基于密度体积插值方法的结构拓扑优化

发布时间：2017-12-31 04:42

  本文关键词：基于密度体积插值方法的结构拓扑优化　出处：《中国机械工程》2017年11期 　论文类型：期刊论文

  更多相关文章： 插值方法 变密度法 位移约束 拓扑优化

【摘要】：针对变密度法结构拓扑优化中灰度单元的控制问题,提出了一种密度体积插值方法。该方法构造的刚度与相对密度之间的线性关系保证了迭代中单元刚度变化的稳定性;构造体积与相对密度之间的惩罚关系以实现惩罚中间密度,同时更有利于在中间密度向两端逼近的同时降低灰度单元的数量。应用该插值方法对位移约束体积最小化问题进行求解,所得结果显示,增大惩罚程度,优化过程浮动较小,算法相对稳定。与应用SIMP方法和RAMP方法的优化结果相比较可知,在求解同一结构拓扑优化问题时,采用该方法且增大惩罚程度后的优化结果中灰度单元减少明显。
[Abstract]:The control problem of gray element in topology optimization of variable density method is discussed. A density volume interpolation method is proposed, in which the linear relation between stiffness and relative density ensures the stability of element stiffness in iteration. The penalty relation between volume and relative density is constructed to realize the penalty intermediate density. At the same time, it is more favorable to reduce the number of gray elements while the intermediate density is approaching both ends. The proposed interpolation method is used to solve the displacement constrained volume minimization problem. The results show that the penalty degree is increased. Compared with the optimization results of SIMP method and RAMP method, when solving the same structural topology optimization problem, the optimization process is small and the algorithm is relatively stable. By using this method and increasing the penalty degree, the gray units of the optimization results are obviously reduced.
【作者单位】： 燕山大学先进锻压成形技术与科学教育部重点实验室;
【基金】：国家自然科学基金资助项目(51575474) 河北省自然科学基金资助项目(E2015203223)
【分类号】：TH122
【正文快照】： 0　引言自1988年BENDSOE等[1]提出用于求解连续体拓扑优化的均匀化方法以来,连续体结构拓扑优化一直是结构优化领域研究的热点。变密度法[2-5]是在均匀化方法的基础上发展形成的一种算法,该方法由于建模简单、易于求解等特点而得到了广泛应用[6-7]。变密度法中常用的密度插值，

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