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Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method

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Abstract

Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality local error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.

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Authors and Affiliations

  1. Applied Mechanics Laboratory, School of Aerospace, Tsinghua University, Beijing, 100084, P. R. China

    Zhi-jia Lin  (林治家), Xiao-chuan You  (由小川) & Zhuo Zhuang  (庄 茁)

Authors
  1. Zhi-jia Lin  (林治家)
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  2. Xiao-chuan You  (由小川)
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  3. Zhuo Zhuang  (庄 茁)
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Corresponding author

Correspondence to Zhuo Zhuang  (庄 茁).

Additional information

Project supported by the National Natural Science Foundation of China (No. 10876100)

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Lin, Zj., You, Xc. & Zhuang, Z. Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method. Appl. Math. Mech.-Engl. Ed. 33, 539–552 (2012). https://doi.org/10.1007/s10483-012-1569-x

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  • DOI: https://doi.org/10.1007/s10483-012-1569-x

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Chinese Library Classification

2010 Mathematics Subject Classification

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