细分曲面边界元法的黏附吸声材料结构拓扑优化分析

等几何分析采用样条基函数构造几何模型和实施变量近似,实现了计算机辅助设计和辅助工程的无缝连接,并已广泛应用于弹性力学、电磁场和位势问题等领域.然而直接采用等几何方法难以构造复杂模型,限制了该方法在大规模实际工程问题上的应用.细分曲面法可用于克服这一问题,该方法对传统模型的离散网格进行细分和拟合操作,构造出极限光滑曲面,连续性更高,对复杂结构的适用性更强.该方法主要有以下优点:(1)适用于任意拓扑结构;(2)数值计算稳定;(3)实施简单;(4)局部细化与连续性控制.由于该方法在复杂结构模型构造方面具有较强的灵活性和便利性,已被广泛应用于航空航天、汽车、动画、游戏制作等建模领域.将细分曲面法与边界元法相结合进行结构声学分析,几何场与物理场均采用箱样条基函数进行插值近似.以黏附吸声材料结构的声散射问题为例,建立吸声材料分布拓扑优化数学模型,并采用移动渐进线算法进行设计变量更新,最终获得最优材料分布. 

TOPOLOGY OPTIMIZATION ANALYSIS OF ADHESIVE SOUND ABSORBING MATERIALS STRUCTURE WITH SUBDIVISION SURFACE BOUNDARY ELEMENT METHOD

Isogeometric analysis (IGA) realizes the seamless integration of CAD and CAE by using spline basis functions to represent geometric models and implement the numerical analysis, and is widely used in elastic mechanics, electromagnetic field, potential problem and other fields. However, it is difficult to construct directly a complex structure by using IGA. The subdivision surface method can be used to subdivide and fit the discrete mesh of a traditional model in order to construct smooth surfaces. Such a method is suitable for complicated problems. This method has the following advantages: (1) It is suitable for any topological structure; (2) The numerical calculation is stable; (3) It is simple to implement; (4) Local refinement and continuity control. Because of its flexibility and convenience in the construction of complex structural models, this method has been widely used in aerospace, automobile, animation, game making and other modeling fields. The subdivision surface method (SSM) and the boundary element method (BEM) were integrated to perform structural acoustic analysis. The box-spline interpolation of SSM was used for both geometric interpolation and physical interpolation, achieving high-order approximation of the structural surface and physical field. The acoustic scattering of the structure of adhesive sound absorption materials was taken as an example to test the effectiveness of the algorithm. The above analysis was combined with the method of moving asymptotes (MMA) algorithm to conduct a topological optimization of the distribution of sound absorption materials. In this study, the adjoint variable method and the acoustic BEM were used to analyze the sensitivity of the distribution of sound absorption materials on the surface of the structure. Each update of design variables brings small changes in the layout of sound absorbing materials, and ultimately the optimal solution is obtained. The resulting solvers provide an efficient computational tool for topology optimization design. The proposed algorithm is then applied to some numerical examples to illustrate the potential for engineering optimization design.