Dynamics of Rigid-Flexible-Thermal Coupled System With Temperature-Dependent Material Elastic Modulus

YANG Yulin; TIAN Qinglong; CAI Chensheng; TANG Yucong; REN Jianwei; DONG Yang; GAO Huiyao; ZHAO Zhenyu; LU Tianjian

doi:10.21656/1000-0887.450255

Volume 46 Issue 9

Sep. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(9): 1130-1146

YANG Yulin, TIAN Qinglong, CAI Chensheng, TANG Yucong, REN Jianwei, DONG Yang, GAO Huiyao, ZHAO Zhenyu, LU Tianjian. Dynamics of Rigid-Flexible-Thermal Coupled System With Temperature-Dependent Material Elastic Modulus[J]. Applied Mathematics and Mechanics, 2025, 46(9): 1130-1146. doi: 10.21656/1000-0887.450255

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Dynamics of Rigid-Flexible-Thermal Coupled System With Temperature-Dependent Material Elastic Modulus

doi: 10.21656/1000-0887.450255

1. State Key Laboratory of Mechanics and Control for Aerospace Structures，Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China;
2. MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures (MLMS),Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China;
3. College of Mechanical and Electrical Engineering, Hohai University, Changzhou, Jiangsu 213002, P.R.China;
4. Shanghai Key Laboratory of Aerospace Intelligent Control Technology,Shanghai 201109, P.R.China

Funds:

The National Science Foundation of China(11972185；12002156；12302047)

Received Date: 2024-09-19
Rev Recd Date: 2024-10-24

Available Online: 2025-10-17

Abstract

Abstract

During space missions, spacecrafts are subjected to complex thermal loads in the space environment, suffering significant temperature variations in their flexible structures. These temperature variations can induce strongly nonlinear thermo-dynamic coupling responses, which may, in severe cases, cause spacecraft failure. For large and low-stiffness flexible structures, even a slight change in the material elastic modulus can result in significant system responses. Therefore, it is essential to analyze the effects of temperature-dependent elastic moduli on the dynamics of rigid-flexible-thermal coupled systems. The absolute nodal coordinate formulation (ANCF) was applied, where both displacement and temperature fields are described with positions and gradients as generalized coordinates. The temperature-dependent material elastic modulus was considered, and an isoparametric element with unified shape function interpolation for both displacement and temperature fields was proposed. The system’s dynamic equations were derived based on the principle of virtual work, and the heat transfer equations were derived from the law of energy conservation. The generalized-α method was used to simultaneously solve these 2 sets of equations at each time step. The validity of the proposed model was first verified with the Boley simply supported beam. Then, the rigid-flexible-thermal coupled dynamic models were established for a rotating flexible beam and a spacecraft with a central rigid body and laminate solar panels. Dynamic analyses and comparisons were conducted for cases with and without temperature-induced changes in the material elastic modulus. The results show that, during the heat transfer process, compared to the effects of thermal stress on the system responses, the decrease in the material elastic modulus under thermal environment has a more significant impact on the system response. For rotating flexible beams, Ｅwith angular velocity ω₀=2 rad/s and 10 rad/s, the maximum tip deformation increases by 9.7% and 4.5% respectively compared to that in the rigid flexible coupling case. For the central rigid body sandwich panel, with moment M₀=200 N·m and 2 000 N·m, the maximum deformation at the test point increases by 8.7% and 7.1% respectively compared to that in the rigid flexible coupling case. The effects of temperature induced changes in the material elastic modulus on the dynamic responses of rigid flexible thermal coupling systems cannot be ignored, and the work provides a reference for the design of spacecraft control systems.

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References(35)

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