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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (4): 476-490    
    
带损伤弹性反问题的数值分析
郑聪, 程晓良, 梁克维
浙江大学 数学科学学院, 浙江杭州 310027
Numerical analysis of inverse elastic problem with damage
ZHENG Cong, CHENG Xiao-liang, LIANG Ke-wei
School of Math. Sci., Zhejiang Univ., HangZhou 310027, China
 全文: PDF 
摘要： 考虑一类由椭圆性方程和热传导方程共同来刻画的准静态弹性模型, 通过给定观测值来反演边界的牵引力. 首先构造一个凸目标泛函, 并引入Tikhonov正则化方法, 使之极小化得到一个稳定的近似解. 再用有限元离散求解, 导出误差估计. 最后,用数值例子说明算法的可行性和有效性.
关键词： 变分不等式;  有限元方法;  误差估计;  数值模拟    
Abstract: The quasistatic elastic problem is formulated as an elliptic system for the displacements coupled with a parabolic equation for the damage field. The corresponding inverse problem is reformulated as an optimal control problem to find a stable traction, by a given observation data. Firstly, a convex functional is constructed with Tikhonov regularization, and a stable approximation of surface traction is obtained by minimizing it. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. At last, a numerical algorithm is detailed and three examples illustrate the efficiency of the algorithm.
Key words: variational inequality    finite element method    error estimates    numerical simulations
收稿日期: 2016-01-15 出版日期: 2018-05-16
CLC:  O241.82  
基金资助: 国家自然科学基金(11271258; 11471253; 11571311)
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郑聪
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引用本文:

郑聪, 程晓良, 梁克维. 带损伤弹性反问题的数值分析[J]. 高校应用数学学报, 2016, 31(4): 476-490.

ZHENG Cong, CHENG Xiao-liang, LIANG Ke-wei. Numerical analysis of inverse elastic problem with damage. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 476-490.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I4/476

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