• Journal of computational fluids engineering
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• v.2 no.1
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• pp.13-20
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• 1997

A fundamental study for the numerical scheme to simulate unsteady nonlinear waves by solving Euler equations is presented. First a conservation form and a non-conservation form of the Euler equations with a free surface fitted coordinate system are compared. Next, a time splitting fractional step method and an alternating direction implicit(ADI) method for the time integration are compared. For the comparative study, flow calculations around a bottom bump in a channel and a NACA 0012 hydrofoil in a flume are performed. The results show that the ADI method with a third order upwind differencing scheme is very efficient in reducing the computing time with keeping the accuracy, And, there is no distinct difference between two expression forms except that the non-conservative form shows faster wave propagating velocity than the conservation form. Some results are compared with experiments and show good agreement.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.135-138
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• 1990

For transient stability analysis of a power system, the new method using transition matrix is introduced in this paper. At the present the, Runge-Kutta, Modified-Euler and Trapezoidal methods have been very popular in most stability programs, Modified-Euler and Trapezoidal methods are inferior in accuracy and Runge-Kutta method has problems in computation time. The proposed algorithm requires transition matrix and its integrated values with derivatives of nonlinear parts in nonlinear differential equations for stability analysis. The method presented in this paper is between Modified-Euler and Runge-Kutta methods from the view point of computation time and is superior to the other methods in accuracy.

• Structural Engineering and Mechanics
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• v.35 no.5
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• pp.645-658
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• 2010

In this study, the Differential Transform Method (DTM) is employed in order to solve the governing differential equation of a moving Bernoulli-Euler beam with axial force effect and investigate its free flexural vibration characteristics. The free vibration analysis of a moving Bernoulli-Euler beam using DTM has not been investigated by any of the studies in open literature so far. At first, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Bernoulli-Euler beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equation of the motion. The calculated natural frequencies of the moving beams with various combinations of boundary conditions using DTM are tabulated in several tables and are compared with the results of the analytical solution where a very good agreement is observed.

• 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.

• Structural Engineering and Mechanics
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• v.42 no.1
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• pp.95-119
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• 2012

In this paper, forced vibration differential equations of motion of Euler-Bernoulli beams with different boundary conditions and dynamic loads are solved using differential transform method (DTM), analytical solutions. Then, the modal deflections of these beams are obtained. The calculated modal deflections using DTM are represented in tables and depicted in graphs and compared with the results of the analytical solutions where a very good agreement is observed.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2012.06a
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• pp.212-213
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• 2012

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.19-27
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• 1999

An orientation-shift model for unit random vectors in $R^3$ is defined. The Euler angles are introduced to parametrize orientation-shifts and their moment estimators are found. Through the analytic perturbation method, the asymptotic distributions of the estimators are obtained.

• The KIPS Transactions:PartB
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• v.13B no.1 s.104
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• pp.15-20
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• 2006

This paper describes research on intelligent game character through performance enhancements of physics engine in computer games. The algorithm that recognizes the physics situation uses momentum back-propagation neural networks. Also, we present an experiment and its results, integration methods that display optimum performance based on the physics situation. In this experiment on integration methods, the Euler method was shown to produce the best results in terms of fps in a simulation environment with collision detection. Simulation with collision detection was shown similar fps for all three methods and the Runge-kutta method was shown the greatest accuracy. In the experiment on physics situation recognition, a physics situation recognition algorithm where the number of input layers (number of physical parameters) and output layers (destruction value for the master car) is fixed has shown the best performance when the number of hidden layers is 3 and the learning count number is 30,000. Since we tested with rigid bodies only, we are currently studying efficient physics situation recognition for soft body objects.

• 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.

• Advances in nano research
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• v.9 no.2
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• pp.91-104
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• 2020

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.