形状自由的高性能有限元方法研究的一些进展

发布时间：2018-02-12 09:05

本文关键词： 有限元网格畸变形状自由杂交应力/位移函数有限元新型非对称有限元　出处：《工程力学》2017年03期 　论文类型：期刊论文

【摘要】：作为工程和科学计算的主要工具,有限元方法已经得到了广泛的应用,但是仍然受到网格畸变敏感等固有难题的困扰,并且一直没有能够彻底根治。该文系统介绍了新型有限元方法——形状自由的高性能有限元方法研究的最新进展,包括平面问题和二维断裂问题的杂交应力函数有限元方法,中厚板问题的杂交位移函数有限元法,平面和三维问题的新型非对称有限元方法。这些方法在已有的杂交应力元法和非对称有限元法基础上,综合利用了解析试函数法、新型自然坐标方法、广义协调方法等先进技术,获得重要进展:所发展的单元模型精度高且稳定,在网格极端畸变的情况下仍可保持原有精度,具有形状自由的优异特性;同时破解了Mac Neal局限定理,解决了中厚板边缘效应计算等难题。论文的最后对上述方法的特点以及后续的研究工作进行了讨论。
[Abstract]:As the main tool of engineering and scientific calculation, finite element method (FEM) has been widely used, but it is still beset by the inherent problems, such as sensitivity of mesh distortion, and so on. This paper systematically introduces the new finite element method-the high performance finite element method with free shape, including the hybrid stress function finite element method for plane problem and two-dimensional fracture problem. The hybrid displacement function finite element method for plate problems, the new asymmetric finite element method for plane and three-dimensional problems, and the analytical trial function method are used in these methods based on the existing hybrid stress element method and asymmetric finite element method. New natural coordinate method, generalized coordination method and other advanced technologies have obtained important progress: the developed element model has high accuracy and stability, can still maintain the original accuracy in the case of extreme grid distortion, and has excellent characteristics of free shape; At the same time, the limitation theorem of Mac Neal is solved, and the problem of calculating the edge effect of plate is solved. Finally, the characteristics of the above method and the research work in the future are discussed.
【作者单位】：清华大学航天航空学院工程力学系AML;南京航空航天大学航空宇航学院;吉林大学交通学院;浙江工业大学机械工程学院;
【基金】：国家自然科学基金项目(11272181,11602219) 清华大学自主科研项目(2014z09099) 浙江省自然科学基金项目(LQ16A020004)
【分类号】：O241.82

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