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For the Euler-Bernoulli beam problem with variable flexural stiffness and elastic foundation, the EEP (Element Energy Projection) superconvergence method can provide solutions of higher order accuracy than the conventional finite element (FE) solutions and hence can be used as an error estimator for adaptive FE analysis. Based on the conventional EEP technique, an enhanced EEP form is proposed with even higher order accuracy than the conventional EEP solution for elements of degree \(m\ge 5\) . This allows to develop the EEP element for adaptive FE analysis, which takes the conventional EEP solutions as the final solution and employs the enhanced EEP solution as a pointwise error estimator to guide the adaptive process. As a result, an adaptive FE algorithm based on the EEP element is developed with the errors being controlled by the maximum norm and the final number of elements used being radically reduced. Typical numerical examples are given to show the effectiveness and efficiency of the proposed algorithm.

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EEP Element for Euler-Bernoulli Beam with Its Application to Adaptive Analysis

  • 会议论文

  • 发表日期：

    2025年

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  • Shuai Yang,
  • Si Yuan

摘要

For the Euler-Bernoulli beam problem with variable flexural stiffness and elastic foundation, the EEP (Element Energy Projection) superconvergence method can provide solutions of higher order accuracy than the conventional finite element (FE) solutions and hence can be used as an error estimator for adaptive FE analysis. Based on the conventional EEP technique, an enhanced EEP form is proposed with even higher order accuracy than the conventional EEP solution for elements of degree \(m\ge 5\) . This allows to develop the EEP element for adaptive FE analysis, which takes the conventional EEP solutions as the final solution and employs the enhanced EEP solution as a pointwise error estimator to guide the adaptive process. As a result, an adaptive FE algorithm based on the EEP element is developed with the errors being controlled by the maximum norm and the final number of elements used being radically reduced. Typical numerical examples are given to show the effectiveness and efficiency of the proposed algorithm.