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Structural Engineering and Mechanics Volume 54, Number 6, June25 2015 , pages 1153-1174 DOI: https://doi.org/10.12989/sem.2015.54.6.1153 |
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Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix |
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Ping Xiang, Minger Wu and Rui Q. Zhou
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| Abstract | ||
| Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS. | ||
| Key Words | ||
| multibody system; deployable structure; dynamic analysis; constraint equations; equations of motion; generalized inverse matrix | ||
| Address | ||
| Ping Xiang: Department of Architecture, Waseda University, 3-4-1 Okubo, Tokyo 169-8555, Japan Minger Wu: Department of Building Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China Rui Q. Zhou: Shanghai Institute of Mechanical & Electrical Engineering Co., Ltd, 1287 West Beijing Road, Shanghai 200040, China | ||