• Proceedings of the KIEE Conference
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• 2000.07b
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• pp.825-827
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• 2000

자성체를 포함하는 자기 시스템을 해석하는데 있어 비선형과 히스테리시스(Hysteresis)는 매우 중요한 역할을 한다. 특히 재질의 히스테리시스 특성을 유한요소법(FEM)을 이용하여 계산하기 위해서 많은 방법들이 소개되었다. 단순 반복법이나 Fixed Point Technique(FPT), M-iteration 법. 뉴튼 랍슨 (Newton-Raphson) 법 등이 그 예이다. 이 방법들 중에서 뉴튼 랍슨법은 빠른 수렴 특성으로 가장 많이 사용되고 있다. 하지만 뉴튼-랍슨법을 이용하여 히스테리시스 재질을 해석할 때는 매 반복 계산 때마다 계 계수행렬(System Stiffness matrix)이 변화하기 때문에 요소의 수가 매우 많을 경우 역행렬을 계산하기 위한 시간이 많이 소요되는 단점이 있다. 특히 히스테리시스 해석의 경우에는 주로 time-step법을 이용하여 계산하므로 가장 시간이 많이 소요되는 행렬 계산 시간을 단축함으로써 전체 계산 시간을 크게 줄일 수 있다. 최근 비선형 해석에서 TLM(Transmission Line Modeling)법이 도입되어 비선형 해석 시의 계산 시간을 크게 단축할 수 있게 되었다. 본 논문에서는 비선형 해석에 적용된 TLM법을 히스테리시스 해석에 적용하는 방법을 새로 제안한다. TLM법은 뉴튼-랍슨법과 달리 각 반복 계산 때마다 계수행렬식이 변화하지 않고 단지 구동항만 변하기 때문에 행렬의 LU를 한 번 저장해 두면 forward와 backward substitution만 시행하면 된다. 따라서 요소의 수가 증가할 경우 TLM법을 사용하면 뉴튼-랍슨법에 비해 매우 큰 계산 이득을 얻을 수 있다. 본 논문에서는 TLM법을 히스테리시스에 적용하는 방법을 기술하고 간단한 모델에 이 방법을 적용하여 뉴튼-랍슨법과의 비교를 통해 TLM법의 효용성을 보인다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6D
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• pp.895-904
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• 2008

CWR (Continuous Welded Rail) may be broken when a temperature drop below the neutral temperature changes in axial force, causing tensile fracture and rail gap, in winter. Rail-breaks may lead to the damage of the rail and wheel by dynamic load, and the reduction of running safety if not detected before the passage of a train. In this study, the track and train coupled model with open gap for dynamic interaction analysis, is proposed. Linear track and train systems is coupled by the nonlinear Herzian contact spring and the complete system matrices of total track-train system is constructed. And the interaction phenomenon considering open gap, was defined by assigning the irregularity functions between the two sides of a gap. Time history analysis, which have an iteration scheme such as $Newmark-{\beta}$ method based on Modified Newton-Raphson methods, was performed to solve the nonlinear equation. Finally, numerical studies are performed to assess the effect of various parameters of system, apply to various speeds, open gap size and the support stiffness of rail.

• Journal of the Korean Recycled Construction Resources Institute
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• v.6 no.2
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• pp.100-107
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• 2018

The material and geometrical nonlinear finite elment analysis of UHPFRC 50M composite box girder was carried out. Constitute law in tension and compressive region of UHPFRC and HPC were modeled based on specimen test. The accuracy of nonlinear FEM analysis was verified by the experimental result of UHPFRC 50M composite girder. The UHPFRC 50M segmental composite box girder which has 1.5% steel fiber of volume fraction, 135MPa compressive strength and 18MPa tensile strength was tested. The post-tensioned UHPFRC composite girder consisted of three segment UHPFRC U-girder and High Strength Concrete reinforced slab. The parts of UHPFRC girder were modeled by 8nodes hexahedron elements and reinforcement bars and tendons were built by 2nodes linear elements by Midas FEA software. The constitutive laws of concrete materials were selected Multi-linear model both of tension and compression function under total strain crack model, which was included in classifying of smeared crack model. The nonlinearity of reinforcement elements and tendon was simulated by Von Mises criteria. The nonlinear static analysis was applied by incremental-iteration method with convergence criteria of Newton-Raphson. The validation of numerical analysis was verified by comparison with experimental result and numerical analysis result of load-deflection response, neutral axis coordinate change, and cracking pattern of girder. The load-deflection response was fitted very well with comparison to the experimental result. The finite element analysis is seen to satisfactorily predict flexural behavioral responses of post-tensioned, reinforced UHPFRC composite box girder.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.3
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• pp.49-59
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• 1985

Formulation of the geometric optimization for truss structures based on the elasticity theory turn out to be the nonlinear programming problem which has to deal with the Cross sectional area of the member and the coordinates of its nodes simultaneously. A few techniques have been proposed and adopted for the analysis of this nonlinear programming problem for the time being. These techniques, however, bear some limitations on truss shapes loading conditions and design criteria for the practical application to real structures. A generalized algorithm for the geometric optimization of the truss structures which can eliminate the above mentioned limitations, is developed in this study. The algorithm developed utilizes the two-phases technique. In the first phase, the cross sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Raphson method. In the second phase, the geometric shape is optimized utilizing the unidirctional search technique of the Rosenbrock method which make it possible to minimize only the objective function. The algorithm developed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examme its applicability and stability. The numerical comparisons show that the two-phases algorithm developed in this study is safely applicable to any design criteria, and the convergency rate is very fast and stable compared with other iteration methods for the geometric optimization of truss structures.

• Nuclear Engineering and Technology
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• v.20 no.2
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• pp.88-104
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• 1988

The FUel Rod Analysis(FURA) code is developed using two-dimensional finite element methods for axisymmetric and plane stress analysis of fuel rod. It predicts the thermal and mechanical behavior of fuel rod during normal and load follow operations. To evaluate the exact temperature distribution and the inner gas pressure, the radial deformation of pellet and clad, the fission gas release are considered over the full-length of fuel rod. The thermal element equation is derived using Galerkin's techniques. The displacement element equation is derived using the principle of virtual works. The mechanical analysis can accommodate various components of strain: elastic, plastic, creep and thermal strain as well as strain due to swelling, relocation and densification. The 4-node quadratic isoparametric elements are adopted, and the geometric model is confined to a half-pellet-height region with the assumption that pellet-pellet interaction is symmetrical. The pellet cracking and crack healing, pellet-cladding interaction are modelled. The Newton-Raphson iteration with an implicit algorithm is applied to perform the analysis of non-linear material behavior accurately and stably. The pellet and cladding model has been compared with both analytical solutions and experimental results. The observed and predicted results are in good agreement. The general behavior of fuel rod is calculated by axisymmetric system and the cladding behavior against radial crack is used by plane stress system. The sensitivity of strain aging of PWR fuel cladding tube due to load following is evaluated in terms of linear power, load cycle frequency and amplitude.