Purpose

This paper attempts to develop an efficient algorithm to solve the inverse problem of identifying constitutive parameters in VFG (viscoelastic functionally graded) materials/structures.

Design/methodology/approach

An adaptive recursive algorithm with high fidelity is developed to acquire the derivatives of displacements with respect to constitutive parameters, which are required for the accurate and stable gradient based inverse analysis. A two-step strategy is presented in the process of identification, by which the unknown parameters can be separately identified and the scale and complexity of the inverse VFG problem are reduced. At each step, the process of identification is treated as an optimization problem that is solved by the Levenberg–Marquardt method.

Findings

The solution accuracy of forward problems and derivatives of displacements can be stably achieved with different step sizes, and constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures can be effectively and accurately identified. By examining the reliability, resolution, impacts of reference information and noisy data, the effectiveness of the proposed approach is numerically verified via three numerical examples.

Originality/value

An adaptive recursive algorithm is developed for derivatives computing with high fidelity, providing a solid platform for the sensitivity analysis and thereby a two-step strategy in conjunction with Levenberg–Marquardt method is presented in the process of identification. Consequently, an effective algorithm is developed to identify constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures.

中文翻译：

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粘弹性功能梯度材料/结构参数辨识反问题的数值模拟

目的

本文试图开发一种有效的算法来解决识别 VFG（粘弹性功能梯度）材料/结构中的本构参数的逆问题。

设计/方法/方法

开发了一种具有高保真度的自适应递归算法来获取位移关于本构参数的导数，这是基于梯度的准确和稳定的逆分析所必需的。在识别过程中提出了两步策略，通过该策略可以单独识别未知参数，降低逆VFG问题的规模和复杂度。在每一步，识别过程都被视为一个优化问题，由 Levenberg-Marquardt 方法解决。

发现

通过不同的步长，可以稳定地实现正问题和位移导数的求解精度，并且可以有效准确地识别同质/区域-非同质VFG材料/结构的本构参数。通过检查参考信息和噪声数据的可靠性、分辨率、影响，通过三个数值例子对所提出方法的有效性进行了数值验证。

原创性/价值

针对高保真导数计算开发了自适应递归算法，为敏感性分析提供了坚实的平台，从而在识别过程中提出了结合Levenberg-Marquardt方法的两步策略。因此，开发了一种有效的算法来识别同质/区域非同质 VFG 材料/结构的本构参数。