基于单元的子区间摄动有限元方法研究

Static sub-interval perturbed finite element method based on the elements

针对区间相关性导致区间扩张的问题,探讨了区间数之间的相关性并给出了降低区间扩张的子区间摄动方法。文中给出了基于单元的子区间摄动有限元计算公式和子区间划分数目的近似计算公式,同时文中讨论了区间有限元计算精度问题,给出了可提高计算效率的一些措施。对桁架结构和平面应力问题梁结构算例分析结果表明文中方法可以达到一定的计算精度,并且是合理可行的。

Interval correlation results in the extension of interval. The methods of considering interval correlation are discussed and the methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate formula of computing is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. By analyzing the truss structure and the planar stress beam structure, the numerical results indicate the sub-interval perturbed finite element method may obtain some certain precision and the method is reasonable and feasible.