基于同伦技术的偶应力反问题求解

Solving inverse couple stress problem via homotopy method

引入Bregman距离构造同伦函数,建立偶应力反问题的一种求解模式,可以对偶应力理论相关参数进行识别。利用有限元技术,建立了偶应力正/反问题数值求解模型,该模型不仅考虑了非均质的影响,而且也便于反问题的敏度分析。文中给出了相关的数值算例,并对信息误差和不同的函数形式计算结果做了初步探讨,得到满意的结果。数值算例表明该模型具有一定的计算精度和抗不适定性。

This paper presents a general numerical model to identify parameters for inverse couple-stress problem with homotopic method based on Bregman distances function.A finite element model is given,taking account of inhomogeneity and facilitating to sensitivity analysis for direct and inverse problems.Satisfactory numerical validation is given including a preliminary investigation of effect of noise data and the terms for different Bregman functions.Results show that the proposed method can identify parameters for the inverse couple-stress problem with high computational efficiiency and the ability of anti-noisy data.