三心底结构是国防、航空及航天等领域经常采用的结构，其旋转母线是由三段弧线组成的，对应着三个圆心，故得名三心底。三心底结构可调整的参数变量少，优化潜力小。根据三心底的形状推广出五心底结构，增加可调整的参数变量，然后对其进行优化。将响应面方法与模型参数化相结合，建立了以结构重量为目标及以结构强度为约束的形状优化模型。根据结构形状选取独立的设计变量，推导结构重量的解析表达式和结构重量对设计变量的一阶导数，将结构重量进行一阶泰勒展开，采用响应面方法将结构最大应力拟合为设计变量的一次函数表达式，建立形状优化的线性规划模型。通过PCL（Patran Command Language）语言编写函数，用于建立分析模型，并将跟设计变量有关的数值参数化，在迭代过程中不断对结构进行调整，最后得到最优设计。数值结果表明，该方法具有很强的灵活性，适用范围较广，优化结果具有一定的稳定性和准确性。%Three-center shell structure is often adopted in the domain of national defense, aviation and spaceflight,and so on. The generatrix of three-center shell structure is composed of three arcs with three centers, so the name is called. The three-center shell structure has few adjustable parameter variables and less potential of optimization. The three-center shell structure is developed to five-center shell structure to increase the adjustable parameter variables, and then to optimize the structure. Combining the response surface method and the parameterized model,the model with structural weight as object function and structural strength as constraint is built. According to the structural shape, the independent design Variables are selected. The analytical expression of the structural weight and the first derivative of the widely, and the optimization results are stable and exact.
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