Mindlin板非协调广义混合弯曲元

NONCONFORMING GENERALIZED MIXED BENDING ELEMENT FOR MINDLIN PLATES

  • 摘要: 高阶的板单元形函数构造复杂,而低阶的板单元精度低,且通常不适用于薄板。为了改善一般板单元的剪切自锁现象,基于广义混合变分原理和Mindlin板理论,提出了仅要求C0连续的非协调混合弯曲元(NGME)。该单元作为混合元,为应力边界条件的引入提供了便利,为数值结果精度的提高奠定了基础。多个算例表明该单元具有稳定的收敛性,且适用于薄板问题。在不规则网格模型下,数值结果精度高。相较于传统的Mindlin板元,该单元厚跨比适用范围大。

     

    Abstract: The construction of high-order plate element shape functions is complex, while lower-order plate elements have low accuracy and are generally not suitable for thin plates. In order to improve the shear self-locking phenomenon of general plate elements, a nonconforming mixed bending element (NGME) which only requires C0 continuity is proposed by the generalized mixed variational principle and Mindlin plate theory. As a mixed element, the element facilitates the introduction of stress boundary conditions and lays the foundation for the improvement of the accuracy of the numerical results. Several numerical examples have showed that the element has the capability of stable convergence and is suitable for thin plate problems. In the irregular mesh model, the numerical results are highly accurate. Compared with traditional Mindlin plate elements, the thickness to span ratio of this element has a wide application range.

     

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