基于改进离散材料插值格式的复合材料结构优化设计

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基于改进离散材料插值格式的复合材料结构优化设计

段尊义¹, 阎军¹, 牛斌², 辛星³, 赵国忠¹

1. 大连理工大学工程力学系工业装备结构分析国家重点实验室, 辽宁大连 116024;
2. 奥尔堡大学机械工程系, 奥尔堡丹麦 DK-9220;
3. 中国航天科技集团公司四院四十一所, 陕西西安 710025

收稿日期:2011-12-22 修回日期:2012-02-21 出版日期:2012-12-25 发布日期:2012-12-24
通讯作者: 阎军 E-mail:yanjun@dlut.edu.cn
作者简介:段尊义男, 博士研究生。主要研究方向: 结构与多尺度优化。Tel: 0411-84706382 E-mail: duanzunyi@163.com
基金资助:
国家自然科学基金(90816025, 10902018, 11072049); 科技重大专项基金(2011ZX02403-002); 国家"973"计划(2011CB610304); 大连理工大学理学学科研究基金(DUT11LK05)

Design Optimization of Composite Materials Based on Improved Discrete Materials Optimization Model

DUAN Zunyi¹, YAN Jun¹, NIU Bin², XIN Xing³, ZHAO Guozhong¹

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;
2. Department of Mechanical Engineering, Aalborg University, Aalborg DK-9220, Denmark;
3. 41st Institute of the Fourth Academy, China Aerospace Science and Technology Corporation, Xi’an 710025, China

Received:2011-12-22 Revised:2012-02-21 Online:2012-12-25 Published:2012-12-24
Supported by:
National Natural Science Foundation of China (90816025, 10902018, 11072049); Major National Science and Technology Project (2011ZX02403-002); National Basic Research Program of China (2011CB610304); Science Research Foundation of Dalian University of Technology (DUT11LK05).

摘要/Abstract

摘要：

针对采用离散材料优化(DMO) 模型优化复合材料纤维分布时角度优化结果收敛率低的问题,将连续化惩罚策略与Heaviside惩罚函数引入传统DMO模型中,提出了一种改进的HPDMO (Heaviside Penalization of Discrete Material Optimization)模型,从而提高结构的收敛率。建立了复合材料单层板基于最小柔顺性设计的优化列式,给出了多种离散材料构成结构的灵敏度信息求解方法。分析比较了DMO模型、连续化惩罚模型和HPDMO模型对最终优化结果收敛率、目标函数、迭代历史的影响。数值算例表明,改进的离散材料惩罚模型不但可以显著地提高优化结果的收敛率,给出清晰的优化构型,而且可以通过较少的优化迭代步数实现这一结果,为纤维增强复合材料的优化设计在工程中的应用提供了新的技术手段。

关键词: 复合材料, 离散材料优化, 惩罚模型, 纤维铺角, 收敛率

Abstract:

An improved discrete materials optimization (DMO) model, HPDMO (Heaviside Penalization of Discrete Materials Optimization) model, is established in this paper with continuous penalization and Heaviside penalization to improve the convergence rate of the optimization results of composite materials using traditional DMO. A minimum structural compliance design model is built to optimize the distribution of ply angles of composite materials. A sensitivity analysis is carried out via the direct method based on the HPDMO model. The convergence rate of optimization results, the value of objective function and the iteration history of the traditional DMO, continuous DMO and HPDMO models are compared. Numerical example shows that the HPDMO model can not only improve significantly the convergence rate of optimization of the ply angles of composite materials and provide a clear optimization result, but also do so with a relatively small number of optimization iterations. Thus the paper presents a new approach for the optimization of composite materials in engineering structures.

Key words: composite materials, discrete materials optimization, penalization model, fiber ply angle, convergence rate

中图分类号:

V258⁺.3

段尊义, 阎军, 牛斌, 辛星, 赵国忠. 基于改进离散材料插值格式的复合材料结构优化设计[J]. 航空学报, 2012, 33(12): 2221-2229.

DUAN Zunyi, YAN Jun, NIU Bin, XIN Xing, ZHAO Guozhong. Design Optimization of Composite Materials Based on Improved Discrete Materials Optimization Model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2012, 33(12): 2221-2229.

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E-mail：hkxb@buaa.edu.cn

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基于改进离散材料插值格式的复合材料结构优化设计

Design Optimization of Composite Materials Based on Improved Discrete Materials Optimization Model

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