• Structural Engineering and Mechanics
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• 제85권2호
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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.

• Coupled systems mechanics
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• 제12권5호
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• pp.419-428
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• 2023

We have developed a model for estimating the parameters of viscous materials from indirect tensile tests for asphalt. This is a simple Burger nonlinear rheological two-cell model or standard model. At the same time, we begin to develop a more versatile and complex multi-cell model. The simple model is validated using experimental load-displacement results from laboratory tests: The recorded displacements are used as input values and the measured force data are simulated with the model. The optimal model parameters are estimated using the Levenberg-Marquardt method and a very good agreement between the experimental results and the model calculations is shown. However, not all parts of the model are active in the loading phase of the experiment, so we extended the validation of the model to the simulation of the relaxation behaviour. In this stage, the other model parameters are activated and the simulation results are consistent with the literature. At this stage, we have estimated the parameters only for the two-cell uniaxial model, but further work will include results for the multi-cell model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• 대한기계학회논문집A
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• 제37권9호
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• pp.1069-1075
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• 2013

무인 국방 로봇의 실시간 해석을 위해서는 효과적인 해석기법이 필수적인 요소이다. 이러한 효과적인 해석을 위하여 부분시스템 합성방법이 개발되었다. 부분시스템 합성방법은 기준 물체의 운동방정식과 각 부분시스템들의 운동방정식을 독립적으로 계산함으로써 계산량의 이득을 볼 수 있다. 운동방정식은 미분방정식과 대수방정식이 혼합된 미분대수방정식으로 표현된다. 이러한 미분대수방정식의 정확하고 효과적인 해석을 위해서 직접 적분방법, 구속조건식 안정화기법, 일반 좌표 분할기법 등이 개발되었다. 본 논문에서는 무인 국방 로봇의 효과적인 해석을 위하여 부분시스템 합성방법을 적용하고 위에서 기술한 세 가지의 미분대수방정식 해석기법을 비교하는 연구를 수행하였다.

• Smart Structures and Systems
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• 제18권6호
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• pp.1125-1143
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• 2016

Forced vibration analysis of a simple supported viscoelastic nanobeam is studied based on modified couple stress theory (MCST). The nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. The elastic medium is considered as Winkler-Pasternak elastic foundation.The damping effect is considered by using the Kelvin-Voigt viscoelastic model. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Timoshenko beam theory by using finite element method. The effects of the transverse shear deformation and rotary inertia are included according to the Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Numerical results are presented to investigate the influences the material length scale parameter, the parameter of the elastic medium and aspect ratio on the dynamic response of the nanobeam. Also, the difference between the classical beam theory (CBT) and modified couple stress theory is investigated for forced vibration responses of nanobeams.

• Structural Engineering and Mechanics
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• 제45권1호
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 하계학술대회 논문집 B
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• pp.635-637
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• 2000

To analyze the transient state of an induction motor, there have been studies for using the magnetic equivalent circuit method (MECM) instead of the time differential finite-element method, MECM which analyzes magnetic equivalent circuits after converting each part of an electric machine into the magnetic circuit elements. has the merits of short calculation-time and comparatively accurate results. To analyze an electric machine with MECM, we have to replace stator and rotor with the magnetic elements and express the air gap, where electromechanical energy conversion takes place, with the permeance. So in this paper, to analyze an Induction Motor with MECM, we express the magnetic equivalent circuit as algebraic equations and then as the matrix for solving easily them.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• 대한기계학회논문집
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• 제13권4호
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• pp.583-594
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• 1989

본 연구는 기계적 간극의 존재로 양면 접촉에 의한 강성 및 감쇠가 대칭적 으로 두번 생기는 강제 대칭 편적 선형(forced symmetric piecewise-linear vibarti- on)에 대하여 비선형진동의 분수조화 정상해 과정을 설명한 Stoker 가설로부터 분수조화진동을 포함한 복수의 정상해를 구하고 피로, 마멸 연구를 위한 접촉시간 및 접촉력을 계산하였다. 또한 강제 대칭 편적 선형진동자의 운동방정식을 무차원화 하고 각 무차원 시스템 변수에 따른 주파수응답특성을 살펴보았다.