A 12-node conforming straight-sided quadrilateral element with high-order completeness (QH12-C1)

A new 12-node conforming quadrilateral element with high-order completeness, denoted as QH12-C1 was proposed in this paper. The main steps are outlined as follows: first, build the expression of the interpolation displacement function satisfying the requirements for the high order completeness in the global coordinate system; Second, transform the displacement function expression by global coordinates into isoparametric coordinate and find the relationship of two series coefficients of two kind displacement function expression; Third, modify the displacement function expression to satisfy the requirements of the nodal freedoms and inter-element boundary continuity. The key to the new element construction is the acquisition of the linear relationship expressions among twenty-four coefficients of element displacement interpolation polynomial in the global coordinate system and isoparametric coordinate system. As a result, the relationship between cube completeness and inter-element continuity is explicitly given, and the proof of completeness and continuity was conducted to guarantee the validity of the derivation results theoretically. Because the explicit expressions of the element shape function are given, the calculation time consumption of the element shape function is greatly saved. Further, to verify the correctness of the theoretical work, nine numerical examples were executed. The computation results from these examples demonstrate that the QH12-C1 possessed of excellent performances, including high simulation accuracy, fast convergence speed, insensitivity to mesh distortion, and excellent monotone convergence.