空间结构瞬态温度场的Fourier—有限元分析

Fourier-finite element analysis of temperature fields in space structures

针对航天结构常用的空心圆杆 ,提出了一种计算其温度场的 Fourier—有限单元法 ,沿杆长用有限元离散 ,沿周向温度分布展成三角函数。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。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。在每个时间步内求解一组平均温度增量的非线性方程组 ,根据每一时刻的平均温度求解两组关于截面内温差的线性方程组 ,从而得到薄壁圆管的温度分布。利用该方法 ,对 Hubble太空望远镜的太阳能帆板瞬态温度场进行了分析 。

Space structures consisting of thin walled beams are subjected to incident solar heat flux and emit thermal energy by radiation. This thermal analysis considers the nonlinear and time dependent heat conduction in complex structures. A Fourier finite element thermal analysis method for a circular tube is presented. The structure is modelled using the finite element method in the longitudinal direction and by Fourier series in the circumferential direction. Each node in the circle tube elements possesses three degrees of freedom: the average temperature and the amplitudes of the cos and sine shaped perturbation temperatures. The changes of the average temperature and the perturbation temperatures are decoupled in each time step. Therefore, the solution can be obtained in each time 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 temperatures. The present method was used to calculate the time dependent temperature fields for the solar array of the Hubble space telescope. A thermal effect could cause twisting of the solar array.