叶康生, 曾强. 结构自由振动问题有限元新型超收敛算法研究[J]. 工程力学, 2017, 34(1): 45-50,68. DOI: 10.6052/j.issn.1000-4750.2015.05.0421
引用本文: 叶康生, 曾强. 结构自由振动问题有限元新型超收敛算法研究[J]. 工程力学, 2017, 34(1): 45-50,68. DOI: 10.6052/j.issn.1000-4750.2015.05.0421
YE Kang-sheng, ZENG Qiang. A NEW SUPERCONVERGENT RECOVERY METHOD FOR FE ANALYSIS ON STRUCTURAL FREE VIBRATION PROBLEMS[J]. Engineering Mechanics, 2017, 34(1): 45-50,68. DOI: 10.6052/j.issn.1000-4750.2015.05.0421
Citation: YE Kang-sheng, ZENG Qiang. A NEW SUPERCONVERGENT RECOVERY METHOD FOR FE ANALYSIS ON STRUCTURAL FREE VIBRATION PROBLEMS[J]. Engineering Mechanics, 2017, 34(1): 45-50,68. DOI: 10.6052/j.issn.1000-4750.2015.05.0421

结构自由振动问题有限元新型超收敛算法研究

A NEW SUPERCONVERGENT RECOVERY METHOD FOR FE ANALYSIS ON STRUCTURAL FREE VIBRATION PROBLEMS

  • 摘要: 该文以杆件轴向自由振动问题为例提出一个结构自由振动问题的新型超收敛计算方法。该法基于有限元解答中频率和振型结点位移的超收敛特性,建立了单元上振型近似满足的线性常微分方程边值问题,对该线性边值问题采用更高次数的多项式进行有限元求解获得各单元上振型的超收敛解,将振型的超收敛解代入Rayleigh商,获得结构频率的超收敛解。该法简单、直接,通过很少量的计算即能显著提高频率和振型的精度和收敛阶。数值算例显示,该法高效、可靠,是一个颇具潜力的新方法。

     

    Abstract: This paper presents a new superconvergent recovery method for the finite element analysis on structural free vibration problems. Based on the superconvergence properties on frequencies and nodal displacements in modes, a linear ordinary differential boundary value problem (BVP) is set up, which approximately governs the mode on each element. This linear BVP is solved by using a higher order element from which the mode on each element is recovered. Then by substituting the recovered mode into the Rayleigh quotient, the frequency is recovered. This method is simple and direct. It can enhance the accuracy and convergence order of the frequencies and modes significantly with small computation. Numerical examples demonstrate that this method is efficient, reliable and potential.

     

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