钢-复合材料组合结构材料选型优化设计映射解法

Mapping function method for hybrid steel-composite materials-structure selection optimization design

建立了基于拓扑分布的钢-复合材料组合结构材料选型优化的数学模型,通过变量连续化,用映射函数对材料选型优化模型进行函数变换,使其能适应更多的优化算法进行求解。分别采用线性函数、指数函数、对数函数、阶跃函数、反三角函数和分段函数等对原始模型进行了变换,得到相应材料选型优化模型并求解。以组合浮筏材料选择动力学优化为例,对比研究了不同函数变换下优化模型的求解效率和精度。算例结果表明:基于幂函数映射、对数映射的MSO求解中,尽管其中有的函数在结构拓扑优化中有非常好的筛选效果,但拓扑变量值出现中间结果,难以根据拓扑变量值进行材料变更;基于Sigmoid映射、分段映射和反正切映射的MSO求解中,拓扑变量无中间值,基本上趋于0或1,拓扑指示性较好,优化效率较高。分析原因,可能是材料选型优化不同于结构拓扑优化,材料选型优化中传力路径的改变不剧烈,不宜采用拓扑优化的常见映射函数。

Materials selection optimization inherently belongs to discrete optimization design which is difficult to solve by traditional optimization algorithms.In this paper,materials selection optimization formulations for hybrid steel-composite with 0-1 topological design variables are presented.The solutions are obtained by the method of continuation with variables and mapping function transformation in optimization formulations.Taken dynamic optimization design of hybrid floating raft as an example,the optimization results are compared for the linear,exponential,logarithmic,sigmoid,arc tangent,and subsection mapping functions.Computational results show that material selection optimization is quite different from the topology optimization.The variation of force transition path in material selection optimization is not sharper than that of in topology optimization under the strong mapping function transformation.