周期性两相层状带隙材料优化模型  

The optimaztion model of two-phase periodic layered band-gap material

作　　者：黄毓[1] 刘书田[1] 陈文炯[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室工程力学系,大连116023

出　　处：《计算力学学报》2012年第6期811-818,共8页Chinese Journal of Computational Mechanics

基　　金：国家重点基础发展(973)计划(2011CB610304);国家自然科学基金(11172052);高等学校博士学科点研究基金(20090041110023)资助项目

摘　　要：研究并建立了一种在给定频段具有带隙性质的周期性两相层状材料的优化设计模型。首先基于层状材料波传播问题的解析解,得到了波数余弦函数与层状材料微结构参数间的解析表达式。进而分析了波数余弦函数与衰减系数的关系,提出了以波数余弦函数的平方在给定频段的积分为弹性波带隙特性的描述指标,以最大化该指标实现在给定频段使弹性波衰减系数最大化的思想,建立了设计在给定频段具有最优带隙性质的周期性两相层状材料优化提法和求解方法。最后,以几个典型的设计算例为对象,得到了给定微结构尺度约束下在特定频段具有最优带隙性质的材料微结构参数,讨论了材料微结构尺寸对最优材料结构参数的影响,以及最优结构参数对材料带隙性质的鲁棒性,验证了本文优化模型的有效性。A simple design optimization formulation is investigated and developed for two-phase periodic layered material with band gaps in specified frequency ranges. First, based on the analytical solution of elastic wave propagation in periodic layered material, an analytical solution of cosine function of wave number and the configurations of the microstructure in periodic layered material is obtained. Next, the relation between cosine function of wave number and attenuate coefficient is analyzed, and the band gap characteristic is descripted as an index which is integration of cosine function of wave number in given frequency ranges, such that the idea of maximizing attenuate coefficient within given frequency ranges can be carried out by maximizing this index, then the optimization formulation and the solving strategy of designing two-phase periodic layered material with band gaps in specified frequency ranges are formula- ted. Finally, the effectiveness of the optimization design model is demonstrated by several design exam- pies,optimal configurations of the material subject to certain scale constraints of the microstructure are obtained,and both the influences of scale constraints on the optimal configurations and the robustness of the optimal configurations on the band gap characteristics are discussed.

关 键 词：材料设计 弹性波带隙 优化模型 约束函数 鲁棒性 

分 类 号：O347.41[理学—固体力学]