涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计

Clear Structural Topology Optimization Designs Including Minimum Allowable Length Scale Limit on Fabrication Holes

针对以结构柔顺度最小为目标函数,涉及空腔制造的最小长度尺寸限制的结构拓扑优化设计问题,提出了一种新的拓扑优化求解方法。首先,为了消除现有的结构实体相及空洞相的相同的光滑Heaviside映射导致的强烈对立矛盾,引入光滑Heaviside映射和修改的光滑Heaviside映射分别进行实体相及空洞相的设计变量过滤;而后,构建了合理和协同的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化模型;利用MMA算法,形成了一种新的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化算法。给出的算例结果表明,与现有方法比,该方法可解决结构实体相和空洞相的几何最小长度尺寸控制问题。且所提方法可获得清晰0/1分布的优化结构拓扑。

For the problem of structural topology compliance minimization with a minimum allowable length scale limit on fabrication holes(void phase), a new topology optimization method of continuum structures with a volume constraint is proposed. Firstly, in order to destroy strong antagonistic contradictions brought by two same smooth Heaviside projections of the solid phase and void phase, a smooth Heaviside projection and a modified smooth Heaviside projection are introduced to make design variable filtering of the solid phase and void phase, respectively. Hence, a reasonable and coordinating structural topology optimization model with the minimum allowable length scale limits on fabrication holes and solid material, is constructed;Being integrated with the MMA algorithm, a new structural topology optimization procedure, dealing with the minimum allowable length scale limits on fabrication holes and solid material, is proposed. It is concluded from given examples that the proposed method can solve the problem of structural topology compliance minimization with the minimum allowable length scale limits on fabrication holes and solid material, and may obtain an optimal topology with more clear 0/1 distribution than the existed methods.