振动和屈曲特征值形状灵敏度的连续和离散分析方法

Giuseppe Maurizio Gagliardi, Mandar D. Kulkarni, Francesco Marulo
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引用次数: 0

摘要

基于梯度的优化技术需要精确和高效的灵敏度。有限差分等数值灵敏度方法易于实现,但精度不高,计算效率低。相比之下,分析灵敏度方法,如离散法和连续法,具有较高的准确性和效率。连续统灵敏度分析(CSA)是一种用于计算形状或值参数导数的分析方法。虽然CSA已经成功地应用于时域的静态分析和动态问题,但这项工作首次将该方法扩展到特征值灵敏度。然而,CSA揭示了局限性,促使探索基于离散分析微分的替代方法。该方法首次应用于形状灵敏度分析。该方法所需的刚度矩阵和质量矩阵的导数均采用解析计算,具有较高的精度和计算效率。此外,一个元素不可知论的方法已经开发利用初级分析矩阵来计算他们的导数。这种特性,加上非侵入性,使得该方法适用于标准的商业软件。这两种方法已经在广泛的场景中得到了应用和验证,包括振动和屈曲问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Continuum and Discrete Analytical Methods for Vibration and Buckling Eigenvalues Shape Sensitivities

Gradient-based optimization techniques need precise and efficient sensitivities. Numerical sensitivity methods such as finite differences are easy to implement but imprecise and computationally inefficient. In contrast, analytical sensitivity methods, such as the discrete and continuum ones are highly accurate and efficient. Continuum Sensitivity Analysis (CSA) is an analytical method used to calculate derivatives of shape or value parameters. While CSA has been successfully applied in static analysis and dynamic problems in the time domain, this work presents an extension of the approach to eigenvalue sensitivities for the first time. However, CSA revealed limitations, prompting the exploration of an alternative approach based on discrete analytical differentiation. This method is employed for the first time in shape sensitivities. The derivatives of the stiffness and mass matrices required by the method are calculated analytically, resulting in high accuracy and computational efficiency. In addition, an element agnostic approach has been developed leveraging primary analysis matrices to calculate their derivative. This characteristic, along with the nonintrusivity, makes the method employable with standard commercial software. Both approaches have been applied and validated in a wide range of scenarios, involving vibration and buckling problems.

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