求解固体力学反问题的广义边界控制方法

A General Boundary Control Method for Inverse Solid Mechanics Problems

基于广义边界控制方法和有限元方法,探讨了一类固体力学反问题的数值求解方法.将柯西反问题转化成线性代数方程组,得到一个求解此类柯西反问题的直接算法.为克服测量数据中随机扰动带来的不适定性,得到一组稳定的解.此外,还应用Tikhonov正则化方法,并用L曲线法为正则化方法选取合适的正则化参数.数值实验结果表明,基于有限元方法的广义边界控制是稳定且有效的.

The inverse problem of solid mechanics was discussed,which Cauchy inverse problem was converted into linear algebraic equations based on the finite element method and the generalized boundary control method,to get a direct solution of Cauchy inverse problem.To overcome the ill-posedness caused by the unavoidable random noises in the measure data and obtain stable and reliable solutions,we employed the Tikhonov regularization method with the L-curve method to choose the regularization parameter for the regularization approach.The examples show that the method can work stably and effectively for the inverse solid mechanics problems with the general boundary control method based on the finite element method.