• Title/Summary/Keyword: nonlinear matrix equation

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Level Set Based Topological Shape Optimization of Hyper-elastic Nonlinear Structures using Topological Derivatives (위상 민감도를 이용한 초탄성 비선형 구조의 레벨셋 기반 위상 및 형상 최적설계)

  • Kim, Min-Geun;Ha, Seung-Hyun;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.25 no.6
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    • pp.559-567
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    • 2012
  • A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.

A Comprehensive Groundwater Modeling using Multicomponent Multiphase Theory: 1. Development of a Multidimensional Finite Element Model (다중 다상이론을 이용한 통합적 지하수 모델링: 1. 다차원 유한요소 모형의 개발)

  • Joon Hyun Kim
    • Journal of Korea Soil Environment Society
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    • v.1 no.1
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    • pp.89-102
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    • 1996
  • An integrated model is presented to describe underground flow and mass transport, using a multicomponent multiphase approach. The comprehensive governing equation is derived considering mass and force balances of chemical species over four phases(water, oil, air, and soil) in a schematic elementary volume. Compact and systemati notations of relevant variables and equations are introduced to facilitate the inclusion of complex migration and transformation processes, and variable spatial dimensions. The resulting nonlinear system is solved by a multidimensional finite element code. The developed code with dynamic array allocation, is sufficiently flexible to work across a wide spectrum of computers, including an IBM ES 9000/900 vector facility, SP2 cluster machine, Unix workstations and PCs, for one-, two and three-dimensional problems. To reduce the computation time and storage requirements, the system equations are decoupled and solved using a banded global matrix solver, with the vector and parallel processing on the IBM 9000. To avoide the numerical oscillations of the nonlinear problems in the case of convective dominant transport, the techniques of upstream weighting, mass lumping, and elementary-wise parameter evaluation are applied. The instability and convergence criteria of the nonlinear problems are studied for the one-dimensional analogue of FEM and FDM. Modeling capacity is presented in the simulation of three dimensional composite multiphase TCE migration. Comprehesive simulation feature of the code is presented in a companion paper of this issue for the specific groundwater or flow and contamination problems.

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The Control of Flexible Robot Arm using Adaptive Control Theory (적응제어 이론을 이용한 유연한 로봇팔의 제어)

  • Han, Jong-Kil
    • The Journal of the Korea institute of electronic communication sciences
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    • v.7 no.5
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    • pp.1139-1144
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    • 2012
  • The ration of payload to weight of industrial robot amounts form 1:10 to 1:30. Compared with man who have a ration of 3:1, it is very low. One of the goals for the next generation of robots will be a ration. This might be possible only by developing lightweight robots. When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}-2C$ is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed by using Lyapunov stability theory. We propose deterministic and adaptive control laws for two link flexible arm, and the validity of the proposed control scheme is shown in computer simulation for two-link flexible arm.

The Simulator Design for the Analysis of Aircraft Longitudinal Dynamic Characteristics (항공기 세로 동특성 해석을 위한 시뮬레이터 설계)

  • Yoon, Sun-Ju
    • Journal of the Korea Computer Industry Society
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    • v.7 no.4
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    • pp.427-436
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    • 2006
  • State-space method for the analysis of the dynamic characteristics of a body motion is set up as mathematical tool for the solution of differential equation by computer. Representation of a system is described as a simple form of matrix calculation and unique form of model is available for the linear or nonlinear, time variant or time invariant, mono variable or multi variable system etc. For the analysis of state-space method a complicated vector calculation is required, but this analysis can be simplified with the specific functions of a software package. Recently as the Graphical User Interface softwares are well-developed, then it is very simplified to execute the simulation of the dynamic characteristics for the state-space model with the interactive graphics treatment. The purpose of this study is to developed the simulator for the educational analysis of the dynamic characteristics of body motion, and for the analysis of the longitudinal dynamic characteristics of an aircraft that is primarily to design the simulator for the analysis of the transient response of an aircraft longitudinal stability.

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Breakthrough Curves and Miscible Displacement of Cadmium Through Double-Layered Reclaimed Soils Amended with Macroporous Granule

  • Kim, Hye-Jin;Ryu, Jin-Hee;Kim, Si-Ju;Park, Mi-Suk;Chung, Doug-Young
    • Korean Journal of Soil Science and Fertilizer
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    • v.44 no.1
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    • pp.15-21
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    • 2011
  • Transport of heavy metals such as Cd is affected by several rate-limiting processes including adsorption and desorption by exchange reactions in soils. In this study, column transport and batch kinetic experiments were performed to assess Cd mobility in a double-layered soil with a reclaimed saline and sodic soil (SSS) as top soil and macroporous granule (MPG) as a bottom layer. For individual soil layer having different physical and chemical properties, Cd was considered to be nonlinear reactivity with the soil matrix in layered soils. The dispersive equation for reactive solutes was solved with three types of boundary conditions for the interface between soil layers. The adsorption of Cd with respect to the saline-sodic sandy loam and the MPG indicated that the nature of the sites or the mechanisms involved in the sorption process of Cd was different and the amounts of Cd for both of samples increases with increasing amounts of equilibrium concentration whereas the amount of Cd adsorbed in saline-sodic sandy loam soil was higher than that in MPG. The results of breakthrough curve indicating relative Cd retardation accompanied by layer material and sequence during leaching showed that the number of pore volumes to reach the maximum relative concentration of 1 increased in the order of MPG, SSS, and double layer of SSS-MPG. Breakthrough curves (BTCs) from column experiments were well predicted with our double-layered model where independently derived solute physical and retention parameters were implemented.

Assessment of Multiple Delamination in Laminated Composites for Aircrafts using X-ray Backscattering (X-ray 후방산란 기술을 이용한 항공기용 복합재료의 다중 층간 박리 평가)

  • Kim, Noh-Yu
    • Journal of the Korean Society for Nondestructive Testing
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    • v.30 no.1
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    • pp.46-53
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    • 2010
  • A Compton X-ray backscatter technique has been developed to quantitatively assess impact damage in quasi-isotropic laminated composites made by a drop-weight tester. X-ray backscatter imaging system with a slit-type camera is constructed to obtain a cross-sectional profile of impact-damaged laminated composites from the electron-density variation of the cross section. A nonlinear scattering model based on Boltsman equation is introduced to compute Compton X-ray backscattering field for the defect assessment. An adaptive filter is also used to reduce noises from many sources including quantum noise and irregular distributions of fibers and matrix in composites. Delaminations masked or distorted by the first delamination are detected and characterized effectively by the Compton X-ray backscatter technique, both in width and location, by application of error minimization algorithm.

Application of Hermite-Collocation Method for Unsteady Flow Analysis (부정류 해석을 위한 Hermite-Collocation 기법의 적용)

  • Han, Geon-Yeon;Lee, Eul-Rae;Park, Jae-Hong
    • Journal of Korea Water Resources Association
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    • v.32 no.3
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    • pp.237-246
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    • 1999
  • A finite element model is studied to simulate unsteady free surface flow based on dynamic wave equation and collocation method. The collocation method is used in conjunction with Hermite polynomials, and resulting matrix equations are solved by skyline method. The model is verified by applying to hydraulic jump, nonlinear disturbance propagation and dam-break flow in a horizontal frictionless channel. The computed results are compared with those by Bubnov-Galerkin and Petrov-Galerkin methods. It is also applied to the North Han River to simulate the floodwave propagation. The computed results have good agreements with those of DWOPER model in terms of discharge hydrographs. The suggested model has proven to be one of the promising scheme for simulating the gradually and rapidly varied unsteady flow in open channels.

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The Effect of Internal Flow on Vortex-Induced Vibration of Marine Riser (Riser의 내부유체 흐름이 소용돌이로 인한 Riser 동적반응에 미치는 영향)

  • Hong, Nam-Seeg;Hsiang Wang
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.7 no.2
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    • pp.198-208
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    • 1995
  • Combining Iwan-Blevin's model into the approximated form of the nonlinear model derived for the dynamic analysis of the riser system with the inclusion of internal flow, current-vortex model is developed to investigate the effect of internal flow on vortex-induced vibration due to inline current The riser system includes a steadly flow inside the pipe which is modeled as an extensible or inextensible tubular beam. Galerkin's finite element approximation are implemented to derive the matrix equation of equilibrium for the finite element system. The investigations of the effect of internal flow on vibration due to inline current are performed according to the change of various parameters such as top tension, infernal flow velocity. current velocity, and so on. It is found that the effect of internal flow on vibration due to vortex shedding can be controlled by the increase of top tension. However, careful consideration has to be given, in design point in order to avoid the resonance band occurding near vortex shedding frequency, particularly for the long riser.

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Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam

  • Zerrouki, Rachid;Karas, Abdelkader;Zidour, Mohamed;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • v.78 no.2
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    • pp.117-124
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    • 2021
  • This work focused on the novel numerical tool for the bending responses of carbon nanotube reinforced composites (CNTRC) beams. The higher order shear deformation beam theory (HSDT) is used to determine strain-displacement relationships. A new exponential function was introduced into the carbon nanotube (CNT) volume fraction equation to show the effect of the CNT distribution on the CNTRC beams through displacements and stresses. To determine the mechanical properties of CNTRCs, the rule of the mixture was employed by assuming that the single-walled carbon nanotubes (SWCNTs)are aligned and distributed in the matrix. The governing equations were derived by Hamilton's principle, and the mathematical models presented in this work are numerically provided to verify the accuracy of the present theory. The effects of aspect ratio (l/d), CNT volume fraction (Vcnt), and the order of exponent (n) on the displacement and stresses are presented and discussed in detail. Based on the analytical results. It turns out that the increase of the exponent degree (n) makes the X-beam stiffer and the exponential CNTs distribution plays an indispensable role to improve the mechanical properties of the CNTRC beams.

An Improved Bond Slip Model of CFT Columns for Nonlinear Finite Element Analysis (CFT 기둥의 비선형 유한요소해석을 위한 개선된 강관-콘크리트 간 부착 모델 개발)

  • Kwon, Yangsu;Kwak, Hyo-Gyoung;Hwang, Ju-Young;Kim, Jin-Kook;Kim, Jong-Min
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.28 no.2
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    • pp.213-220
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    • 2015
  • CFT column has a lot of structural advantages due to the composite behavior between in-filled concrete and steel tube. This paper deals with the development of an effective numerical model which can consider the bond-slip behavior between both components of concrete matrix and steel tube without taking double nodes. Since the applied axial load to in-filled concrete matrix is delivered to steel tube by the confinement effect and the friction, the governing equation related to the slip behavior can be constructed on the basis of the force equilibrium and the compatability conditions. In advance, the force and displacement relations between adjacent two nodes make it possible to express the slip behavior with the concrete nodes only. This model results in significant savings in the numerical modeling of CFT columns to take into account the effect of bond-slip. Finally, correlation studies between numerical results and experimental data are conducted to verifying the efficiency of the introduced numerical model.