基于Kriging代理模型的结构形状优化方法研究

A method of structural shape optimization based on Kriging model

建立了一种进行结构形状优化的工程方法。该方法利用试验设计法选取位置变量样本点,并对各个样本点对应的结构进行尺寸优化,然后根据样本点和尺寸优化结果建立Kriging代理模型,再利用遗传算法求出位置变量最优解,进而得到结构最优解。最后进行了15杆平面拱式桁架、悬臂梁和25杆空间桁架三个形状优化算例,算例分析结果表明:该方法思路清晰、适应性强、优化效果明显,具有较大的工程应用价值。

A structural optimization method for shape and size is built in this paper. In this method the samples of shape variables are created by ex corresponding to these samples are analyzed perimental design methods, the responses of the structure by FEM with size optimization method, the approximation model of Kriging which can be used to determine the responses of the structure is derived through the responses analyzed, the optimal locations of structural elements are found with genetic algorithms （GA） based on the approximation model, and, finally, the optimal sizes of structural elements corresponding to the optimal locations are found with FEM. A planar truss, a cantilever and a spatial truss are analyzed and optimized. The results of the three examples show that this method has good adaptation and the ability to find out approximate global optimal solutions, and it can be used in shape optimization of complicated structures conveniently.