论文部分内容阅读
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。
A mathematic model of steel-composite material selection and optimization based on topological distribution is established. Through continuous variable, the mapping function is used to transform the material selection and optimization model to adapt to more optimization algorithms. The original model is transformed by linear function, exponential function, logarithmic function, step function, inverse trigonometric function and piecewise function, respectively, and the corresponding material selection and optimization model is obtained and solved. Taking the optimization of material selection kinetics of floating raft as an example, the efficiency and accuracy of the optimization model under different transformations are compared. The results of the example show that in the MSO solution of logarithmic mapping based on power function mapping, although some of them have very good filtering effect in structural topology optimization, intermediate values of topological variables appear and it is difficult to make material based on topological variables In the MSO solution based on Sigmoid mapping, segment mapping and arc tangent mapping, the topological variables tend to be 0 or 1 with no intermediate value, and the topological indication is better and the optimization efficiency is higher. The reasons for the analysis may be that the material selection optimization is different from the structural topology optimization. The change of the force transmission path in the material selection optimization is not drastic and the common mapping function of topology optimization should not be adopted.