• Structural Engineering and Mechanics
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• v.73 no.4
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• pp.455-462
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• 2020

The hybrid method using the extended finite element method (XFEM) and the forward Euler approach is widely employed to predict the fatigue life of plate structures. Due to the accuracy of the forward Euler approach is determined by a small step size, the performance of fatigue life prediction of the hybrid method is not agreeable. Instead the forward Euler approach, a prediction method using midpoint method and support vector regression (SVR) is presented to evaluate the stress intensity factors (SIFs) and the fatigue life. Firstly, the XFEM is employed to calculate the SIFs with given crack sizes. Then use the history of SIFs as a function of either number of fatigue life cycles or crack sizes within the current cycle to build a prediction model. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Three numerical cases composed by a homogeneous plate with edge crack, a composite plate with edge crack and center crack are introduced to verify the performance of the proposed method. The results show that the proposed method enables large step sizes without sacrificing accuracy. The method is expected to predict the fatigue life of complex structures.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1179-1189
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• 2016

We provide a combination of the forward Euler method and the trapezoidal quadrature rule leads to a two-step conservative numerical method which possesses TV-stable property together with consistency.

• Structural Engineering and Mechanics
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• v.30 no.3
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• pp.369-382
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• 2008

An oscillator of two lumped masses linked through a vertical spring moves forward in the horizontal direction, initially at a certain height, over a horizontal Euler beam and descends on it due to its own weight. Vibration of the beam and the oscillator is excited at the onset of the ensuing impact. The impact produced by the descending oscillator is assumed to be either perfectly elastic or perfectly plastic. If the impact is perfectly elastic, the oscillator bounces off and hits the beam a number of times as it moves forward in the longitudinal direction of the beam, exchanging its dynamics with that of the beam. If the impact is perfectly plastic, the oscillator (initially) sticks to the beam after its first impact and then may separate and reattach to the beam as it moves along the beam. Further events of separation and reattachment may follow. This interesting and seemingly simple dynamic problem actually displays rather complicated dynamic behaviour and has never been studied in the past. It is found through simulated numerical examples that multiple events of separation and impact can take place for both perfectly elastic impact and perfectly plastic impact (though more of these in the case of perfectly elastic impact) and the dynamic response of the oscillator and the beam looks noisy when there is an event of impact because impact excites higher-frequency components. For the perfectly plastic impact, the oscillator can experience multiple events of consecutive separation from the beam and subsequent reattachment to it.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.77-94
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• 1991

A finite difference method based on MAC method is used to simulate free-surface waves around a ship. Euler equations and continuity equation are differentiated using the forward time and central space, and solved by time marching scheme. By the employment of variable mesh system in horizontal and vertical direction, the numerical accuracy of wave simulation results is grossly improved. To verify the improvement of numerical accuracy, some numerical simulations are accomplished for Wigley, Series 60($C_{b}$=0.6) and a bulk carrier model. The computational results are compared to the various experimental data and show good agreements.

• Smart Structures and Systems
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• v.12 no.5
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.9
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• pp.836-843
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• 2000

A sequence planning method is proposed to reduce the assembly time of gantey-type chip mounters with single head. The overall path of the chip mounter is divided into forward and backward path, and formulate the optimization problem is formulated as an transpoetation problem and an Euler's tour problem. The transportation alforithm is applied to find optimal backward path, and Euler's tour algorithm used to generate an assembly sequence. Simulation results are presented to verify the usefulness of the proposed method.

• Ocean Science Journal
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• v.40 no.4
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• pp.201-208
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• 2005

An accurate particle tracking method for a finite difference method model is developed using a constant acceleration method. Being assumed constant temporal and spatial gradients, the new method permits temporal-spatial variability of particle velocity. Test results in a solid rotating flow show that the new method has second-order accuracy. The performance of the new method is compared with that of other methods; the first-order Euler forward method, and the second-order Euler predictor-corrector method. The new method is the most efficient method among the three. It is more accurate and efficient than the other two.

• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.101-109
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• 1998

Using airborne magnetic data, magnetic characteristics were studied at the Samryangjin caldera area developed in the volcanics of the Yuchon sub-basin, the south eastern part of the Gyeongsang basin. Residual magnetics, reduction to the pole, horizontal derivative, and vertical derivative maps are prepared. Using these maps, the magnetic lithofaces are zoned and the geological structures such as caldera and faults were qualitatively interpreted. In addition, the two quantitative interpretations were performed. Firstly, the forward modelling were done to the 14.5 line km crossing the caldera area to the northeast-southwest direction. Applying the 3-D Euler deconvolution method to the whole study area, the depth extent and the characteristics of the magnetic anomalous bodies were studied. According to the results, the magnetic lithofaces of the area are zoned by 4 units. In general, these are well matched with the geological distributions. But the biotite granites intruded in the northern boundary of the Samryangjin caldera show the high magnetic intensity, while the biotite granites of the other areas show the low magnetic intensity and the different magnetic lithofaces. Thus, we interpreted that the biotite granites are closely related with the volcanic activity of the Samryngjin caldera, and are intruded in the fracture zones developed along the caldera rim. The Samryangjin caldera and fault structures of the area can be easily recognized by the distinct magnetic structures from the various magnetic anomaly maps. Also the topographic characteristics well reflect these structures. The results of the forward modelling show that the magnetic basement depth of the Gyeongsang sedimentary basin is on the average about 6 km and in maximum 10 km. And the depth becomes shallower toward the caldera boundary due to the shallow intrusion of the volcanics. The results of the 3-D Euler method also show the caldera and fault structures. And the relatively shallow magnetic anomalous bodies which are related with the volcanics are generally developed to the east-west and northeast directions, while the deep magnetic anomalous bodies to the northwest direction.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.261-267
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• 2005

The unsteady flow analysis of staging system is conducted. This study focuses on comparing the results of two different governing equations between Euler equations and Navier-Stokes equations. The Chimera grid scheme is applied to moving simulations for unsteady flow analysis with dynamic simulation. As a result, it is certified that inviscid simulation have capabilities enough to analyze the present staging problem.