有限元新型自然坐标方法研究进展

网格畸变敏感问题一直是当前有限元法难以解决的问题,而新型自然坐标方法的诞生可以在一定程度上对解决这个难题有所帮助。该文介绍了有限元新型自然坐标方法研究的新近进展。包括第一类四边形面积坐标及其应用(单元构造,解析刚度矩阵的建立,以及在几何非线性问题中的应用等);第二类四边形面积坐标及其应用;六面体体积坐标及其应用。数值算例表明:无论网格如何扭曲畸变,这些基于新型自然坐标方法的有限元模型仍然保持高精度,对网格畸变不敏感。这显示了新型自然坐标方法是构造高性能单元模型的有效工具。

ADVANCES IN NEW NATURAL COORDINATE METHODS FOR FINITE ELEMENT METHOD

The sensitivity problem to mesh distortion is a challenging difficulty in the field of the finite element method. Recently, some new natural coordinate methods have been successfully established for developing robust finite element models. They provide possible ways to overcome the problem. This paper introduces some newest advances in the research on this area, including the quadrilateral area coordinate method of type I and its applications (construction of finite element model, establishment of analytical element stiffness matrix, and application in geometrically nonlinear problem);the quadrilateral area coordinate method of type II and its application;and the hexahedral volume coordinate method and its applications. Numerical examples show that element models formulated by these new natural coordinate systems are quite insensitive to various mesh distortions. It demonstrates that these new natural coordinate methods are powerful tools for constructing high-performance hexahedral finite element models.