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基于真实转角与“试探-修正”插值的四边形单元
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Quadrilateral Element Based on True Rotation Angle and “Trial-correction” Interpolation
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    摘要:

    为解决不同单元间的兼容性问题,提出一种“试探-修正”位移插值方法,用于构造具有旋转自由度的四节点四边形平面单元.基于“试探-修正”插值的四节点四边形平面单元以平动位移和转动角度作为节点参数,采用双线性插值对位移场进行试探,根据转角的偏差,采用双三次插值对位移场进行校正.通过分片测试证明了该方法构造的四节点四边形平面单元的收敛性,并用三个算例进一步验证了其性能.数值结果表明,基于“试探-修正”插值的四节点四边形平面单元不仅收敛速度快,数值精度高,还能与梁单元兼容,方便混合单元建模.此外,“试探-修正”插值方法可参数化,具有良好的可扩展性,为今后研究其他具有真实转角的单元奠定了基础.

    Abstract:

    To address the problem of incompatibility between different elements, the paper introduces a “trial-correction” displacement interpolation scheme. This scheme is utilized to construct a four-node quadrilateral plane element that incorporates a drilling degree of freedom. The “trial-correction” interpolation-based four-node quadrilateral plane element takes translational displacements and the drilling degree of freedom as nodal parameters, and higher-order interpolation functions are employed to approximate the displacement field. Firstly, bi-linear interpolation is used to trail the displacement fields. And then, according to the deviation of the drilling degree of freedom, the displacement fields are corrected with bi-cubic interpolation. The convergence of the “trial-correction” interpolation-based four-node quadrilateral plane element is proved by the patch test, and its performance is further verified by three examples. The numerical results show that the “trial-correction” interpolation-based four-node quadrilateral plane element has a high convergence rate, a high numerical accuracy, and can be compatible with beam elements for convenient mix-element modeling. Moreover, the “trial-correction” interpolation method is parameterized and has good extendibility, which lays a foundation for future research about other elements with true rotation angle.

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黄观新 ,卢永和 ,李航行 ,杨志军 ?,陈新 .基于真实转角与“试探-修正”插值的四边形单元[J].湖南大学学报:自然科学版,2025,52(6):134~143

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  • 在线发布日期: 2025-07-02
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