Thermal uncertainty analysis of spacecraft is an important method to avoid overdesign and underdesign problems. In the context of uncertainty analysis, thermal models representing multiple operating conditions must be invoked repeatedly, leading to substantial computational costs. The ray tracing calculation of Earth infrared and albedo radiation heat flux is an important reason for the slow calculation speed. As the rays emitted during external heat flux calculations under different operating conditions are independent and unconnected, the rays produced across various conditions are effectively wasted. In this study, the external heat flow equation is thoroughly expanded and the derived factors are clustered and analyzed to develop a novel formula for calculating external heat flow. When this formula is employed to compute the uncertain external heat flux, only one condition necessitates ray tracing, while the remaining conditions utilize simple matrix operations in place of complex ray tracing. Within the aforementioned procedure, certain matrices demonstrate sparse characteristics. The optimization calculations for these matrices can, therefore, benefit from the application of sparse matrix optimization algorithms. Using a spacecraft as an example, the uncertain external heat flux calculation outcomes of the new and traditional formulas are compared and assessed. The findings reveal that the new formula is highly suitable for estimating uncertain Earth radiation heat flow, with a marked improvement in efficiency. The accuracy is essentially equivalent to that of the traditional formula and the calculation precision can be dynamically adjusted to meet user requirements. The methodology can be further generalized to assess the uncertainties associated with radiative external heat fluxes for other celestial bodies within the solar system. This offers a valuable theoretical framework for addressing the uncertainties in the thermal design of deep space exploration vehicles.

Extreme cyclic temperature fluctuations (−200 °C to 200 °C) and inherent clearance nonlinearity in deployment hinges severely threaten the on-orbit deployment accuracy and dynamic stability of large variable-geometry spacecraft antennas for geosynchronous Earth orbit applications. However, current modeling approaches suffer from three critical limitations: single-configuration models requiring manual switching, there are inherent geometric nonlinear errors from conventional floating frame formulations, and incomplete thermo-mechanical coupling neglects the temperature effects on contact stiffness and friction. To address these gaps, we propose a unified high-fidelity dynamic model based on the Absolute Nodal Coordinate Formulation (ANCF). This model eliminates geometric errors and mesh mismatch, enables seamless multi-configuration deployment without switching, and fully incorporates temperature-dependent material properties and nonlinear contact forces. An improved Hilber–Hughes–Taylor-$\alpha$ implicit integration algorithm with second-order accuracy and unconditional stability is adopted to solve the strongly nonlinear differential-algebraic equations. Numerical results demonstrate that the proposed model achieves a calculation error below 3% against experimental data, significantly outperforming the traditional floating frame of reference formulation with an error of 15–22%. Non-uniform temperature fields increase thermally induced vibration amplitudes by 32–45%, and every 0.1 increase in the friction coefficient raises the impact force at the clearance hinge by 15–20%. The proposed unified modeling framework provides a solid theoretical basis for deployment stability prediction and the on-orbit control optimization of large variable-geometry spacecraft antennas.

Extreme orbital thermal cycling and temperature-dependent clearance nonlinearity make it difficult to predict contact–impact, stick–slip, and bifurcation responses of flexible deployable space structures with sufficient stability, accuracy, and computational efficiency. An Adaptive Dissipation–Precision Coordinated Multi-Scale Implicit Integration Algorithm (ADPC-MSIIA) is proposed. First, an absolute nodal coordinate formulation (ANCF)-based thermo-mechanical clearance-joint model with thermal-viscosity-modified contact and frictional/impact heat feedback is established; second, a dual-time-scale implicit integration scheme with dual-$\alpha$ stability–dissipation control and third-order compensation is developed; finally, numerical validation is performed using a linear single-degree-of-freedom (SDOF) benchmark, a temperature-dependent clearance impact oscillator, finite-element and published benchmark comparisons, and a deployable annular truss antenna case. Simulation results show that ADPC-MSIIA achieves a high-frequency spectral radius of $0.867$, an effective convergence order of $2.98$, a maximum contact force error of $3.1\%$, and a $51.7\%$ reduction in the global cumulative error compared with the generalized-$\alpha$ method. This study contributes to knowledge by linking temperature-driven clearance evolution, frictional heat feedback, and adaptive numerical dissipation within a unified framework for predicting non-smooth thermo-mechanical deployment dynamics of large flexible space structures with clearance joints.