• Title/Summary/Keyword: Nonlinear equations

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Buckling Analysis of Axisymmetric Shells by Incremental Finite Element Mothod (증분형(增分形) 유한요소법(有限要素法)에 의한 축대칭(軸對稱) Shell구조(構造)의 좌굴해석(挫屈解析))

  • J.B.,Kim;C.Y.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.22 no.1
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    • pp.21-30
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    • 1985
  • This paper deals whth the buckling as well as postbuckling analysis of axisymmertric shells taking the initial deflection effects into account. Incremental equilibrium equations, based on the principle of virtual work, were derived by the finite element method, the successive step-by-step Newton-Raphson iterative technique was adopted. To define the transition pattern of postbuckling behavior from the prebuckling state more accurately, a simple solution method was developed, i.e. the critical load was calculated by the load extrapolation method with the determinant of tangent stiffness matrix and the equilibrium configuration in the immediate postbuckling stage was obtained by perturbation scheme and eigenvalue analysis. Degenerated isoparametric shell elements were used to analyse the axisymmetric shell of revolution. And by the method developed in this paper, the computer program applicable to the nonlinear analysis of both thin and moderately thick shells was constructed. To verify the capabilities and accuracies of the present solution method, the computed results were compared with the results of analytical solutions. These results coincided fairly well in both the small deflection and large deflection ranges. Various numerical analyses were done to show the effect of initial deflection and shape of shells on buckling load and postbuckling behavior. Futhermore, corrected directions of applied loads at every increment steps were used to determine the actual effects of large deflection in non-conservative load systems such as hydrostatic pressure load. The following conclusions can be obtained. (1) The method described in this paper was found to be both economic and effective in calculating buckling load and postbuckling behavior of shell structure. (2) Buckling and postbuckling behavior of spherical caps is critically dependent upon their geometric configuration, i.e. the shape of spherical cap and quantities of the initial deflection. (3) In the analysis of large deflection problems of shells by the incremental method, corrections of the applied load directions are needed at every incremental step to compensate the follower force effects.

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Transformation of TSK fuzzy systems into fuzzy systems with singleton consequents and its applications (TSK 퍼지시스템을 결론부가 singleton인 퍼지시스템으로 표현하는 방법과 그 응용)

  • Chae, Yang-Beom;Lee, Won-Chang;Gang, Geun-Taek
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.39 no.1
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    • pp.48-59
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    • 2002
  • TSK(Takagi-Sugeno-Kang) fuzzy models with linear equations consequents, which represent complex nonlinear systems very well with a few rules, can be easily identified systematically by using input-output data. Many algorithms designing TSK fuzzy controllers based on TSK fuzzy models, which guarantees the stability of the closed system, have been suggested. On the contrary, singleton fuzzy models with singleton consequents can be easily understood and adjusted. In this paper, in order to utilize the merits of TSK fuzzy systems and singleton fuzzy systems, an algorithm transforming a TSK fuzzy model into a singleton fuzzy model having the same input-output relation is suggested. The suggested algorithm is applied to a fuzzy modelling example and a fuzzy controller design example.

An Optimality Criteria applied to the Design of Plane Frames (평면 뼈대 구조물의 설계에 적용된 최적규준)

  • 정영식;김봉익;김창규
    • Computational Structural Engineering
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    • v.9 no.2
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    • pp.121-131
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    • 1996
  • This work proposes an optimality criteria applicable to the optimum design of plane frames subject to multiple behavioral constraints on member stresses and lateral displacements of nodes and also to side constraints on design variables. The method makes use of a first order approximation for both deflection and stress constraints instead of the zero order approximation based on the concept of FSD (fully stressed design). A redesign algorithm is derived from a mathematically rigorous method which uses the Newton-Raphson method to solve the system of nonlinear constraint equations and reduces the design space whenever minimum size restrictions become active. When applied to worked examples it proved more accurate and efficient, and it is often found that optimum designs are not fully stressed designs. This fact suggests that this rigorous method is worth what it claims for complicated computing and thus had better replace the crude stress ratio algorithm adopted by the majority of optimality criteria approaches. This is particularly true as long as we enjoy ever-increasing computing power at negligible costs.

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Numerical Prediction of elastic Material Properties of Composites by A Constrained Nonlinear Optimization Method (구속적 비선형 최적화에 의한 합성재료 탄성물성치의 수치적 예측)

  • 신수봉;고현무
    • Computational Structural Engineering
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    • v.10 no.2
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    • pp.225-232
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    • 1997
  • Material properties of a new composite composed of components with known material properties are usually investigated through experiments. Elastic modulus and Poisson's ratio are measured at various volume fractions of mixed components and utilized as the base information on an analytical model for predicting the mechanical behaviors of a structure constructed by the composite. Elastic material properties of a composite at various volume fractions are numerically estimated by minimizing the error between the static displacements computed from a model for the composite and those computed from a model of homogeneous and isotropic material. A finite element model for a composite is proposed to distribute different types of material components easily into the model depending on the volume fraction. Then, the material properties of a composite filled with solid mircospheres are predicted numerically through a sample study and the estimated results are compared with experimental results and some theoretical equations.

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Elastic-Damage Constitutive Model for Nonlinear Tensile Behavior of Polymeric Foam (폴리머 폼의 비선형 인장거동을 모사하기 위한 기공이 고려된 손상 탄성 구성방정식)

  • Kwon, Sun-Beom;Lee, Jae-Myung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.31 no.4
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    • pp.191-197
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    • 2018
  • This paper details the development of an isotropic elastic-damage constitutive model for polymeric foam based on irreversible thermodynamics to consider the growth and coalescence of voids. The constitutive equations describe the material behavior sustaining unilateral damage. To facilitate finite element analysis, the material properties for specific types of polymeric foams are applied to the developed model; the model is then implemented in ABAQUS as a user-defined material subroutine. To validate the developed damage model, the simulated results are compared to the results of a series of tensile tests on various polymeric foams. The proposed damage model can be utilized to further research on continuum damage mechanics and finite element analysis of polymeric foams in computational engineering.

Gonadal Development, Age and Growth of the Shortnecked Clam, Ruditapes philippinarum ( Pelecypoda : Veneridae ), on the Coast of Kimje, Korea ) (금제연안에 서식하는 바지락 , Ruditapes philippinarum ( Pelecypoda : Veneridae ) 의 생식소발달과 연령 및 성장)

  • Chung, Ee-Yung;Ryou, Dong-Ki;Lee, Ju-Ha
    • The Korean Journal of Malacology
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    • v.10 no.1
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    • pp.38-48
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    • 1994
  • Gonadal developmint, age and growth of Ruditapes philippinarum were investigated using samples from the intertidal zone of Simpo on the coast of Kimje, Korea, which were collected onthly for one year from Februaty 1993 to January 1994.Ruditapes philippinarum is diecious in sex. The gonads are located between the subregion of the midintestinal glands and reticular connective tissue of the foot. The ovary is composed of a number of ovarian sacs, and the testis is composed of numerous seminiferous tubules. The clam spawns once a year from early June to darly October, and the main spawning occurred between July and August when the water temperature went above 23$^{\circ}C$. Ripe oocytes are about 65-70${\mu}{\textrm}{m}$ in diameter. Gonadal phases of this species can be divided into five successive stages; multiplicative(February to March), growing (April to May), mature(Aprilto Septimber), spent(June to October), and degenerative and resting(july to March). Spawning is closely related to the sea water temperature. Based on the monthly variations of marginal index (MI')of the shell, it was suggested that the annual ring mark formation occurred in March once a year and took approximately 8 months (0.67 year) for first ring to be formed on the shell. The relationship between the shell length(SL) and the total weight (TW) was represented by nonlinear equation; TW=1.208 x 10/ sup -4/ S $L^{3.158}$, and also in the relationship be-tweenthe shell length (SL) and the shell height(SH), the shell length and the shell width (SW) were represented by the linear equations; SH=0.726 SL-0.483, SW=0.542 SL-0.803.Growth curves for shell length and total weight fitted to von Bertalanffs equation were expressed as: S $L_{t}$ =68.34(1- $e^{0.221}$(t+0.418)) T $W_{t}$ =75.16(1- $e^{0.221}$(t=0.418))$^{3.158/3.158}$

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Three-dimensional dynamics of vortex-induced vibration of a pipe with internal flow in the subcritical and supercritical regimes

  • Duan, Jinlong;Chen, Ke;You, Yunxiang;Wang, Renfeng;Li, Jinlong
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.10 no.6
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    • pp.692-710
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    • 2018
  • The Three-dimensional (3-D) dynamical behaviors of a fluid-conveying pipe subjected to vortex-induced vibration are investigated with different internal flow velocity ${\nu}$. The values of the internal flow velocity are considered in both subcritical and supercritical regimes. During the study, the 3-D nonlinear equations are discretized by the Galerkin method and solved by a fourth-order Runge-Kutta method. The results indicate that for a constant internal flow velocity ${\nu}$ in the subcritical regime, the peak Cross-flow (CF) amplitude increases firstly and then decrease accompanied by amplitude jumps with the increase of the external reduced velocity. While two response bands are observed in the In-line (IL) direction. For the dynamics in the lock-in condition, 3-D periodic, quasi-periodic and chaotic vibrations are observed. A variety of CF and IL responses can be detected for different modes with the increase of ${\nu}$. For the cases studied in the supercritical regime, the dynamics shows a great diversity with that in the subcritical regime. Various dynamical responses, which include 3-D periodic, quasi-periodic as well as chaotic motions, are found while both CF and IL responses are coupled while ${\nu}$ is beyond the critical value. Besides, the responses corresponding to different couples of ${\mu}_1$ and ${\mu}_2$ are obviously distinct from each other.

Underwater Docking of an AUV Using a Visual Servo Controller (비쥬얼 서보 제어기를 이용한 자율무인잠수정의 도킹)

  • Lee, Pan-Mook;Jeon, Bong-Hwan;Lee, Chong-Moo
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.142-148
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    • 2002
  • Autonomous underwater vehicles (AUVs) are unmanned underwater vessels to investigate sea environments, oceanography and deep-sea resources autonomously. Docking systems are required to increase the capability of the AUVs to recharge the batteries and to transmit data in real time for specific underwater works, such as repeated jobs at sea bed. This paper presents a visual servo control system for an AUV to dock into an underwater station with a camera mounted at the nose center of the AUV. To make the visual servo control system, this paper derives an optical flow model of a camera, where the projected motions of the image plane are described with the rotational and translational velocities of the AUV. This paper combines the optical flow equation of the camera with the AUVs equation of motion, and derives a state equation for the visual servoing AUV. This paper proposes a discrete-time MIMO controller minimizing a cost function. The control inputs of the AUV are automatically generated with the projected target position on the CCD plane of the camera and with the AUVs motion. To demonstrate the effectiveness of the modeling and the control law of the visual servoing AUV, simulations on docking the AUV to a target station are performed with the 6-dof nonlinear equations of REMUS AUV and a CCD camera.

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Numerical Analysis of Wave Impact Forces in Numerical Wave Basin (수치파 수조를 이용한 파랑 충격력 수치해석)

  • Shin, Young-Seop;Hong, Key-Yong
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • v.1
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    • pp.205-210
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    • 2006
  • The impact forces of the highly nonlinear waves are one of the important factors in designing the ocean structures. The impact forces are very difficult to analyze numerically and experimentally because they are impulsive in magnitude and occur instantaneously. In this study the numerical program based on N.S. equations are used to investigate the impact forces of steep waves where the waves are gene rated by the wave maker in the numerical wave basin. The arbitrary steep waves are generated by the superposition of waves of single frequency and the impact forces on vertical cylinder are simulated on the multiblock grids. V.O.F. and the local height function methods are used to track the free surfaces. To validate the numerical analysis the numerical results are compared with the experimental ones and the acceptable agreements are found. It is thought that more studies on the simulations of the incoming breaking waves and the impact forces on the vertical cylinder should be made to obtain the useful results to be applied in the offshore design.

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Evaluation of Pumping Rates for Multiple-Well Systems (군정 시스템의 취수량 평가)

  • Park, Nam-Sik;Kim, Sung-Yun;Kim, Boo-Gil;Kim, Il-Ryong
    • The Journal of Engineering Geology
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    • v.18 no.4
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    • pp.439-446
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    • 2008
  • We have developed a method to evaluate pumping rates from a system of pumping-well family. For a given system actual pumping rates depend on pump characteristics and the sum of the static head and the dynamic head. The static head is the elevation difference between the natural groundwater level and the outlet of the pipeline that connects all the wells. Major components of the dynamic head are groundwater drawdown in the well and pipeline head loss. The dynamic head and the pump characteristics depend on the pumping rates. Actual pumping rates are determined at the intersections of the system total-head curves and the pump characteristic curves. The Newton-Raphson's method is used to solve the nonlinear simultaneous equations. The method is applied to a hypothetical well family. Impacts of various design and operational parameters on the pumping rates are analyzed.