Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method
Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method
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使用凸目标和连续牛顿法识别基尔霍夫板模型中的弯曲刚度
DOI：
10.1155/2015/290301
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发表时间：
2015
影响因子：
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通讯作者：
B. Winkler
中科院分区：
文献类型：
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作者：
B. Jadamba;R. Kahler;Akhtar A. Khan;F. Raciti;B. Winkler
本文对Kirchhoff板模型抗弯刚度识别反问题进行了详细的理论和数值研究。从数学的角度来看，这个逆问题需要估计一个四阶边值问题中的可变系数。这个逆问题和相关的估计问题与一般的板壳模型已经研究了许多研究人员通过一个优化框架，使用输出最小二乘（OLS）制定。OLS产生一个非凸的框架，因此，它是适合于调查只有当地的行为的解决方案。在这项工作中，我们提出了一个新的凸框架识别一个可变参数的四阶反问题的反问题。存在性结果，最优性条件，和离散化问题进行了详细讨论。离散反问题的求解采用连续牛顿法。数值结果表明了所提出的框架的可行性。
This work provides a detailed theoretical and numerical study of the inverse problem of identifying flexural rigidity in Kirchhoff plate models. From a mathematical standpoint, this inverse problem requires estimating a variable coefficient in a fourth-order boundary value problem. This inverse problem and related estimation problems associated with general plates and shell models have been investigated by numerous researchers through an optimization framework using the output least-squares (OLSs) formulation. OLS yields a nonconvex framework and hence it is suitable for investigating only the local behavior of the solution. In this work, we propose a new convex framework for the inverse problem of identifying a variable parameter in a fourth-order inverse problem. Existence results, optimality conditions, and discretization issues are discussed in detail. The discrete inverse problem is solved by using a continuous Newton method. Numerical results show the feasibility of the proposed framework.