• Structural Engineering and Mechanics
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• 제64권4호
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• pp.495-504
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• 2017

This paper proposes a new direct numerical integration algorithm for solving equation of motion in structural dynamics problems with nonlinear stiffness. The new implicit method's degree of accuracy is higher than that of existing methods due to the higher order of the acceleration. Two parameters are defined, leading to a new family of unconditionally stable methods, which helps to take greater time steps in integration and eliminate concerns about the duration of solving. The method developed can be utilized for a number of solid plane finite elements, examples of which are given to compare the proposed method with existing ones. The results indicate the superiority of the proposed method.

• 한국지반공학회논문집
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• 제22권9호
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• pp.45-59
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• 2006

탄소성 구성방정식은 주로 미분방적식(rate equation)으로 이루어져 있기 때문에 유한요소법 등을 이용한 지반구조물 해석시 미분방정식들에 대한 수치적분을 수행할 수 있는 방법이 필요하다. 구조물의 거동을 해석할시 미분방정식들을 위한 적분방법은 해석결과의 정확성과 유한요소법 모델링의 안전성에 큰 영향을 미치고 있다. 본 논문에서는 최근에 개발되어 사용되고 있는 흙에 관한 구성모델인 "Two-surface soil plasticity model (Manzari and Dafalias 1997)"을 Implicit return-mapping 수치적분방법을 이용하여 실행하는 과정을 제시한다. 본 연구에서 사용된 수치적분방법은 Closest-Point-Projection Method(CPPM) 방법으로 탄성 예측자-소성 교정자(elastic predictor-plastic corrector) 개념을 Implicit Backward Euler방법으로 체계화 시킨 알고리듬이다. 본 연구에서 수행한 "Two-surface soil plasticity model"은 조립토의 비선형거동을 해석하며, Bounding surface 개념 및 비선형 등방경화와 이동경화법칙을 사용하는 모델이다. 본 연구는 CPPM 방법이 정확하고 안정되며 유용한 수치적분을 수행할 수 있는 알고리듬이라는 것을 제시한다. 또한, CPPM 알고리듬은 구성방정식의 해를 반복적으로 해석하는 동안 "Consistent tangent operator $d{\sigma}/d{\varepsilon}$"를 제공하므로, 비선형 유한요소 해석이 2차(quadratic convergence rate)의 수렴 조건을 만족하는데 기여한다는 것을 보여준다.

• 수산해양기술연구
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• 제32권2호
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• pp.164-176
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• 1996

The main intention of this paper is to develop and compare the algorithm based on finite element procedures for nonlinear transient dynamic analysis which has combined effects of material and geometric nonlinearities. Incremental equilibrium equations based on the principle of virtual work are derived by the finite element approach. For the elasto - plastic large deformation analysis of shells and the determination of the displacement-time configuration under time-varying loads, the explicit, implicit and combined explicit-implicit time integration algorithm is adopted. In the time structure is selected and the results are compared with each others. Isoparametric 8-noded quadrilateral curved elements are used for shell structure in the analysis and for geometrically nonlinear elastic behaviour, a total Lagrangian coordinate system was adopted. On the other hands, material nonlinearity is based on elasto-plastic models with Von-Mises yield criteria. Thus, the combined explicit-implicit time integration algorithm is benefit in general case of shell structure, which is the result of this paper.

• 한국지반공학회지:지반
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• 제12권6호
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• pp.87-100
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• 1996

본 연구에서는 동반논문(오세붕 & 이승래, 1996)에서 정식화한 비등방경화 구성모델에 대한 내재적인 응력적분 알고리즘의 정확성과 효율성을 검증하였다. 비배수 삼축압축시험경로에 대한 오차평가를 통하여 정확도해석을 수행하였고 수치적인 굴착해석예제를 수행함으로써 정확도 및 수렴도를 분석하였다. 그 결과 제안된 알고리즘이 비등방경화 구성관계에 대하여 음력을 정화하게 적분하고 Newton 법을 이용한 비선형 해석시에 점근적인 2차 수렴도를 확보함을 알 수 있었다. 그리고 이러한 검증을 토대로 지반의 초기조건 및 시공단계를 고려한 유한요소법을 이용하여 실제 굴착문제를 해석하였다. 비등방경화 구성관계를 이용함으로써, 추정된 벽체의 변위는 Cainflay모델에 비하여 실제와 더 유사한 해석결과를 얻을 수 있었다.

• 소음진동
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• 제5권2호
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• pp.207-213
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• 1995

본 논문에서 구조동력학 문제를 풀기 위한 명시적(explicit) 예측 수정자 시간적분법을 개발하였으며, 이 알고리즘은 최근 개발된 암시적(implicit) 일반화된 $\alpha$ 방법으로부터 유도하였다. 암시적 방법과 같이 명시적 일반화된 .alpha. 방법도 하나의 변수를 갖는 알고리즘의 집합이며, 이 변수는 고주파 영역에서 수치 감쇠의 양을 정의한다. 제안된 알고리즘은 수치감쇠가 없는 시간적분법으로 파의 젼달 문제를 풀때 나타나는 가상의 진동을 감소시키는 수치감쇠를 가지고 있기 때문 에 선형 혹은 비선형의 구조동력학 문제에 효과적으로 이용될 수 있다.

• Earthquakes and Structures
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• 제7권2호
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• pp.159-178
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• 2014

Although the family methods with unconditional stability and numerical dissipation have been developed for structural dynamics they all are implicit methods and thus an iterative procedure is generally involved for each time step. In this work, a new family method is proposed. It involves no nonlinear iterations in addition to unconditional stability and favorable numerical dissipation, which can be continuously controlled. In particular, it can have a zero damping ratio. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it can save many computationally efforts when compared to the currently available dissipative implicit integration methods.

• 소성∙가공
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• 제8권1호
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• pp.22-28
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• 1999

The explicit and implicit time integration methods are applied effectively to analyze sheet metal stamping processes, which include the forming stage and the springback stage consecutively. The explicit time integration method has better merits in the forming stage including highly complicated three-dimensional contact conditions. By contrary, the implicit time integration method is better for analyzing springback since the complicated contact conditions are removed and the computing time to get the final static state is short. In this work, brief descriptions of the formulation and the factor study for springack simulations are presented. Further, the simulated results for the S-rail and the roof panel stamping processes are shown and discussed.

• Structural Engineering and Mechanics
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• 제38권3호
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• pp.283-300
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• 2011

A new conception of fundamental tasks in dynamics of the bridge-track-train systems (BTT), with the aim to evaluate moving load's models adequacy, has been developed. The 2D physical models of BTT systems, corresponding to the fundamental tasks, have been worked out taking into account one-way constraints between the moving unsprung masses and the track. A method for deriving the implicit equations of motion, governing vibrations of BTT systems' models, as well as algorithms for numerical integration of these equations, leading to the solutions of high accuracy and relatively short times of simulations, have been also developed. The derived equations and formulated algorithms constitute the basis for numerical simulation of vibrations of the considered systems.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1998년도 제2회 박판성형심포지엄 논문집 박판성형기술의 현재와 미래
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• pp.1-8
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• 1998

The explicit and implicit time integration methods are applied effectively to analyze sheet metal stamping processes, which include the forming stage and the springback stage consecutively. The explicit time integration method has better merits in the forming stage including highly complicated three-dimensional contact conditions. By contrary, the implicit time integration method is better for analyzing springback since the complicated contact conditions are removd and the computing time to get the final static state is short. In this work, brief descriptions of the formulation and the factor study for springback simulations are presented. Further, the simulated results for the S-rail and the roof pannel stamping processes are shown and discussed.

• 한국전산유체공학회지
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• 제21권1호
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.