• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.385-393
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• 2005

This paper established the dynamic model of a flexible Timoshenko beam capable of geometrical nonlinearities subject to large overall motions by using the finite element method. Equations of motion are derived by using Hamilton principle and are formulated in terms of finite elements in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. The Newmark direct integration method and the Newton-Raphson iteration are employed here for the numerical study which is to demonstrate the efficiency of the proposed formulation.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.2
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• pp.247-258
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• 2004

The composite shell element is developed for the solution of undamped forced vibration problem of composite curved panels. The finite element used in the current study is an 4-node enhanced assumed shell element with six degrees of freedom per node. The composite shell element is free of both shear and membrane locking phenomenon by using the enhanced assumed strain(EAS) method. A modification to the first-order shear deformation shell theory is proposed, which results in parabolic thorough-thickness distribution of the transverse shear strains and stresses. It eliminates the need for shear correction factors in the first order theory. Newmark's direct integration technique is used for carrying out the integration of the equation motion, to obtain the repones history. Parametric studies of curved composite panels are carried out for forced vibration analysis by geometrical shapes and by laminated composite; such as fiber orientation, stacking sequence.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.719-722
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• 2011

본 연구에서는 이동최소제곱 차분법을 2차원 동적고체문제를 해석하기 위하여 확장시켰으며 Newmark ${\beta}$ 방법을 통해 explicit와 implicit 시간적분법을 모두 적용하여 그 차이를 비교하였다. 이동최소제곱 차분법은 Taylor 다항식을 이용하여 미분계산을 근사화 함으로써 내부 및 경계에서도 강형식을 그대로 이용할 수 있다. 그래서 계산이 빠르고 수치적분이 필요하지 않아 무요소법의 장점을 잘 살릴 수 있고 해석차수를 손쉽게 조정할 수 있어 cubic 등의 고차 근사계산이 간편하다. 두 가지 수치예제를 통하여 동적해석에 대한 이동최소제곱 차분법의 적용성과 안정성을 검증하였다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.642-651
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• 1988

The present paper develops finite element procedures to calculate displacements, strains and stresses in initially stressed elastic solids subjected to static or time-dependent loading conditions. As a point of departure, we employ Hamilton's principle to obtain nonlinear equations of motion characterizing the displacement in a solid. The equations of motion reduce to linear equations of motion if incremental stresses are assumed to be infinitesimal. In the case of linear problem, finite element solutions are obtained by Newmark's direct integration method and by modal analysis. An analytic solution is referred to compare with the linear finite element solution. In the case of nonlinear problem, finite element solutions are obtained by Newton-Raphson iteration method and compared with the linear solution. Finally, the effect of the order of Gauss-Legendre numerical integration on the nonlinear finite element solution, has been investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.139-148
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• 2012

The MLS(Moving Least Squares) Difference Method is a numerical scheme that combines the MLS method of Meshfree method and Taylor expansion involving not numerical quadrature or mesh structure but only nodes. This paper presents an dynamic algorithm of MLS difference method for solving transient solid mechanics problems. The developed algorithm performs time integration by using Newmark method and directly discretizes strong forms. It is very convenient to increase the order of Taylor polynomial because derivative approximations are obtained by the Taylor series expanded by MLS method without real differentiation. The accuracy and efficiency of the dynamic algorithm are verified through numerical experiments. Numerical results converge very well to the closed-form solutions and show less oscillation and periodic error than FEM(Finite Element Method).

• Journal of Korean Society of Steel Construction
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• v.9 no.3 s.32
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• pp.333-340
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• 1997

This paper will expand the third-order shear deformation theory by the double-Fourier series and reduce to the solution of a system of ordinary differential equations in time, which are integrated numerically using Newmark's direct integration method and clarify the undamped dynamic responses for the cross-ply and antisymmetric angle-ply laminated composite plates and shells with simply supported boundary condition. Numerical results for deflections are presented showing the effect of side-to-thickness ratio, aspect ratio, material anisotropy, and lamination scheme.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.5
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• pp.525-533
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• 2010

Direct time integration method such as Newmark method is numerically performed under the assumption that continuous load function such as constant amplitude load can be treated as a discontinuous load fuction. It is due that the load can be treated as a constant value at the given time period regardless of variation of load at the time increment interval. It means the numerical results should be accompanied by the error due to approximation of load fuction. In contrast, the load function is calculated by convolution integral for the given time interval at finite element equation based on Gurtin's variation equation. Therefore. precise numerical results can be obtained by Gurtin's method because of convolution integral for the continuous load fuction curve even at the variation of load function in the given time interval. In this study, we prove that Gurtin's method can be more suitable than Newmark method in the problem of constant amplitude loading, using the numerical results for the free end of the one-dimensional rod. This study also shows that Gurtin's method is more effective in constant amplitude loading than in constant loading. The accuracy and the validity are verified by comparison between the results of in-house FORTRAN code and ADINA, a commercial software supporting Newmark method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.17-26
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• 2014

This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.9
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• pp.674-684
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• 2002

In order to decrease remarkably the computation time and storage used in the direct integration method without the loss of accuracy, authors suggest a new transient analysis algorithm. This algorithm is derived from the combination of three techniques, that is, the transfer technique of the transfer stiffness coefficient method, the modeling technique of the finite element method, and the numerical integration technique of the Newmark method. In this paper, the transient analysis algorithm of a frame structure is formulated by the proposed method. The accuracy and computation efficiency of the proposed method are demonstrated through the comparing with the computation results by the direct integration method for three computation models under various excitations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1503-1509
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• 1994

An analysis method is suggested and experimentally studied in order to solve a vibration problem of a flexible structure while it is moving. In this method, substructure synthesis method, modal analysis method and Newmark's integral method were used. Total deformation of a structure was composed of quasistatic component and dynamic component. Rigid body modes were considered in calculation of dynamic component. Combining those two component, deformation behavior and a real structural model of a transfer feeder showed good agreements with computational results.