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中文摘要：
基于解析试函数的有限单元法是一种将有限单元的离散法与解析法成果有机融合的方法，在有限单元理论的几个传统问题中取得了一些进展。该文介绍近几年该类方法在克服剪切闭锁以及消除网格畸变对单元性能影响等方面的研究进展；通过运用含应力函数变分原理，得到了一类不受网格畸变影响的高次精度精确单元；利用特征微分方程解法，给出了一个在弹性力学问题中构造独立完备解析试函数的通用方法。
英文摘要：
The finite element method based on the analytical trial functions is an organic integration of the analytical method with the discrete method. This method has overcome some challenges to the tradition finite element method. This paper introduces some newest advances in the research of shear locking problems and the sensitivity of mesh distortions. According to the variational principle containing stress functions, the study of the high-performance and high-order element models shows the way to obtain the high-order exact element models which are not sensitive to the mesh distortion. According to ＂Operator matrix＂ theory of partial differential equations, the solving of characteristic differential equations is proposed as a general mehod for constructing complete and independent analytical trial functions.
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