多位移约束下渐进结构拓扑优化设计

发布时间：2018-02-10 07:03

本文关键词： 多位移约束渐进结构优化拓扑优化拉格朗日乘子　出处：《现代制造工程》2017年08期 　论文类型：期刊论文

【摘要】：渐进结构优化方法通用性好,程序实现简单,能获得一系列黑白分布的优化拓扑,但它难于求解多约束拓扑优化问题。为了将渐进结构优化方法拓展到求解多约束拓扑优化问题,针对多位移约束下结构体积最小的结构拓扑优化问题,采用有理分式材料模型,建立刚度与拓扑变量的关系;构建求解多约束拉格朗日乘子的近似优化问题模型和其光滑对偶算法;而后,给出单元灵敏度数计算公式和渐进结构优化算法;最后给出了两个验证算例,所得结果验证了该方法的正确性和有效性。
[Abstract]:The asymptotic structure optimization method has the advantages of good generality, simple program implementation and a series of black and white distribution optimization topologies. But it is difficult to solve multi-constrained topological optimization problem. In order to extend the asymptotic structural optimization method to solve multi-constrained topological optimization problem, the rational fractional material model is used to solve the structural topology optimization problem with minimal volume under multi-displacement constraints. The relationship between stiffness and topological variables is established, the approximate optimization model and its smooth duality algorithm for solving Lagrange multipliers with multiple constraints are constructed, and the formulas for calculating the sensitivity number of elements and the asymptotic structure optimization algorithm are given. Finally, two verification examples are given, and the results show that the method is correct and effective.
【作者单位】：长沙理工大学汽车与机械工程学院;长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室;长沙理工大学工程车辆安全性设计与可靠性技术湖南省重点实验室;
【基金】：国家自然科学基金项目(11372055,11302033)
【分类号】：TH122

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