袁全, 袁驷, 李易, 闫维明, 邢沁妍. 线性元时程积分按最大模自适应步长公式的证明[J]. 工程力学, 2018, 35(8): 9-13. DOI: 10.6052/j.issn.1000-4750.2018.03.0106
引用本文: 袁全, 袁驷, 李易, 闫维明, 邢沁妍. 线性元时程积分按最大模自适应步长公式的证明[J]. 工程力学, 2018, 35(8): 9-13. DOI: 10.6052/j.issn.1000-4750.2018.03.0106
YUAN Quan, YUAN Si, LI Yi, YAN Wei-ming, XING Qin-yan. PROOF OF ADAPTIVE TIME-STEP SIZE FORMULA BASED ON MAXIMUM NORM IN TIME INTEGRATION OF LINEAR ELEMENTS[J]. Engineering Mechanics, 2018, 35(8): 9-13. DOI: 10.6052/j.issn.1000-4750.2018.03.0106
Citation: YUAN Quan, YUAN Si, LI Yi, YAN Wei-ming, XING Qin-yan. PROOF OF ADAPTIVE TIME-STEP SIZE FORMULA BASED ON MAXIMUM NORM IN TIME INTEGRATION OF LINEAR ELEMENTS[J]. Engineering Mechanics, 2018, 35(8): 9-13. DOI: 10.6052/j.issn.1000-4750.2018.03.0106

线性元时程积分按最大模自适应步长公式的证明

PROOF OF ADAPTIVE TIME-STEP SIZE FORMULA BASED ON MAXIMUM NORM IN TIME INTEGRATION OF LINEAR ELEMENTS

  • 摘要: 该文对运动方程时程积分解法曾提出一种线性有限元自适应步长求解的算法,给出了按最大模自适应步长的计算公式,其中含有步长h的5/2阶的分数阶次。该文对该公式给出数学证明,并通过单自由度和多自由度的数值算例验证了其5/2分数阶次是最优的。

     

    Abstract: An algorithm for time integration of motion equations using linear finite elements with adaptive time-step size had been proposed by the authors, in which a formula for the calculation of adaptive time-step size h based on maximum norm, characterized by containing a term of 5/2 order of h, was also presented. This paper gives a mathematical proof for the proposed formula. In addition, the numerical examples of both single and multiple degreed systems are obtained to verify that 5/2 order is optimal.

     

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