A direct differentiation method based on forward recursive formulation for flexible multibody system sensitivity analysis

IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Structures Pub Date : 2024-08-06 DOI:10.1016/j.compstruc.2024.107465
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Abstract

Sensitivity analysis plays a significant role in the dynamic optimization of flexible multibody systems. The forward recursive formulation (FRF) is widely used for the dynamic modeling of multibody systems. However, it has not yet been extended to sensitivity analysis. In this paper, a new direct differentiation method is developed based on FRF for flexible multibody systems sensitivity analysis. The recursive nature of FRF allows for the Jacobian derivatives to be derived recursively, with detailed matrix expressions provided to facilitate implementation in computer code. The validity and correctness of the presented direct sensitivity analysis method based on FRF are verified by numerical examples. Besides, a modified staggered direct scheme is presented to improve the efficiency of the sensitivity analysis. In this scheme, different update strategies are adopted by different components of the tangent stiffness matrix for the implicit integrator, which balances the iteration performance and the additional computational cost. The presented scheme is compared with two conventional schemes through three examples. It demonstrates that the presented scheme can significantly improve the computational efficiency of the sensitivity analysis, particularly for complex problems, when the appropriate update strategies are employed.

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基于前向递归公式的直接微分法,用于柔性多体系统敏感性分析
灵敏度分析在柔性多体系统的动态优化中发挥着重要作用。前向递推公式(FRF)被广泛用于多体系统的动态建模。然而,它尚未扩展到灵敏度分析。本文在 FRF 的基础上开发了一种新的直接微分方法,用于柔性多体系统灵敏度分析。FRF 的递归性质允许对雅各布导数进行递归推导,并提供了详细的矩阵表达式以方便计算机代码的执行。所介绍的基于 FRF 的直接灵敏度分析方法的有效性和正确性通过数值示例得到了验证。此外,还提出了一种改进的交错直接方案,以提高灵敏度分析的效率。在该方案中,隐式积分器的切线刚度矩阵的不同组成部分采用了不同的更新策略,从而平衡了迭代性能和额外的计算成本。我们通过三个实例将所提出的方案与两种传统方案进行了比较。结果表明,如果采用适当的更新策略,所提出的方案可以显著提高灵敏度分析的计算效率,特别是对于复杂问题。
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来源期刊
Computers & Structures
Computers & Structures 工程技术-工程:土木
CiteScore
8.80
自引率
6.40%
发文量
122
审稿时长
33 days
期刊介绍: Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.
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