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基于水平集法的薄板加强筋分布优化理论研究
引用本文:崔荣华,崔天晨,孙直,张维声,郭旭.基于水平集法的薄板加强筋分布优化理论研究[J].固体力学学报,2018,39(6):587-593.
作者姓名:崔荣华  崔天晨  孙直  张维声  郭旭
作者单位:1. 大连理工大学运载工程与力学学部;2. 大连理工大学工业装备结构分析国家重点实验室;
基金项目:National Natural Sciences Foundation of China;National Natural Sciences Foundation of China;National Natural Sciences Foundation of China;Natural Science Fundation of Liaoning Province
摘    要:基于水平集方法,提出薄板加强筋分布的拓扑优化理论。采用Kirchhoff板单元,通过刚度等效,分别使用不同的抗弯刚度表征薄板与加强筋,继而通过水平集方法描述加强筋的布局并进行加强筋分布拓扑优化。以最小柔顺度为设计目标,进行了几种典型载荷下加筋板结构的加筋分布优化设计,通过与变密度方法(SIMP)结果以及现有文献设计结果进行对比,验证了本文提出的加强筋分布拓扑优化理论。结果显示,本文方法能够避免灰度单元,获得清晰的加强筋优化布局和尺寸。

关 键 词:拓扑优化  加筋板  水平集方法  薄板  等效刚度  topology  optimization    stiffened  plate    level  set  method    thin  plate    equivalent  stiffness  
收稿时间:2018-06-28

TOPOLOGY OPTIMIZATION FOR STIFFENER LAYOUT OF THIN PLATE STRUCTURES BASED ON LEVEL SET METHOD
Abstract:A topology optimization approach for stiffener layout of thin plate structures is proposed based on level set method. The thin plate and stiffeners are considered as plates with different bending stiffness, with use of equivalent stiffness method. Then the location of stiffeners were described by Level set method to perform topology optimization. With the objective of maximizing structural stiffness, several typical cases with various loading and boundary conditions were selected as numerical examples. The optimized stiffened plates of the proposed method were compared with optimized results in literatures to verified the validity of the proposed method. Numerical examples showed that the proposed method can provide clear stiffener layout and avoid “gray elements”.
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