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Abstract
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In this paper, a ’trial-correction’ displacement interpolation scheme is developed for constructing four-node plane element with drilling degree of freedom. The ’trialcorrection’ interpolation based four-node plane element takes translational displacements and drilling degree of freedom as nodal parameters, and the displacement fields are interpolated by cubic functions. Firstly, bilinear interpolation is used to trail the displacement fields. And then, according to the deviation of drilling degree of freedom, the displacement fields are corrected with bi-cubic interpolation. The convergence of the ’trial correction’ interpolation based four-node 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 plane element has high convergence rate, high numerical accuracy, and can be compatible with beam element for convenient mix element modeling. Moreover, the ’trialcorrection’ interpolation method is parameterized and has good extendibility, which lays a foundation for future research about other elements with true rotation nodal parameters.
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