针对三维打印工件的热残余应力和变形现象，引入底板和动态降温梯度两个关键要素，建立了三维打印过程中热残余应力和变形的解析表达式，并进行了算例验证。结果表明：引入底板和动态降温梯度后，计算结果与实际情况相符；底板温度与成形温度相差越大，降温梯度、热残余应力和变形越大；打印完成后无论何时拆除底板都不会影响热残余应力和变形程度；忽略底板的影响会使解析解产生很大的误差；底板保持恒温可显著降低热残余应力，且保温温度越接近制备温度，热残余应力越小。

For the thermal residual stress and deformation phenomenon of 3D printing parts, two key factors of platform and dynamic cooling gradient were introduced, and the analytical expressions of thermal residual stress and deformation were established and verified by numerical examples. The results show that the calculation was consistent with the actual situation after introducing the platform and dynamic cooling gradient. The greater the difference between the platform temperature and the forming temperature, the greater the cooling gradient, the thermal residual stress and the deformation. The platform removal time after printing had no effect on the thermal residual stress and deformation level, but ignoring the influence of the platform caused a large error in the analytical solution. Keeping the platform at a constant temperature significantly reduced the thermal residual stress, and the closer the holding temperature to the printing temperature, the lower the thermal residual stress.