辐射换热条件下空间薄壁圆管结构瞬态温度场、热变形有限元分析

对航天结构中常见的辐射换热条件下的空间薄壁圆管结构，构造了一种用于非线性瞬态温度计算的傅立叶－有限单元。圆管温度沿杆长用有限元离散，沿周向分布展成三角函数。圆管温度单元每个结点包含平均温度、余弦和正弦分布温度幅三个自由度，并且在每个时间步内实现了平均温度增量与沿截面温差增量的解耦。在结构热变形分析时圆管单元节点上既承受温度轴力，又承受截面温差导致的热弯矩。采用这种单元对非线性换热条件下的复杂空间结构进行离散可以较准确地反映结构的温度场与热变形。经与前人的解析解和三维有限元结果的验证，证明该单元是可靠的。对太阳能帆板梁与空间抛物面天线的热－结构分析说明这种新单元的应用价值。

Thermal-structural finite element analysis of space structures consisting of thin walled beams

Space structures consisting of thin walled beams are subjected to incident solar heat flux and emit thermal energy by radiation.This thermal structural analysis should consider nonlinear and time dependent heat conduction and structural response.A Fourier finite element thermal analysis method for a circular tube is presented in this paper.The tube is modeled using the finite element method in the longitudinal direction and the temperature in the circumferential direction are modeled by Fourier series.Each node in the circular tube element possesses three degrees of freedom:the average temperature and the amplitudes of the cos and sine shaped perturbation temperatures.The change of average temperature and the perturbation temperatures are decoupled in each time step.Therefore,the solution can be obtained in each step by solving a set of nonlinear equations for the average temperature,then the average temperature is used to solve two sets of linear equations for the cos and sine shaped perturbation temperature.According to the temperature field of the circular tube,the initial forces in structural analysis include not only axial force caused by average temperature,but also moments caused by perturbation temperatures of the tube.Using the present method,the thermal and structural response of space structure can be simulated accurately.Numerical calculations for the Solar Array Beam and Space Parabolic Antenna demonstrate the effectiveness of the new element.