• Title/Summary/Keyword: Differential and Algebraic Equations

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High-speed simulation for fossil power plants uisng a parallel DSP system (병렬 DSP 시스템을 이용한 화력발전소 고속 시뮬레이션)

  • 박희준;김병국
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.35C no.4
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    • pp.38-49
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    • 1998
  • A fossil power plant can be modeled by a lot of algebraic equations and differential equations. When we simulate a large, complicated fossil power plant by a computer such as workstation or PC, it takes much time until overall equations are completely calculated. Therefore, new processing systems which have high computing speed is ultimately needed for real-time or high-speed(faster than real-time) simulators. This paper presents an enhanced strategy in which high computing power can be provided by parallel processing of DSP processors with communication links. DSP system is designed for general purpose. Parallel DSP system can be easily expanded by just connecting new DSP modules to the system. General urpose DSP modules and a VME interface module was developed. New model and techniques for the task allocation are also presented which take into account the special characteristics of parallel I/O and computation. As a realistic cost function of task allocation, we suggested 'simulation period' which represents the period of simulation output intervals. Based on the development of parallel DSP system and realistic task allocation techniques, we cound achieve good efficiency of parallel processing and faster simulation speed than real-time.

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A new and simple analytical approach to determining the natural frequencies of framed tube structures

  • Mohammadnejad, Mehrdad;Kazemi, Hasan Haji
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.111-120
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    • 2018
  • This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

The effect of in-plane deformations on the nonlinear dynamic response of laminated plates

  • Kazanci, Zafer;Turkmen, Halit S.
    • Structural Engineering and Mechanics
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    • v.42 no.4
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    • pp.589-608
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    • 2012
  • In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

Numerical simulation of single-phase two-components flow in naturally fractured oil reservoirs

  • Debossam, Joao Gabriel Souza;dos Santos Heringer, Juan Diego;de Souza, Grazione;Souto, Helio Pedro Amaral
    • Coupled systems mechanics
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    • v.8 no.2
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    • pp.129-146
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    • 2019
  • The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

Wave propagation in a microbeam based on the modified couple stress theory

  • Kocaturk, Turgut;Akbas, Seref Doguscan
    • Structural Engineering and Mechanics
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    • v.46 no.3
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    • pp.417-431
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    • 2013
  • This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

Time-discontinuous Galerkin quadrature element methods for structural dynamics

  • Minmao, Liao;Yupeng, Wang
    • Structural Engineering and Mechanics
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    • v.85 no.2
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    • pp.207-216
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    • 2023
  • Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, single-field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak-form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low-frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.

Grid Generation about Full Aircraft Configuration Using Interactive Grid Generator (상호 대화형 격자생성 환경을 이용한 항공기 전기체 격자계 생성)

  • Kim Y. S.;Kwon J. H.
    • 한국전산유체공학회:학술대회논문집
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    • 1999.11a
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    • pp.145-151
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    • 1999
  • An Interactive grid generation program(KGRID) with graphical user interface(GUI) has been improved. KGRID works on the UNLX environment and GUI has been implemented with OSF/Motif and X Toolkit and the graphics language is Open GL for visualization of the 3D objects. It supports more convenient user environment to generate 2D and 3D multi-block structured grid systems. It provides various useful field grid generation methods, which are the algebraic methods, the elliptic partial differential equations method and the predictor-corrector method. It also supports 3D surface grid generation with NURBS(Non-Uniform Rational B-Spline) and various stretching functions to control grid points distribution on curves and surfaces. And some menus are added to perform flexible management, for the objects. We generated surface and field grid system about full aircraft configuration using KGRID. The performance and stability of the KGRID is verified through the generation of the grid system about a complex shape.

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A Study on Stable Grasping Motion Control of Dual-Finger (듀얼-핑거의 안정적 파지 운동 제어에 관한 연구)

  • Um Hyuk;Choi Jong-Hwan;Kim Seung-Soo;Han Hyun-Yong;Yang Soon-Yong;Lee Jin-Gul
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.14 no.4
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    • pp.81-88
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    • 2005
  • This paper attempts to derive the dynamic model of handling tasks in finger robot which grasps stable and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, the roblems of controlling both the forces of pressing object and the rotation angle of the object under the geometric constraints are discussed. The effect of geometric constraints of area-contacts between the link's end-effector and the object is analyzed and the model based on the differential-algebraic equations is presented. In this paper, the control method for dynamic stable grasping and enhancing dexterity in manipulating things is proposed. It is illustrated by computer simulation and the experiment that the control system gives the performance improvement in the dynamic stable grasping and nimble manipulating of the dual fingers robot with soft tips.

Analysis of Dynamic Contact and Stress of a Valve in Internal Combustion Engine (내연기관 밸브의 동적 접촉 및 응력 해석)

  • 이기수;김동우;박상호;조성호;김방원
    • Transactions of the Korean Society of Automotive Engineers
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    • v.10 no.2
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    • pp.159-165
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    • 2002
  • Numerical analysis of dynamic contact and stress developing in the high-speed driven valve of an internal combustion engine is presented. The valve is modeled by finite element techniques, and the dynamic contact between the valve and the valve seat is analyzed by the solution strategies of differential algebraic equations. Also an iterative scheme similar to the augmented Lagrange multiplier method is employed to enforce the contact constraints. It is shown that the contact and separation between the valve and the valve seat can be computed by the finite element techniques without assuming the artificial springs, and the efficiency and accuracy of the solution are demonstrated by the numerical examples.

Strong formulation finite element method for arbitrarily shaped laminated plates - Part II. Numerical analysis

  • Fantuzzi, Nicholas;Tornabene, Francesco
    • Advances in aircraft and spacecraft science
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    • v.1 no.2
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    • pp.145-175
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    • 2014
  • The results of a series of numerical experiments are presented to verify some of the important developments made in the first part of this paper. Firstly, the static solution of an algebraic system obtained through Strong Formulation Finite Element Method (SFEM) is presented. Secondly, the stress and strain recovery procedure is descripted for the present technique. It will be clear that the present approach is suitable for any strong formulation finite element methodology, due to the presented general approach based on the unknown displacements and on the elasticity equations. Thirdly, the numerical solutions for some classical and other numerical results found in literature are exposed. Finally, an arbitrarily shaped composite plate is solved and good agreement is observed for all the presented cases.