A framework for establishing constraint Jacobian matrices of planar rigid-flexible-multibody systems

Lina Zhang; Xiaoting Rui; Jianshu Zhang; Guoping Wang; Junjie Gu; Xizhe Zhang; Lina Zhang; Xiaoting Rui; Jianshu Zhang; Guoping Wang; Junjie Gu; Xizhe Zhang

doi:10.3934/math.20231096

AIMS Mathematics

2023, Volume 8, Issue 9: 21501-21530. doi: 10.3934/math.20231096

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Research article

A framework for establishing constraint Jacobian matrices of planar rigid-flexible-multibody systems

Institute of Launch Dynamics, Nanjing University of Science and Technology, Jiangsu, China

Received: 03 January 2023 Revised: 14 June 2023 Accepted: 19 June 2023 Published: 06 July 2023
MSC : 65D17, 65D30

Constraint violation correction is an important research topic in solving multibody system dynamics. For a multibody system dynamics method which derives acceleration equations in a recursive manner and avoids overall dynamics equations, a fast and accurate solution to the violation problem is paramount. The direct correction method is favored due to its simplicity, high accuracy and low computational cost. This method directly supplements the constraint equations and performs corrections, making it an effective solution for addressing violation problems. However, calculating the significant Jacobian matrices for this method using dynamics equations can be challenging, especially for complex multibody systems. This paper presents a programmatic framework for deriving Jacobian matrices of planar rigid-flexible-multibody systems in a simple semi-analytic form along two paths separated by a secondary joint. The approach is verified by comparing constraint violation errors with and without the constraint violation correction in numerical examples. Moreover, the proposed method's computational speed is compared with that of the direct differential solution, verifying its efficiency. The straightforward, highly programmable and universal approach provides a new idea for programming large-scale dynamics software and extends the application of dynamics methods focused on deriving acceleration equations.
- constraint violation correction,
- Jacobian matrix,
- semi-analysis,
- direct differentiation method,
- numerical integration
Citation: Lina Zhang, Xiaoting Rui, Jianshu Zhang, Guoping Wang, Junjie Gu, Xizhe Zhang. A framework for establishing constraint Jacobian matrices of planar rigid-flexible-multibody systems[J]. AIMS Mathematics, 2023, 8(9): 21501-21530. doi: 10.3934/math.20231096

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Abstract

Constraint violation correction is an important research topic in solving multibody system dynamics. For a multibody system dynamics method which derives acceleration equations in a recursive manner and avoids overall dynamics equations, a fast and accurate solution to the violation problem is paramount. The direct correction method is favored due to its simplicity, high accuracy and low computational cost. This method directly supplements the constraint equations and performs corrections, making it an effective solution for addressing violation problems. However, calculating the significant Jacobian matrices for this method using dynamics equations can be challenging, especially for complex multibody systems. This paper presents a programmatic framework for deriving Jacobian matrices of planar rigid-flexible-multibody systems in a simple semi-analytic form along two paths separated by a secondary joint. The approach is verified by comparing constraint violation errors with and without the constraint violation correction in numerical examples. Moreover, the proposed method's computational speed is compared with that of the direct differential solution, verifying its efficiency. The straightforward, highly programmable and universal approach provides a new idea for programming large-scale dynamics software and extends the application of dynamics methods focused on deriving acceleration equations.

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