基于等几何边界元法的声学敏感度分析  

Acoustic shape sensitivity analysis using isogeometric BEM

作　　者：刘程 赵文畅 陈磊磊[2] 陈海波[1] LIU Cheng;ZHAO Wen-chang;CHEN Lei-lei;CHEN Hai-bo(CAS Key Laboratory of Mechanical Behavior and Design of Materials,Department of Modern Mechanics, University of Science and Technology of China,Hefei 230027,China;School of Civil Engineering,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]中国科学技术大学近代力学系中国科学院材料力学行为和设计重点实验室,合肥230027 [2]信阳师范学院土木工程学院,信阳464000

出　　处：《计算力学学报》2018年第5期603-610,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11772322);中国科学院战略性先导科技专项B类(XDB22040502)资助项目

摘　　要：基于非均匀有理B样条(NURBS)曲面建模技术,边界物理量同样用NURBS基函数插值,推导出三维声场等几何边界积分方程。进一步以控制点为设计变量,用直接微分法推导出等几何敏感度边界积分方程,给出声场声压对形状参量的敏感度。针对边界积分方程中的超奇异积分,使用奇异相消技术并结合Cauchy主值积分和Hadamard有限部分积分处理,给出了超奇异积分的NURBS插值半解析表达式。数值算例验证了本文算法求解声学结构形状敏感度的有效性,为声学结构的整体形状优化打下基础。An isogeometric boundary element method in three dimensional acoustics and a related sensitivity analysis are presented.The structure geometry is built by NURBS surface.In sensitivity analysis,the control points are selected as design variables,and the direct differentiation method is used.The boundary integral equations and their sensitivity boundary integral equations are formulated under isogeometric discretization.An isogeometric version of the subtracting and adding back technique is adopted to eliminate singularities,in which the Cauchy principal value and the Hadamard finite part integral methods are also used.Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

关 键 词：等几何分析 NURBS 边界元法 敏感度分析 直接微分法 

分 类 号：O348.8[理学—固体力学]