分片试验与有限元法

提出分片试验在有限元法中有着重要的作用，它是近代有限元发展的一个主要特色。得出分片试验对位移和应变函数的要求，这些要求便是一个好的有限元法所应保证的；分析了几何方程弱形式与分片试验的关系，借此分析了杂交元、拟协调元如何满足这些要求，以及在满足这些要示的同时产生的对其他条件的影响；分析了精化直接刚度法、广义协调元和双参数法如何保证分片试验的满足；最后作为位移条件的应用例子，改进了ＢＣＩＺ元。

Patch Test and Finite Element Method

This paperrealizes that the Patch Test is very important to Finite Element Methods and derives therequirement to strain and displacement of Patch Test. Also gives the relationship betweenweak form of continuity equation and the Patch Test, through which the hybrid elementmethod and quasi-conform element method are analyzed. Refined direct stiffness method andgeneralized conforming elements are also analyzed about why they can pass patch test. Atlast, as an example of using the requirement of patch test for displacement, improves theBCIZ Element.