A novel nonsmooth approach for flexible multibody systems with contact and friction in 3D space
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ORIGINAL PAPER
A novel nonsmooth approach for flexible multibody systems with contact and friction in 3D space Ningning Song . Haijun Peng
. Ziyun Kan . Biaosong Chen
Received: 5 February 2020 / Accepted: 19 September 2020 Springer Nature B.V. 2020
Abstract For computational multibody system dynamics, contact and friction problems are very complex and important problems. Therefore, this paper proposes a novel nonsmooth method for flexible multibody systems with contact and friction in 3D space. Considering the nonsmooth effect of contact and friction on the state variable of the multibody systems, the proposed method is divided into two parts: (i) the change of state variables under the action of smooth force and (ii) the change of state variables caused by contact and friction. Furthermore, for the contact part, the Newton’s impact law and the classical Coulomb friction model are employed to deal with normal impact contact impulse and tangential friction contact impulse, respectively. In addition, Fischer– Burmeister function and Karush–Kuhn–Tucker conditions are also used to solve the normal impact contact impulse and tangential friction contact impulse. What’s more, since the symplectic discrete format performs well robustness to numerical results, the discrete format of the proposed method is based on the symplectic discreteness, and it is expected to obtain the robust numerical results. Finally, several numerical examples are tested by the proposed
N. Song H. Peng (&) Z. Kan B. Chen Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, People’s Republic of China e-mail: [email protected]
nonsmooth method, and the numerical simulation results verify the effectiveness of the proposed approach. Keywords Flexible multibody systems Nonsmooth dynamics Contact Friction Symplectic discrete format
1 Introduction Multibody system models are ubiquitous in many engineering areas such as aerospace engineering [1], vehicle engineering [2] and robot engineering [3]. With the increase in application requirements, collision and friction inevitably appear in engineering problems [4, 5]; therefore, the effects of collision and friction must be considered in multibody system dynamics. The collision and friction in the multibody system cause the discontinuity in variables such as velocity variables, which increases the complexity and difficulty of solving multibody system dynamics. For the purpose of solving multibody system dynamics with collision and friction, although many scholars have carried out related research, it is still an interesting topic due to its importance. For solving the contact dynamic problems of multibody systems, up to now, there are two main types of numerical methods: (i) the penalty method
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and (ii) the nonsmooth contact method. For the dynamics of contact multibody systems, the discontinuity of state variables (e.
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