A divideandconquer direct differentiation approach for multibody system sensitivity analysis
 Rudranarayan M. Mukherjee,
 Kishor D. Bhalerao,
 Kurt S. Anderson
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In the design and analysis of multibody dynamics systems, sensitivity analysis is a critical tool for good design decisions. Unless efficient algorithms are used, sensitivity analysis can be computationally expensive, and hence, limited in its efficacy. Traditional direct differentiation methods can be computationally expensive with complexity as large as O(n ^{4}+n ^{2} m ^{2}+nm ^{3}), where n is the number of generalized coordinates in the system and m is the number of algebraic constraints. In this paper, a direct differentiation divideandconquer approach is presented for efficient sensitivity analysis of multibody systems with general topologies. This approach uses a binary tree structure to traverse the topology of the system and recursively generate the sensitivity data in linear and logarithmic complexities for serial and parallel implementations, respectively. This method works concurrently with the forward dynamics problem, and hence, requires minimal data storage. The differentiation required in this algorithm is minimum as compared to traditional methods, and is generated locally on each body as a preprocessing step. The method provides sensitivity values accurately up to integration tolerance and is insensitive to perturbations in design parameter values. This approach is a good alternative to existing methodologies, as it is fairly simple to implement for general topologies and is computationally efficient.
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 Title
 A divideandconquer direct differentiation approach for multibody system sensitivity analysis
 Journal

Structural and Multidisciplinary Optimization
Volume 35, Issue 5 , pp 413429
 Cover Date
 20080501
 DOI
 10.1007/s0015800701422
 Print ISSN
 1615147X
 Online ISSN
 16151488
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Multibody dynamics systems
 Sensitivity analysis
 Direct differentiation
 Divide andconquer formulation
 Industry Sectors
 Authors

 Rudranarayan M. Mukherjee ^{(1)}
 Kishor D. Bhalerao ^{(1)}
 Kurt S. Anderson ^{(1)}
 Author Affiliations

 1. Department of Mechanical, Nuclear and Aerospace Engineering, Rensselaer Polytechnic Institute, 1108th Street, Troy, NY, 12180, USA