• Title/Summary/Keyword: Euler-Lagrange model

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Comparison of Seawater Exchange Rate of Small Scale Inner Bays within Jinhae Bay (수치모델을 이용한 진해만 내 소규모 내만의 해수교환율 비교)

  • Kim, Nam Su;Kang, Hoon;Kwon, Min-Sun;Jang, Hyo-Sang;Kim, Jong Gu
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.19 no.1
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    • pp.74-85
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    • 2016
  • For the assessment of seawater exchange rates in Danghangpo bay, Dangdong bay, Wonmun bay, Gohyunsung bay, and Masan bay, which are small-scale inner bays of Jinhae bay, an EFDC model was used to reproduce the seawater flow of the entire Jinhae bay, and Lagrange (particle tracking) and Euler (dye diffusion) model techniques were used to calculate the seawater exchange rates for each of the bays. The seawater exchange rate obtained using the particle tracking method was the highest, at 60.84%, in Danghangpo bay, and the lowest, at 30.50%, in Masan bay. The seawater exchange rate calculated based on the dye diffusion method was the highest, at 45.40%, in Danghangpo bay, and the lowest, at 34.65%, in Masan bay. The sweater exchange rate was found to be the highest in Danghangpo bay likely because of a high flow velocity owing to the narrow entrance of the bay; and in the case of particle tracking method, the morphological characteristics of the particles affected the results, since once the particles get out, it is difficult for them to get back in. Meanwhile, in the case of the Lagrange method, when the particles flow back in by the flood current after escaping the ebb current, they flow back in intact. However, when a dye flows back in after escaping the bay, it becomes diluted by the open sea water. Thus, the seawater exchange rate calculated based on the dye diffusion method turned out to be higher in general, and even if a comparison of the sweater exchange rates calculated through two methods was conducted under the same condition, the results were completely different. Thus, when assessing the seawater exchange rate, more reasonable results could be obtained by either combining the two methods or selecting a modeling technique after giving sufficiently consideration to the purpose of the study and the characteristics of the coastal area. Meanwhile, through a comparison of the degree of closure and seawater exchange rates calculated through Lagrange and Euler methods, it was found that the seawater exchange rate was higher for a higher degree of closure, regardless of the numerical model technique. Thus, it was deemed that the degree of closure would be inappropriate to be used as an index for the closeness of the bay, and some modifications as well as supplementary information would be necessary in this regard.

Modeling, Identification and Control of a Redundant Planar 2-DOF Parallel Manipulator

  • Zhang, Yao-Xin;Cong, Shuang;Shang, Wei-Wei;Li, Ze-Xiang;Jiang, Shi-Long
    • International Journal of Control, Automation, and Systems
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    • v.5 no.5
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    • pp.559-569
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    • 2007
  • In this paper, the dynamic controller design problem of a redundant planar 2-dof parallel manipulator is studied. Using the Euler-Lagrange equation, we formulate the dynamic model of the parallel manipulator in the joint space and propose an augmented PD controller with forward dynamic compensation for the parallel manipulator. By formulating the controller in the joint space, we eliminate the complex computation of the Jacobian matrix of joint angles with end-effector coordinate. So with less computation, our controller is easier to implement, and a shorter sampling period can be achieved, which makes the controller more suitable for high-speed motion control. Furthermore, with the combination of static friction model and viscous friction model, the active joint friction of the parallel manipulator is studied and compensated in the controller. Based on the dynamic parameters of the parallel manipulator evaluated by direct measurement and identification, motion control experiments are implemented. With the experiments, the validity of the dynamic model is proved and the performance of the controller is evaluated. Experiment results show that, with forward dynamic compensation, the augmented PD controller can improve the tracking performance of the parallel manipulator over the simple PD controller.

A Comparative Study on Eigen-Wear Analysis and Numerical Analysis using Algorithm for Adaptive Meshing (마모해석을 위한 고유치해석과 Adaptive Meshing 알고리듬을 이용한 수치해석 비교)

  • Jang, Ilkwang;Jang, Yong Hoon
    • Tribology and Lubricants
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    • v.36 no.5
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    • pp.262-266
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    • 2020
  • Herein, we present a numerical investigation of wear analysis of sliding systems with a constant speed subjected to Archard's wear law. For this investigation, we compared two methods: eigen-wear analysis and adaptive meshing technique. The eigen-wear analysis is advantageous to predict the evolution of contact pressure due to wear using the initial contact pressure and contact stiffness. The adaptive meshing technique in finite element analysis is employed to obtain transient wear behavior, which needs significant computational resources. From the eigen-wear analysis, we can determine the appropriate element size required for finite element analysis and the time increment required for wear evolution by a dimensionless variable above a certain value. Since the prediction of wear depends on the maximum contact pressure, the finite element model should have a reasonable representation of the maximum contact pressure. The maximum contact pressure and wear amount according to this dimensionless variable shows that the number of fine meshes in the contact area contributes more to the accuracy of the wear analysis, and the time increment is less sensitive when the number of contact nodes is significantly larger. The results derived from a two-dimensional wear model can be applied to a three-dimensional wear model.

Extension of a new tailoring optimisation technique to sandwich shells with laminated faces

  • Icardi, Ugo
    • Structural Engineering and Mechanics
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    • v.43 no.6
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    • pp.739-759
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    • 2012
  • The tailoring optimization technique recently developed by the author for improving structural response and energy absorption of composites is extended to sandwich shells using a previously developed zig-zag shell model with hierarchic representation of displacements. The in-plane variation of the stiffness properties of plies and the through-the thickness variation of the core properties are determined solving the Euler-Lagrange equations of an extremal problem in which the strain energy due to out-of-plane strains and stresses is minimised, while that due to their in-plane counterparts is maximised. In this way, the energy stored by unwanted out-of-plane modes involving weak properties is transferred to acceptable in-plane modes. As shown by the numerical applications, the critical interlaminar stress concentrations at the interfaces with the core are consistently reduced without any bending stiffness loss and the strength to debonding of faces from the core is improved. The structural model was recently developed by the author to accurately describe strain energy and interlaminar stresses from the constitutive equations. It a priori fulfills the displacement and stress contact conditions at the interfaces, considers a second order expansion of Lame's coefficients and a hierarchic representation that adapts to the variation of solutions. Its functional d.o.f. are the traditional mid-plane displacements and the shear rotations, so refinement implies no increase of the number of functional d.o.f. Sandwich shells are represented as multilayered shells made of layers with different thickness and material properties, the core being treated as a thick intermediate layer.

NUMERICAL MODELLING OF SHEET-FLOW TRANSPORT UNDER WAVE AND CURRENT

  • Bakhtiary, Abbas-Yeganeh;Hotoshi Gotoh;Tetsuo Sakai
    • Water Engineering Research
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    • v.3 no.2
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    • pp.75-84
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    • 2002
  • An Euler-Lagrange two-phase flow model is presented fur simulation sheet-flow transport under wave and current. The flow is computed by solving the Reynolds Averaged Navier-Stokes equation in conjunction with the k-$\varepsilon$ turbulence model for turbulence closure. The sediment transport is introduced as a motion of granular media under the action of unsteady flow from the Lagragian point of view. In other word, motion of every single particle is numerically traced with Movable Bed Simulator (MBS) code based on the Distinct Element Method (DEM), in which the frequent interparticle collision of the moving particles during the sheet-flow transport is sophisticatedly taken into account. The particle diameter effect on time-dependent developing process of sheet-flow transport is investigated, by using three different diameter sizes of sediment. The influence of an imposed current on oscillatory sheet-flow transport is also investigated. It is concluded that the sediment transport rate increases due to the relaxation process related to the time-lag between flow velocity and sediment motion.

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A Parametric Study of Ridge-cut Explosive Bolts using Hydrocodes

  • Lee, Juho;Han, Jae-Hung;Lee, YeungJo;Lee, Hyoungjin
    • International Journal of Aeronautical and Space Sciences
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    • v.16 no.1
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    • pp.50-63
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    • 2015
  • Explosive bolts are one of pyrotechnic release devices, which are highly reliable and efficient for a built-in release. Among them, ridge-cut explosive bolts which utilize shock wave generated by detonation to separate bolt body produce minimal fragments, little swelling and clean breaks. In this study, separation phenomena of ridge-cut explosive bolts or ridge-cut mechanism are computationally analyzed using Hydrocodes. To analyze separation mechanism of ridge-cut explosive bolts, fluid-structure interactions with complex material modeling are essential. For modeling of high explosives (RDX and PETN), Euler elements with Jones-Wilkins-Lee E.O.S. are utilized. For Lagrange elements of bolt body structures, shock E.O.S., Johnson-Cook strength model, and principal stress failure criteria are used. From the computational analysis of the author's explosive bolt model, computational analysis framework is verified and perfected with tuned failure criteria. Practical design improvements are also suggested based on a parametric study. Some design parameters, such as explosive weights, ridge angle, and ridge position, are chosen that might affect the separation reliability; and analysis is carried out for several designs. The results of this study provide useful information to avoid unnecessary separation experiments related with design parameters.

Development of a Motion Simulator for Portable Type Welding Robot Based on Adaptive Control (적응 제어 기반 Portable 용접 로봇 시뮬레이터 개발)

  • Ku, Nam-Kug;Ha, Sol;Roh, Myung-Il
    • Journal of the Society of Naval Architects of Korea
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    • v.49 no.5
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    • pp.400-409
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    • 2012
  • It is not easy to know the accurate mass and mass moment of inertia of robot. Because of this uncertainty, error may exist when we control the robot based on the inaccurate mass information. Moreover the properties of the portable robot can change during its operation. Therefore we developed the motion simulator based on the adaptive control. First, the computed torque control was carried out in order to minimize an error between target angles and real angles. The computed torque control is based on the equation of robot motion, which is derived from the Lagrange-Euler equation. To minimize the error between the real model and the approximated model, the adaptive control was carried out. During this simulation, the interference check was also carried out. The interference check verifies that the robot can move successfully without any collision.

Nonlinear numerical modelling for the effects of surface explosions on buried reinforced concrete structures

  • Nagy, N.;Mohamed, M.;Boot, J.C.
    • Geomechanics and Engineering
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    • v.2 no.1
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    • pp.1-18
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    • 2010
  • The analysis of structure response and design of buried structures subjected to dynamic destructive loads have been receiving increasing interest due to recent severe damage caused by strong earthquakes and terrorist attacks. For a comprehensive design of buried structures subjected to blast loads to be conducted, the whole system behaviour including simulation of the explosion, propagation of shock waves through the soil medium, the interaction of the soil with the buried structure and the structure response needs to be simulated in a single model. Such a model will enable more realistic simulation of the fundamental physical behaviour. This paper presents a complete model simulating the whole system using the finite element package ABAQUS/Explicit. The Arbitrary Lagrange Euler Coupling formulation is used to model the explosive charge and the soil region near the explosion to eliminate the distortion of the mesh under high deformation, while the conventional finite element method is used to model the rest of the system. The elasto-plastic Drucker-Prager Cap model is used to model the soil behaviour. The explosion process is simulated using the Jones-Wilkens-Lee equation of state. The Concrete Damage Plasticity model is used to simulate the behaviour of concrete with the reinforcement considered as an elasto-plastic material. The contact interface between soil and structure is simulated using the general Mohr-Coulomb friction concept, which allows for sliding, separation and rebound between the buried structure surface and the surrounding soil. The behaviour of the whole system is evaluated using a numerical example which shows that the proposed model is capable of producing a realistic simulation of the physical system behaviour in a smooth numerical process.

Dynamic Speed Control of a Unicycle Robot (외바퀴 로봇의 동적 속도 제어)

  • Han, In-Woo;Hwang, Jong-Myung;Han, Seong-Ik;Lee, Jangmyung
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.1
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    • pp.1-9
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    • 2013
  • This paper presents a new control algorithm for dynamic control of a unicycle robot. The unicycle robot motion consists of a pitch that is controlled by an in-wheel motor and a roll that is controlled by a reaction wheel pendulum. The unicycle robot doesn't have any actuator for a yaw axis control, which makes the derivation of the dynamics relatively simple. The Euler-Lagrange equation is applied to derive the dynamic equations of the unicycle robot to implement the dynamic speed control of the unicycle robot. To achieve the real time speed control of the unicycle robot, the sliding mode control and LQ regulator are utilized to guarantee the stability while maintaining the desired speed tracking performance. In the roll controller, the sigmoid-function based sliding mode controller has been adopted to minimize the chattering by the switching function. The LQR controller has been implemented for the pitch control to drive the unicycle robot to follow the desired velocity trajectory in real time using the state variables of pitch angle, angular velocity, angle and angular velocity of the wheel. The control performance of the two control systems form a single dynamic model has been demonstrated by the real experiments.

Design of a Fuzzy Logic Controller for a Rotary-type Inverted Pendulum System

  • Park, Byung-Jae;Ryu, Chun-ha;Choi, Bong-Yeol
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.2 no.2
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    • pp.109-114
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    • 2002
  • Various inverted pendulum systems have been frequently used as a model for the performance test of the proposed control system. We first identify a rotary-type inverted pendulum system by the Euler-Lagrange method and then design a FLC (Fuzzy Logic Controller) fur the plant. FLC`s are one of useful control schemes fur plants having difficulties in deriving mathematical models or having performance limitations with conventional linear control schemes. Many FLC`s imitate the concept of conventional PD (Proportional-Derivative) or PI (Proportional-Integral) controller. That is, the error e and the change-of-error are used as antecedent variables and the control input u the change of control input Au is used as its consequent variable for FLC`s. In this paper we design a simple-structured FLC for the rotary inverted pendulum system. We also perform some computer simulations to examine the tracking performance of the closed-loop system.