• Structural Engineering and Mechanics
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• v.60 no.5
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• pp.891-902
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• 2016

The beam structure with breathing cracks subjected to harmonic excitations was modeled by FEM based on Euler-Bernoulli theory, and a piecewise dynamical system was deduced. The precise integration method (PIM) was employed to propose an algorithm for analyzing the dynamic responses of the deduced system. This system was first divided into linear sub-systems, between which there are switching points resulted from the breathing cracks. The inhomogeneous terms due to the external excitations were tackled by introducing auxiliary variables to express the harmonic functions, hence the sub-systems are homogeneous. The PIM was then applied to solve the homogeneous sub-systems one by one. During the procedures, a predictor-corrector algorithm was presented to determine the switching points accurately. The presented method can provide solutions with an accuracy to a magnitude of $10^{-12}$ compared with exact solutions obtained by the theories of ordinary differential equations. The PIM results are much more accurate than Newmark ones with the same time step. Moreover, it is found that the PIM can maintain a high level of accuracy even when the time step increases within a relatively wide range.

• International Journal of Naval Architecture and Ocean Engineering
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• v.2 no.3
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• pp.127-131
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• 2010

A two-layer fluid with free surface is simulated in the time domain by a two-dimensional potential-based Numerical Wave Tank (NWT). The developed NWT is based on the boundary element method and a leap-frog time integration scheme. A whole domain scheme including interaction terms between two layers is applied to solve the boundary integral equation. The time histories of surface elevations on both fluid layers in the respective wave modes are verified with analytic results. The amplitude ratios of upper to lower elevation for various density ratios and water depths are also compared.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.2
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• pp.27-34
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• 1985

In this paper, the second order time mean forces acting on the circular cylinder floating on the free surface of a finite water depth are calculated. Under the assumption that fluid is idea and the wave the linear gravity wave, the velocity potential is calculated by the source distribution method, and the second order time mean lateral and vertical drifting forces are calculated by the direct integration of fluid pressures over the immersed body surface. The comparison of the lateral drifting forces with Rhee's results by momentum theorem shows good agreements. And it is shown that the second order time sinkage forces of a floating circular cylinder cross zero for all water depths.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.4
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• pp.437-442
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• 2012

To analyze a multibody system, this paper proposes an implicit numerical integration method for joint coordinates subsystem synthesis method. To verify the proposed method, a multibody model for an unmanned robot vehicle, which consists of six identical independent suspension systems, is developed. The symbolic method is applied to compute the system Jacobian matrix for the implicit integration method. The proposed method is also verified by performing rough terrain run-over simulation in comparison with the conventional implicit integration method. In addition, to evaluate the efficiency of the proposed method, the CPU time obtained by using this method is compared with that obtained by using the conventional implicit method.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.121-125
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• 2006

A new GPS receiver correlator for the deeply-coupled GPS/INS integration system is proposed in order to the computation time problem of the Kalman filter. The proposed correlator consists of two early, prompt and late arm pairs. One pair is for detecting data bit transition boundary and another is for the correlator value calculation between input and replica signal. By detecting the data bit transition boundary, the measurement calculation time can be made longer than data bit period. As a result of this, the computational time problem of the integrated Kalman filter can be resolved. The validity of the proposed method is given through computer simulations.

• Journal of Positioning, Navigation, and Timing
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• v.8 no.4
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• pp.201-208
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• 2019

Numerical integration is necessary for satellite orbit determination and its prediction. The numerical integration algorithm can be divided into single-step and multi-step method. There are lots of single-step and multi-step methods. However, the Runge-Kutta method in single-step and the Adams method in multi-step are generally used in global navigation satellite system (GNSS) satellite orbit. In this study, 4th and 8th order Runge-Kutta methods and various order of Adams-Bashforth-Moulton methods were used for GLObal NAvigation Satellite System (GLONASS) orbit integration using its broadcast ephemeris and these methods were compared with international GNSS service (IGS) final products for 7days. As a result, the RMSE of Runge-Kutta methods were 3.13m and 4th and 8th order Runge-Kutta results were very close and also 3rd to 9th order Adams-Bashforth-Moulton results. About result of computation time, this study showed that 4th order Runge-Kutta was the fastest. However, in case of 8th order Runge-Kutta, it was faster than 14th order Adams-Bashforth-Moulton but slower than 13th order Adams-Bashforth-Moulton in this study.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.3
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• pp.31-36
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• 2004

This paper will describe design process and its results that are minimized unaddressed feature of product development processes. This process provides integrated system design process by context analysis of EIA 632 standard process, interface definition from activity decomposition, integration of related activities, and definition of concurrency & sequential activities flow. This process and method application will contribute to minimize time loss that is emerged from activities iteration by not definitely definition of activities interface.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Smart Structures and Systems
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• v.14 no.6
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• pp.1131-1150
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• 2014

One of the issues in extending the range of applicable problems of real-time hybrid simulation is the computation speed of the simulator when large-scale computational models with a large number of DOF are used. In this study, functionality of real-time dynamic simulation of MDOF systems is achieved by creating a logic circuit that performs the step-by-step numerical time integration of the equations of motion of the system. The designed logic circuit can be implemented to an FPGA-based system; FPGA (Field Programmable Gate Array) allows large-scale parallel computing by implementing a number of arithmetic operators within the device. The operator splitting method is used as the numerical time integration scheme. The logic circuit consists of blocks of circuits that perform numerical arithmetic operations that appear in the integration scheme, including addition and multiplication of floating-point numbers, registers to store the intermediate data, and data busses connecting these elements to transmit various information including the floating-point numerical data among them. Case study on several types of linear and nonlinear MDOF system models shows that use of resource sharing in logic synthesis is crucial for effective application of FPGA to real-time dynamic simulation of structural response with time step interval of 1 ms.

• Wind and Structures
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• v.34 no.1
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• pp.59-72
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• 2022

In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).