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张卫, 徐华, 清水信行. 分数算子描述的黏弹性体力学问题数值方法[J]. 力学学报, 2004, 36(5): 617-622. DOI: 10.6052/0459-1879-2004-5-2003-355
引用本文: 张卫, 徐华, 清水信行. 分数算子描述的黏弹性体力学问题数值方法[J]. 力学学报, 2004, 36(5): 617-622. DOI: 10.6052/0459-1879-2004-5-2003-355
The numerical analysis formulation of the viscoelastic solid modeled by fractional operator[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(5): 617-622. DOI: 10.6052/0459-1879-2004-5-2003-355
Citation: The numerical analysis formulation of the viscoelastic solid modeled by fractional operator[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(5): 617-622. DOI: 10.6052/0459-1879-2004-5-2003-355

分数算子描述的黏弹性体力学问题数值方法

The numerical analysis formulation of the viscoelastic solid modeled by fractional operator

  • 摘要: 讨论由黎曼-刘维尔 (Riemann-Liouville)分数导数描述的黏弹性体力学问题的数值方法. 该方法利用黎曼-刘维尔分数导数定义中核函数的特性,并结合被积函数在单步中的逼近以及Newmark型数值法,建立了分数导数计算公式. 算例表明,该算法具有收敛快、精度高、稳定性好和易于应用和改进的优点. 在对动态系统的瞬态响应分析和有限元分析格式中,算法都获得了满意的结果.

     

    Abstract: The numerical method of mechanical problems for the viscoelastic solids withRiemann-Liouville fractional derivative model is presented in this paper.Instead of using finite Grunwald definition of fractional derivative toapproximate the Riemann-Liouville's, this work has developed a numericalalgorithm directly from Riemann-Liouville's definition by taking advantagesof the features of its integrand kernel, assuming the approximating functionfor the integrand and making use of Newmark-type numerical methods. Thenumerical formulations are used to analyze the transient dynamic responsefor a viscoelastic oscillator and the finite element analysis procedures.The sample results show that the proposed method possesses the advantages offast convergence, higher accuracy, higher stability and easy for applicationand further modification.

     

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