• 제목/요약/키워드: Newton's Approach

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불포화지반에 대한 열-수리-역학 거동의 수식화 (Formulation of Fully Coupled THM Behavior in Unsaturated Soil)

  • 신호성
    • 한국지반공학회논문집
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    • 제27권3호
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    • pp.75-83
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    • 2011
  • 일반적인 불포화지반의 거동뿐만 아니라, 열과 관련된 분야, 지반환경 분야 등 다양한 분야에서 불포화 다공질 재료의 열적-수리적-역학적으로 결합된 문제들이 대두되면서 이러한 문제들을 해석하기 위한 수치도구 개발의 필요성이 대두되고 있다. 본 논문에서는 거시적 접근법(macroscopic approach)에 근거하여 불포화지반에 대한 열-수리-역학거동의 수식화를 하였다. 흙, 물, 공기에 대한 질량보존의 법칙, 에너지 보존법칙, 그리고 하중평형 조건식으로부터 결합된(coupled) 4개의 지배방정식을 유도하였다. Galerkin 간략화와 시간적분으로부터 주 변수인 변위(u), 가스압($P_g$), 유체압($P_1$), 온도(T)를 Newton의 반복과정을 이용하여 구하는 유한요소 프로그램(FEM)을 작성하였다. 개발된 프로그램을 이용하여 다공질재료에서 2상 흐름 문제 중 일차원 배수실험(u-$P_g-P_1$), 온도 압밀(u-$P_1$-T), 그리고 지표면 온도변화에 의한 말뚝의 주변지반에 대한 영향(u-$P_1$-T)에 대하여 수치해석을 수행하고 논의하였다.

Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT

  • Jamali, M.;Shojaee, T.;Mohammadi, B.;Kolahchi, R.
    • Advances in nano research
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    • 제7권6호
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    • pp.405-417
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    • 2019
  • This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

Large deflection analysis of orthotropic, elliptic membranes

  • Chucheepsakul, Somchai;Kaewunruen, Sakdirat;Suwanarat, Apiwat
    • Structural Engineering and Mechanics
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    • 제31권6호
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    • pp.625-638
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    • 2009
  • Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

Large deflection analysis of laminated composite plates using layerwise displacement model

  • Cetkovic, M.;Vuksanovic, Dj.
    • Structural Engineering and Mechanics
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    • 제40권2호
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    • pp.257-277
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    • 2011
  • In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

Optimal Particle Swarm Based Placement and Sizing of Static Synchronous Series Compensator to Maximize Social Welfare

  • Hajforoosh, Somayeh;Nabavi, Seyed M.H.;Masoum, Mohammad A.S.
    • Journal of Electrical Engineering and Technology
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    • 제7권4호
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    • pp.501-512
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    • 2012
  • Social welfare maximization in a double-sided auction market is performed by implementing an aggregation-based particle swarm optimization (CAPSO) algorithm for optimal placement and sizing of one Static Synchronous Series Compensator (SSSC) device. Dallied simulation results (without/with line flow constraints and without/with SSSC) are generated to demonstrate the impact of SSSC on the congestion levels of the modified IEEE 14-bus test system. The proposed CAPSO algorithm employs conventional quadratic smooth and augmented quadratic nonsmooth generator cost curves with sine components to improve the accurate of the model by incorporating the valve loading effects. CAPSO also employs quadratic smooth consumer benefit functions. The proposed approach relies on particle swarm optimization to capture the near-optimal GenCos and DisCos, as well as the location and rating of SSSC while the Newton based load flow solution minimizes the mismatch equations. Simulation results of the proposed CAPSO algorithm are compared to solutions obtained by sequential quadratic programming (SQP) and a recently implemented Fuzzy based genetic algorithm (Fuzzy-GA). The main contributions are inclusion of customer benefit in the congestion management objective function, consideration of nonsmooth generator characteristics and the utilization of a coordinated aggregation-based PSO for locating/sizing of SSSC.

FPGA real-time calculator to determine the position of an emitter

  • Tamura, M.;Aoyama, T.
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2003년도 ICCAS
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    • pp.473-478
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    • 2003
  • To detect motions of bodies, we have discussed them with two viewpoints; one is a detection algorithm, and another is the hardware implementation. The former is to find small terms expansions for sine/cosine functions. We researched Maclaurin and optimum expansions, and moreover to reduce hardware amounts, revised the expansions. The expansions don't include divide calculations, and the error is within 0.01%. As for the former problem, there is another approach also; that is the cordic method. The method is based on the rotation of a vector on the complex plain. It is simple iterations and don't require large logic. We examined the precision and convergence of the method on C-simulations, and implemented on HDL. The later problem is to make FPGA within small gates. We considered approaches to eliminate a divider and to reduce the bit number of arithmetic. We researched Newton-Raphson's method to get reciprocal numbers. The higher-order expression shows rapid convergence and doesn't be affected by the initial guess. It is an excellent algorithm. Using them, we wish to design a detector, and are developing it on a FPGA.

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Partitioned coupling strategies for fluid-structure interaction with large displacement: Explicit, implicit and semi-implicit schemes

  • He, Tao
    • Wind and Structures
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    • 제20권3호
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    • pp.423-448
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    • 2015
  • In this paper the unsteady fluid-structure interaction (FSI) problems with large structural displacement are solved by partitioned solution approaches in the arbitrary Lagrangian-Eulerian finite element framework. The incompressible Navier-Stokes equations are solved by the characteristic-based split (CBS) scheme. Both a rigid body and a geometrically nonlinear solid are considered as the structural models. The latter is solved by Newton-Raphson procedure. The equation governing the structural motion is advanced by Newmark-${\beta}$ method in time. The dynamic mesh is updated by using moving submesh approach that cooperates with the ortho-semi-torsional spring analogy method. A mass source term (MST) is introduced into the CBS scheme to satisfy geometric conservation law. Three partitioned coupling strategies are developed to take FSI into account, involving the explicit, implicit and semi-implicit schemes. The semi-implicit scheme is a mixture of the explicit and implicit coupling schemes due to the fluid projection splitting. In this scheme MST is renewed for interfacial elements. Fixed-point algorithm with Aitken's ${\Delta}^2$ method is carried out to couple different solvers within the implicit and semi-implicit schemes. Flow-induced vibrations of a bridge deck and a flexible cantilever behind an obstacle are analyzed to test the performance of the proposed methods. The overall numerical results agree well with the existing data, demonstrating the validity and applicability of the present approaches.

Imputation of Medical Data Using Subspace Condition Order Degree Polynomials

  • Silachan, Klaokanlaya;Tantatsanawong, Panjai
    • Journal of Information Processing Systems
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    • 제10권3호
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    • pp.395-411
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    • 2014
  • Temporal medical data is often collected during patient treatments that require personal analysis. Each observation recorded in the temporal medical data is associated with measurements and time treatments. A major problem in the analysis of temporal medical data are the missing values that are caused, for example, by patients dropping out of a study before completion. Therefore, the imputation of missing data is an important step during pre-processing and can provide useful information before the data is mined. For each patient and each variable, this imputation replaces the missing data with a value drawn from an estimated distribution of that variable. In this paper, we propose a new method, called Newton's finite divided difference polynomial interpolation with condition order degree, for dealing with missing values in temporal medical data related to obesity. We compared the new imputation method with three existing subspace estimation techniques, including the k-nearest neighbor, local least squares, and natural cubic spline approaches. The performance of each approach was then evaluated by using the normalized root mean square error and the statistically significant test results. The experimental results have demonstrated that the proposed method provides the best fit with the smallest error and is more accurate than the other methods.

초음파계측에 의한 SPOT용접품질의 비파괴평가 (Nondestructive evaluation of spot weld quality using by ultrasonic measurement)

  • 박익근
    • Journal of Welding and Joining
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    • 제12권3호
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    • pp.109-117
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    • 1994
  • Spot welding has wide used with a high work efficiency in the automotive and aerospace industries. Up to the present, the technique mainly used to test spot welds on production lines has been entirely depended upon destructive chisel or peel testing. Therefore, it's being very important assignment to secure the NDE technique which can be evaluate spot weld quality with more efficiency and high reliability. This paper discusses the feasibility of UNDE techniques to evaluate spot weld quality. For the sake of the approach to the quantitative measurement of nugget diameter and the discrimination of a the corona bond from nugget, ultrasonic c-scan image and distribution of reflective echo amplitude was measured by immersion method with the mechanical and the electronic scanning of point-focussed ultrasonic beam(25 MHz). As the results of this study, corona bond which is the most dangerous types of interface defects can be successfully detected, as well as expulsion and voids. Ultrasonic testing results were confirmed and compared by optical microscope and SAM(Scanning Acoustic Microscope) observation of the spot-weld cross section. The results show that the nugget diameter can be successfully measured with the accuracy of 0.8 mm.

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발전소 굴뚝에서의 입자 분산에 대한 수치해석 (Numerical study of particle dispersion from a power plant chimney)

  • 심정보;유동현
    • 한국입자에어로졸학회지
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    • 제13권4호
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    • pp.173-182
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    • 2017
  • An Eulerian-Lagrangin approach is used to compute particle dispersion from a power plant chimney. For air flow, three-dimensional incompressible filtered Navier-Stokes equations are solved with a subgrid-scale model by integrating the Newton's equation, while the dispersed phase is solved in a Lagrangian framework. The velocity ratios between crossflow and a jet of 0.455 and 0.727 are considered. Flow fields and particle distribution of both cases are evaluated and compared. When the velocity ratio is 0.455, it demonstrates a Kelvin-Helmholtz vortex structure above the chimney caused by the interaction between crossflow and a jet, whereas the other case shows flow structures at the top of the chimney collapsed by fast crossflow. Also, complex wake structures cause different particle distributions behind the chimney. The case with the velocity ratio of 0.727 demonstrates strong particle concentration at the vortical region, whereas the case with the velocity ratio of 0.455 shows more dispersive particle distribution. The simulation result shows similar tendency to the experimental result.