Catmull-Clark细分曲面边界元法的结构声学拓扑优化分析  

Structural acoustic topology optimization analysis of a Catmull-Clark subdivision surface boundary element method

作　　者：陈磊磊 王中王 卢闯 高春华 刘林超 CHEN Leilei;WANG Zhongwang;LU Chuang;GAO Chunhua;LIU Linchao(School of architecture and civil engineering,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院建筑与土木工程学院,河南信阳464000

出　　处：《振动与冲击》2020年第20期97-105,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11702238,U1504505);河南省科技攻关项目(172102210453);河南省高等学校重点科研项目(16B560009,17A560009);信阳师范学院“南湖学者奖励计划”青年项目。

摘　　要：细分曲面克服了NURBS方法进行曲面片拼接时出现缝隙的困难,并可以构建带有任意拓扑形状的光滑结构模型。对于声学问题,频率越高,波长越短,为了满足计算精度要求,用于数值分析的离散网格就需要更密,传统算法往往需要对原始结构模型重新进行网格划分,耗费了大量的计算时间。细分曲面法只需对初始离散网格进行一定的细分操作,即可提供多层次多分辨率控制网格,避免了复杂耗时的前处理操作。将Catmull-Clark细分曲面与边界元法相结合,采用高阶双三次B样条基函数进行几何与物理场的插值近似,不仅提供高计算精度结果,而且自适应满足宽频段网格要求。对于黏附吸声材料结构声散射问题,引入声阻抗边界条件,建立以吸声材料单元密度为设计变量,以吸声材料的体积分数为约束的数学优化模型。采用伴随变量法计算目标函数对设计变量的敏感度,移动渐近线法对设计变量进行更新,最终获得最优吸声材料分布。若干实际问题算例验证了算法的正确性和有效性。The use of subdivision surface overcomes the difficulty of the gap in the surface slice splicing of NURBS,and can construct the smooth and continuous overall surfaces with arbitrary free-form topology.In the acoustic field,the higher the frequency,the shorter the wavelength and the larger the number of meshes to meet the calculation accuracy required.The traditional methods require reconstruct the mesh of the original structure model,which takes a lot of time.A subdivision surface method only requires refinement operation of the initial discrete mesh,which can provide multi-level-resolution control grid to avoid complex and time-consuming pre-processing.Combining the Catmull-Clark subdivision surface with the boundary element method,the interpolation approximation of geometry and physical field was carried out by using the high-order bi-cubic B-spline basis function,which not only provides the result of higher calculation accuracy,but also satisfies the requirement of broadband mesh.For the acoustic scattering problem of the structure of the adhesive sound absorbing material,the acoustic impedance boundary condition was introduced.The mathematical optimization model was established,which takes the density of the sound absorbing material element as the design variable and the volume fraction of the sound absorbing material as the constraint.The sensitivity of the objective function to the design variables was calculated by using the adjoint variable method,and the design variables were updated by the method of moving asymptotes.Finally the optimal distribution of sound absorbing materials was obtained.The correctness and validity of the algorithm were verified.

关 键 词：细分曲面 边界元法 伴随变量法 拓扑优化 

分 类 号：O343.2[理学—固体力学]