精細積分法彈塑性歷時分析之研究

郭竣瑋

doi:10.6840/CYCU.2014.00224、10.6840/cycu201400489

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精細積分法彈塑性歷時分析之研究

A Study of Elasto-Plastic Time History Analysis using Precise Integration Method

郭竣瑋 , Masters　　Advisor：莊清鏘;鄭金國　　

繁體中文 DOI： 10.6840/CYCU.2014.00224、10.6840/cycu201400489

近似插值法；精細時間積分法；彈塑性分析；迭代法； Precise Integration Method ； iterative method ； approximate interpolation method ； elasto-plastic analysis

Abstract │ Reference (60) │ Altmetrics

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Solving structural dynamic response was used dynamic equilibrium equations of motion with time integration, and dynamic equilibrium will satisfy discrete time. The selection of time step depends on the features of the time integration, when there is dramatic loading variation or high natural frequency. For getting better numerical accuracy, we usually choose the small time step. This study used the Precise Integration Method which has better accuracy and stability. This method use reduced-order, the approximations of first order system ordinary differential equation,   algorithm method and Extended Precise Integration Method to simulate structural dynamic response. In the other hand, the study also formulates the governing equations of motion to alleviate this problem by momentum equilibrium. The proposed method can capture the dramatic loading variation effectively and reduce the sensitivity of the selection of time step.
    In elasto-plastic system, this study adopts bilinear restoring force model to simulate structural dynamic response analysis. The model has mutation of the stiffness inflection points which exists in two adjacent segments. If we don't deal which this problem, it may reduce the numerical accuracy. Traditional elasto-plastic analysis use iterative method, but this study used the approximate interpolation method. For inflection points analysis, the concept uses Taylor's series and dividing time step. Finally, we use some examples to discuss the feasibility and accuracy of the elasto-plastic EPIM, and compare with Newmark method.

Reference ( 60 ) 〈TOP〉

[1] W.X. Zhong, F.W. Williams, “A precise time step integration method”, Proc. Inst. Mech. Eng., 208(1994) pp.427-430
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[3] Zhong Wanxie, “Precise computation for transient analysis”, Computational Structural Mechanics and Applications, Vol.12, No.1(1995) pp.1-6
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[5] Cleve Moler, Charles Van Loan, “Nineteen dubious ways to compute the exponential of a matrix”, Society for Industrial and Applied Mathematics, Vol.20, No.4(1978) pp.801-836
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[6] Cleve Moler, Charles Van Loan, “Nineteen dubious ways to compute the exponential of a matrix Twenty-Five Years Later”, Society for Industrial and Applied Mathematics, Vol.45, No.1(2003) pp.1-46
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[8] Jiahao Lin, Weiping Shen, F.W. Williams, “A high precision direct integration scheme for structures subjected to transient dynamic loadind”, Computers & Structures, Vol. 56, No. 1(1995) pp.113-120
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