本文把ICM方法中的过滤函数和变密度方法中的惩罚函数统称为映射函数,研究了该函数的选取问题,探讨了其选取对于结构拓扑优化优化迭代收敛效率的影响.为此,本文提出了高效率收敛的映射函数构造途径,写出了 5类常见的具体映射函数形式,提出同高效率收敛映射函数MFHEC(Mapping function with highly effi-cient convergence)相配套的优化模型和寻优解法,先是自行比较了同类映射函数的过滤函数和准过滤函数寻优中收敛的快慢,然后相互比较了不同形式映射函数的快滤函数寻优收敛的快慢.以ICM方法求解位移约束下结构体积极小的拓扑优化问题为例,通过数值计算比较,印证了 MFHEC函数的高效率收敛性.结果表明:同类函数比较中,快滤函数的收敛速度更快;5种不同类型映射函数比较中,幂函数形式的过滤函数收敛速度更快.最后需要强调的是:本文研究的映射函数的结论,包括ICM方法的过滤函数和变密度方法中的惩罚函数,二者都是同样适用的.
Selecting Mapping Function with Highly Efficient Convergence(MFHEC)for ICM Method of Structural Topology Optimization
In this paper,the filter function in the ICM method and the penalty function in the variable density method are both referred as the mapping functions.Different forms of mapping functions have a significant impact on the convergence efficiency of structural topology optimization.Therefore,it is neces-sary to study how to construct a suitable mapping function for the optimization model.Aimed at this prob-lem,how to construct and select a mapping function in the establishment of the structural topology optimi-zation model is studied,and the influence of different mapping functions on the convergence efficiency of structural topology optimization is discussed.An approach is proposed to construct a mapping function to achieve high-efficiency convergence in structural topology optimization.Five common forms of mapping functions are also given.An optimization model and a solution algorithm matching the mapping function with highly efficient convergence(MFHEC)are proposed.Firstly,the convergence rates of the filter func-tion and the quasi-filter function of the same form of mapping functions are compared.Then the conver-gence rates of the fast filter function of different forms of mapping functions are compared.Taking the structural topology optimization problem of minimizing structural volume under displacement constraints as an example,the ICM method is adopted to establish the models and solve the problems.The higher con-vergence efficiency of MFHEC is verified by the results of numerical comparison.The results show that the fast filter function has a faster convergence rate than other functions in the same form of mapping func-tions.Compared with five different forms of mapping functions,the filter function of power function form has the fastest convergence efficiency.Finally,it should be emphasized that the conclusions of the mapping function studied in this paper are equally applicable to the filter function of the ICM method and the penal-ty function of the variable density method.The proposed method for constructing MFHEC is very useful for improving the efficiency of the ICM method and the variable density method.
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