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Quadrilateral Element Based on True Rotation Angle and “Trial-correction” Interpolation
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    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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  • Received:
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  • Online: July 02,2025
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