Asymptotic solutions for predicted natural frequencies of two-dimensional elastic solid vibration problems in finite element analysis.

*(English)*Zbl 0881.73130In order to assess the discretization error of a finite element (FE) solution, the authors present asymptotic solutions for predicted natural frequencies of two-dimensional elastic solid vibration problems. Since the asymptotic solution is more accurate than the original FE solution, it can be considered as an alternative solution against which the original FE solution can be compared. Consequently, the discretization error of the FE solution can be evaluated. Due to the existence of two kinds of two-dimensional problems in engineering practice, both the plane stress problem and the plane strain problem are considered, and the corresponding asymptotic formulae for predicted natural frequencies of two-dimensional solids by the FE method are derived from the fact that a discretized FE system approaches a continuous one if the FE size approaches zero. From the related numerical results of three examples it is demonstrated that the presented asymptotic solution, which can be obtained by using the corresponding formula without any further FE calculation, is indeed more accurate than the original FE solution, so that it can be considered as a corrected solution for the error estimation of a discretized FE solution.

Reviewer: L.Prášek (Plzeň)

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74H45 | Vibrations in dynamical problems in solid mechanics |

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\textit{C. Zhao} and \textit{G. P. Steven}, Int. J. Numer. Methods Eng. 39, No. 16, 2821--2835 (1996; Zbl 0881.73130)

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