基于多相材料的连续体结构动态轻量化设计方法

doi:10.7527/S1000-6893.2017.221022

固体力学与飞行器总体设计

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基于多相材料的连续体结构动态轻量化设计方法

龙凯^1,2, 谷先广³, 王选⁴

1. 华北电力大学能源的安全与清洁利用北京市重点实验室, 北京 102206;
2. 华北电力大学新能源电力系统国家重点实验室, 北京 102206;
3. 合肥工业大学汽车与交通工程学院, 合肥 230009;
4. 大连理工大学工业装备结构分析国家重点实验室, 大连 116024

收稿日期:2016-12-05 修回日期:2017-05-31 出版日期:2017-10-15 发布日期:2017-05-31
通讯作者: 龙凯 E-mail:longkai1978@163.com
基金资助:
国家自然科学基金（51405123）；中央高校基本科研业务费专项资金（2017MS077）

Lightweight design method for continuum structure under vibration using multiphase materials

LONG Kai^1,2, GU Xianguang³, WANG Xuan⁴

1. Beijing Key Laboratory of Energy Safety and Clean Utilization, North China Electric Power University, Beijing 102206, China;
2. State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China;
3. School of Automobile and Traffic Engineering, Hefei University of Technology, Hefei 230009, China;
4. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Received:2016-12-05 Revised:2017-05-31 Online:2017-10-15 Published:2017-05-31
Supported by:
National Natural Science Foundation of China (51405123);Fundamental Research Funds for the Central University (2017MS077)

摘要/Abstract

摘要：

为了实现基于多相材料的结构轻量化设计，遵循独立连续映射法，提出了以结构总重最小化为目标和给定特征值为约束的拓扑优化模型。方法采用2类独立拓扑变量实现了单元刚度矩阵、质量矩阵和重量插值。推导了固有特征值和总重量的敏度表达式，通过1阶和2阶泰勒展开得到其近似表达式。对约束函数一次项过滤转换为偏微分方程的求解，消除了棋盘格现象和网格依赖性等数值不稳定性。通过二维数值算例验证了提出方法的可行性和优越性。结果表明，与单相组分材料拓扑优化结构相比，多相材料拓扑优化结构具有更轻的重量。通过附加相邻频率间隔约束或增加高阶频率约束，避免了模态交换现象。

关键词: 拓扑优化, 独立连续映射法, 连续体结构, 固有频率, 模态分析

Abstract:

To achieve light design of continuum structure containing multiphase materials,a topological optimization model for weight minimization with the given eigenvalue constraint is proposed using the independent continuous mapping method.Two sets of independent topological variables are employed to interpolate the elemental stiffness matrix,the mass matrix and weight.The sensitivity expressions for the eigenvalue and total weight are derived.The approximations of the eigenvalue and total weight can be obtained via the first-order and second-order Taylor expansion.The filtering technique for the first term of the constraint function is adopted as a solution to the partial differential equation.The numerical instabilities including checkerboard patterns and mesh dependence are removed.The feasibility and superiority of the proposed method are validated by two-dimensional numerical examples.The results show that the weight of the optimal structure constructed by multiphase materials is lighter than that composed of constituent phase.The mode switch can be prevented by imposing the constraint on the gap of the adjacent frequency or additional high order frequency constraint.

Key words: topology optimization, independent continuous mapping method, continuum structure, natural frequency, mode analysis

中图分类号:

龙凯, 谷先广, 王选. 基于多相材料的连续体结构动态轻量化设计方法[J]. 航空学报, 2017, 38(10): 221022-221022.

LONG Kai, GU Xianguang, WANG Xuan. Lightweight design method for continuum structure under vibration using multiphase materials[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(10): 221022-221022.

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基于多相材料的连续体结构动态轻量化设计方法

Lightweight design method for continuum structure under vibration using multiphase materials

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