一种基于连续系统仿真验证的剖分有限元方法

Continuous system simulation verification-based partial finite element method

Abstract

本发明公开一种基于连续系统仿真验证的剖分有限元方法。该方法针对目前联立法求解动态优化命题的缺陷,即只保证在有限元配置点上满足约束,不保证在非配置点上满足约束,提出了一种基于连续系统仿真验证的剖分有限元方法。该方法采用连续系统仿真验证方法使得有限元非配置点满足约束,采用剖分有限元方法对原有限元序列进行重新配置,能够得到在尽量少增加有限元个数的前提下保证求解精度的有限元配置方案。本发明针对三维空间下的自由飞行冲突解脱问题采用该方法进行求解,求解结果表明,与原联立法相比,采用这种方法更好的满足了离散化精度和求解精度。
The invention discloses a continuous system simulation verification-based partial finite element method. The method aims at the defect that a dynamic optimization system is solved by a current combination method, and the continuous system simulation verification-based partial finite element method is provided by only guaranteeing that the constraint on a finite element configuration point is met but not guaranteeing that the constraint on a non-configuration point is met. According to the method, the constraint is met on the finite element non-configuration point by using a continuous system simulation verification method; rearrangement is performed on an original finite element sequence by using the partial finite element method, so a finite element configuration scheme can guarantee the solving accuracy on the premise that the number of finite elements is increased as less as possible. Solving is performed by using the method aiming at a free flight conflict resolution problem in a three-dimensional space; the solving result shows that the discretization precision and the solving precision are met better by using the method compared with the original combination method.

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