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首页> 外文期刊>Mathematical Problems in Engineering >Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization
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Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization

机译：通过Tikhonov正则化识别弹性和粘弹性材料参数

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摘要

For studying the interaction of displacements, stresses, and acting forces for elastic and viscoelastic materials, it is of utmost importance to have a decent mathematical model available. Usually such a model consists of a coupled set of nonlinear differential equations together with appropriate boundary conditions. However, since the different material classes vary significantly with respect to their physical andmechanical behavior, the parameters which appear in these equations are unknown and therefore have to be determined before the equations can be used for further investigations or simulations. It is this very step which is addressed in this article where we consider elastic as well as viscoelastic material behavior. The idea is to compute the parameters as solutions of a minimization problem for Tikhonov functionals. Tikhonov regularization is a well-established solution technique for tackling inverse problems. On the one hand, it assures a computation that is stable with respect to noisy input data, and on the other hand, it involves desired a priori information on the solution. In this article we develop problemadapted Tikhonov functionals and prove that a Tikhonov regularization improves the accuracy especially when the underlying system is ill-conditioned.
机译：为了研究弹性和粘弹性材料的位移，应力和作用力之间的相互作用，拥有合适的数学模型至关重要。通常，这种模型由一组耦合的非线性微分方程组以及适当的边界条件组成。但是，由于不同的材料类别在其物理和机械性能方面存在很大差异，因此这些方程式中出现的参数是未知的，因此必须确定这些方程式才能用于进一步的研究或模拟。本文讨论的正是这一步，在此我们考虑了弹性以及粘弹性材料的行为。想法是计算参数作为Tikhonov功能最小化问题的解决方案。 Tikhonov正则化是一种成熟的解决逆问题的解决方案。一方面，它确保了对于嘈杂的输入数据而言是稳定的计算，另一方面，它涉及解决方案上所需的先验信息。在本文中，我们开发了适用于问题的Tikhonov函数，并证明了Tikhonov正则化可以提高准确性，尤其是在基础系统状况不佳时。

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