最佳协调性四边形薄板元

本文利用最佳逼近思想，构造了一种任意四边形广义协调薄板元。文中提出了协调性度量泛函的概念。通过协调性度量泛函的极小化，使单元协调性达到最佳。该方法的特点是非常便于程式化，容易推广到其它类型非协调元的构造，数值检验表明，该类单元精度很好，且对不规则网格有较好的适应性，此外，在使用协调性度量泛函的前提下，令插值基函数在笛卡尔坐标中直接取用，可使小片检验自然满足。

A QUADRILATERAL THIN PLATE ELEMENT WITH OPTIMUM COMPATIBILITY

This paper presents a quadrilateral thin-plate element with generalized compatibility, it being by way of the optimum approach.In the paper,it advances the concept of the Metric Functional of Compatibility. The compatibility of an element will approach optimum by minimizing the Metric Functional of Compatibility. The advantage of this method lies on the fact that is very convenient to be normalized and easy to be applied in the construction of other elements. The numerical test shows that such type of elements is quite accurate and is especially suitable for abnormal meshes. In addition, if the Metric Functional of Compatibility is used, the patch test will be satisfied naturely as long as the base functions have been defined directly in Cartesian coordinates.