中文摘要：

要实现高精度的碳纤维增强聚合物（CFRP）复合材料反射镜的主动成形，使用面内刚度和弯曲刚度均为准各向同性的层合板非常重要。 先建立对称层合板几何模型，根据经典层合板理论，得到准各向同性的要求下，正则化面内刚度系数、弯曲刚度系数以及正则化几何因子应满足的条件，确定单层组数最大的铺层方式， 并提出以正则化刚度系数和几何因子表示的两种铺层顺序优化方法。 然后，针对 M40/环氧 648 材料，通过编程得到不同定向单层数量下的最佳铺层顺序。 最后，用两种优化方法下的优化结果分别建立口径 500 mm 的壳体模型，经有限元静力学分析，得到模型上相同半径上各节点在光轴方向的变形量，并进行数据处理。结果表明：总层数为 24 层时，铺层顺序为[45/-15/-75/90/15/-45/-30/60/-60/0/30/75]s的层合板弯曲刚度的均匀性最佳。采用正则化刚度系数优化方法 Dij＊=Aij＊，可得到准各向同性层合板铺层顺序的最优化方案；当总层数一定且单层组数最大时，增加定向单层数， 将增加层合板弯曲刚度的均匀性。 采用正则化刚度系数法对铺层顺序进行优化为准各向同性CFRP 复合材料反射镜的铺层设计提供了一种方法。

英文摘要：

In order to achieve the active forming of carbon fiber reinforced polymer （CFRP） mirrors, a quasi-isotropic laminate of unified in-plane and flexural stiffness was adopted. Firstly, the relationship of regularization in-plane stiffness coefficient, flexural stiffness coefficient and geometric factor based on classical lamination theory was obtained. On the basis of regularization stiffness coefficient and geometric factor, two methods of optimizing the lay-up sequence were proposed. Secondly, in view of M40/648 material, the best lay-up sequence with different number of orientational laminas was calculated by programming. Finally, the shell model with a diameter of 500 mm was built. By using FEM, on the direction of optical axis, the displacements of those nodes with the same radius on the shell model were acquired and processed. The results indicate that the best lay-up sequence is [45/-15/-75/90/15/-45/-30/ 60/-60/0/30/75]s while the total number of laminas is 24. The analysis results show that the best lay-upsequence of quasi-isotropic laminate can be derived from the regularization stiffness coefficient method Dij＊=Aij＊. While the total number of laminas is assumed, and the group of laminas achieves maximum, the more number of orientational laminas, the better uniformity of laminate＇s flexural stiffness is found. The method using regularization stiffness coefficient to optimize the lay-up sequence advance a method for lay-up design of quasi-isotropic CFRP reflector.