完整帕斯卡插值方案用于近似四边形单元的几何形状
Complete Pascal Interpolation Scheme For Approximating The Geometry Of A Quadrilateral Element
AI总结：
本文提出了一种完整的参数集用于近似四边形单元的几何形状，采用二阶完整帕斯卡多项式作为逼近基函数，通过自然坐标确定六个自由参数，恢复了已知的拉格朗日插值方案，并提出了三阶帕斯卡插值方案。
摘要：
本文应用了一种完整的参数集来近似四边形单元的几何形状。所用的逼近基函数是具有六个自由参数的二阶完整帕斯卡多项式。插值过程是一种自然插值方案。六个自由参数通过四节点（顶点）的自然坐标以及两对相反边交点（极点）确定。所提出的方案在每对相反边平行时恢复了已知的拉格朗日插值方案。还提出了三阶帕斯卡插值方案。四边的中点以及第二阶情况下的六个节点点被用作重要节点点。预计由于形状函数是完整的，因此能够更好地反映几何特性。
英文摘要：
This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a natural interpolation scheme. The six free parameters are determined using the natural coordinates of the four nodal points (vertices) of the quadrilateral element and the two intersections points of the lines crossing every two opposite edges (poles). The presented scheme recovers the well known Lagrangian interpolation scheme, when every two opposite edges are parallel. A third order Pascal interpolation scheme is also presented. The four midpoints of the four edges in addition to the six nodal point from the second order case are used as significant nodal points. It is expected to reflect the geometry properties better since the shape functions are complete
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