene
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    • v.28 no.2
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    • pp.190-199
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    • 2018
  • Objectives: The purpose of this case study is to assess the current airflow and find the ideal ventilation conditions in tank reactors for minimizing the possibility of exposure respiratory dusts(size of $2.5{\mu}m$, $10{\mu}m$) when workers exchange catalysts in the tank reactors. Methods: A Numerical study was performed to determine ideal ventilation conditions, We considered two sizes of airborne respiratory particles($2.5{\mu}m$, $10{\mu}m$) at 12points from the bottom of tank reactor. We changed input & output ventilation conditions and analyzed the particle motion in the tank reactor. The star-ccm+, computational fluid dynamics tool was used to predict air & particle flow patterns in the tank reactor and a numerical simulation was achieved by applying the realized ${\kappa}-{\varepsilon}$ turbulence model and the Lagrangian particle tracking method. Results: From the results, the increase of recirculation air had a significant impact on removing dusts because they are removed by HEPA filter. To the contrary, Increasing the clean air quantity or changing the input position of clean air is not good for workers because it causes the exit of respiratory dusts through workers' entrance or cause it to remail suspended in the air in the workplace tank.

Study on the Improvement Methods of Engine Efficiency in Hybrid Excavator (하이브리드 굴삭기용 엔진의 효율 향상 방안에 관한 연구)

  • Park, Minje;Min, Kyoungdoug
    • Transactions of the Korean Society of Automotive Engineers
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    • v.24 no.4
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    • pp.392-400
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    • 2016
  • In this paper, a study based on engine operating conditions versus hybrid excavator engines was conducted about the engine performance and fuel consumption via the 1-D engine simulation model. First of all, engine operating points with performance and emission were determined by driving patterns. The 1-D HFEM(High Frequency Engine Model) was developed for deep insight into engine combustion and the energy conversion phenomena. In accordance with changing operating points, especially High Idle and Rated output conditions, engine parameters and systems such as turbocharger(Waste Gate Turbocharger and Variable Geometry Turbocharger) injection strategies and EGR(Exhaust Gas Recirculation) should be considered. Therefore, various configurations and parametric analysis with optimization methods in hybrid excavator were simulated and optimized by NLPQL(Non-linear Programming by Quadratic Lagrangian algorithm) in 1-D HFEM. As a result, the fuel consumption with the developed hybrid electric excavator engine could be significantly decreased and bsfc(Brake Specific Fuel Consumption) was also reduced about 5 % to 7 % without any performance degradation.

Numerical Analysis of Tip Vortex Cavitation Behavior and Noise on Hydrofoil using Dissipation Vortex Model and Bubble Theory (소산이 고려된 보오텍스 모델과 버블 이론을 이용한 수중익 날개 끝 보오텍스 캐비테이션 거동 및 소음의 수치적 해석)

  • Park, Kwang-Kun;Seol, Han-Shin;Lee, Soo-Gab
    • Journal of the Society of Naval Architects of Korea
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    • v.43 no.2 s.146
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    • pp.177-185
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    • 2006
  • Cavitation is the dominant noise source of the marine vehicle. Of the various types of cavitation , tip vortex cavitation is the first appearance type of marine propeller cavitation and it generates high frequency noise. In this study, tip vortex cavitation behavior and noise are numerically investigated. A numerical scheme using Eulerian flow field computation and Lagrangian particle trace approach is applied to simulate the tip vortex cavitation on the hydrofoil. Vortex flow field is simulated by combined Moore and Saffman's vortex core radius equation and Sculley vortex model. Tip vortex cavitation behavior is analyzed by coupled Rayleigh-Plesset equation and trajectory equation. The cavitation nuclei are distributed and released in the vortex flow result. Vortex cavitation trajectories and radius variations are computed according to nuclei initial size. Noise is analyzed using time dependent cavitation bubble position and radius data. This study may lay the foundation for future work on vortex cavitation study and it will provide a basis for proper underwater propeller noise control strategies.

Three-Dimensional Vibration Analysis of Cantilevered Laminated Composite Plates (캔틸레버 복합 적층판의 3차원 진동해석)

  • 김주우;정희영
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.14 no.3
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    • pp.299-308
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    • 2001
  • This paper presents the three-dimensional (3-D) study of the natural vibration of cantilevered laminated composite plates. The Ritz method is used to obtain stationary values of the associated Lagrangian functional with displacements approximated by mathematically complete polynomials satisfying the boundary conditions at the clamped edge exactly. The accuracy of the 3-D model is established through a convergence study of non-dimensional frequencies followed by a comparison of the converged 3-D solutions with analytical and experimental findings in the existing literature. A wide scope of 3-D frequency results explain the influence of a number of geometrical and material parameters for cantilevered laminated plates, namely aspect ratio (a/b), width-to-thickness ratio (a/h), orthotropy of material, number of plies (NP), fiber orientation angle(θ), and stacking sequence.

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A Numerical Analysis on the Characteristics of Spray by Swirl Injector in Gas Turbine Combustor (가스터빈연소기에서 스월 인젝터의 분무특성에 관한 연구)

  • 이성혁;유홍선;이인섭;홍성국
    • Journal of the Korean Society of Safety
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    • v.15 no.3
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    • pp.30-39
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    • 2000
  • The present paper deals with the numerical simulation for the spray characteristics with swirling turbulent flows and dilution flows from swirl injectors in a simplified can type of gas turbine combustor. The main objective is to investigate the characteristics of swirling turbulent flows with dilution flows and to provide the qualitative results for the spray characteristics such as the droplet distribution and Sauter Mean Diameter(SMD). The gas-phase equations based on Eulerian approach were discretized by Finite Volume Method, together with SIMPLE algorithm and the Reynolds -Stress-Model. The liquid-phase equations based on Lagrangian method were used to predict the droplet behavior. The results of preliminary test are generally in good agreement with experimental data, and show that the anisotropy exists in the primary zone due to swirl velocity and injected air from primary injector, and then gradually decays due to turbulent mixing and consequently near-isotropy occurs in the region between primary and dilution zones. For the spray characteristics, it is indicated that the swirling flows of primary jet region increase the droplet atomization. In addition, it is showed that the swirling flows at the inlet region lead the air-fuel mixture to be distributed near the igniter and can significantly affect the spray behavior in the primary jet region.

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