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Approximation of the state variables of Navier’s differential equation in transient dynamic problems using finite element method based on complex Fourier shape functions

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Abstract

In this research, the analysis of 2D transient elastodynamic problems is performed using a reformulation of finite element method based on new complex Fourier shape functions, which are able to satisfy exponential and trigonometric function fields in addition to polynomial ones unlike classic Lagrange shape functions. Another superiority of these shape functions over classic Lagrange ones is their ability to obtain much better results using fewer degrees of freedom. Moreover, Runge phenomenon does not occur in the proposed shape functions when high degrees of freedom using equispaced elements are used, unlike classic Lagrange ones. In addition, the approximation of all kinds of surfaces, such as smooth and folded ones, is done perfectly by complex Fourier shape functions. In the end, six numerical examples are provided to show the efficiency and robustness of the suggested method. To do so, its results are compared with the classic Lagrange ones and analytical solutions (if available).

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Authors and Affiliations

  1. Civil Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran

    Saleh Hamzehei-Javaran

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  1. Saleh Hamzehei-Javaran
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Correspondence to Saleh Hamzehei-Javaran.

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Hamzehei-Javaran, S. Approximation of the state variables of Navier’s differential equation in transient dynamic problems using finite element method based on complex Fourier shape functions. Asian J Civ Eng 19, 431–450 (2018). https://doi.org/10.1007/s42107-018-0035-2

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  • DOI: https://doi.org/10.1007/s42107-018-0035-2

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