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采用三层铝板两层蜂窝芯的夹层结构制造高精度反射面板是一种先进、复杂的技术。其中,单层铝板的受力分析和夹层板的回弹计算是成形精度的根本保障。利用Fourier级数表示单层板应力函数、利用幂级数表示夹层板挠度函数,分别对高精度反射面板制造中单层板压贴和夹层板回弹两类边值问题进行了求解。与有限元模拟结果对比表明,本文提出的单层板压贴膜应力计算Fourier级数法具有较高精度;与试验结果对比表明,本文提出的夹层板回弹量幂级数法具有满意精度。
The use of a sandwich structure with three layers of aluminum and two layers of honeycomb core is an advanced and complicated technology. Among them, the stress analysis of single-layer aluminum plate and springback calculation of sandwich plate is the fundamental guarantee of forming accuracy. Using the Fourier series to represent the stress function of the single-layer board and the deflection function of the sandwich board by the power series, two kinds of boundary value problems of the single-layer board and the mezzanine board springback in the manufacture of high-precision reflective panel are respectively solved. The comparison with the finite element simulation results shows that the proposed Fourier series method for the stress calculation of the single-layer pressure-lamination film has higher accuracy. Compared with the experimental results, it shows that the proposed method has satisfactory accuracy.