基于移动可变形孔洞方法的超弹性结构拓扑优化

Topology optimization of hyperelastic structures via Moving Morphable Void (MMV) approach

现有隐式拓扑优化方法在进行超弹性结构拓扑优化设计时,具有设计变量多、中间设计有限元分析存在严重的收敛性和设计结果无法直接导入CAD/CAE系统等问题。为解决这些问题,提出了一种基于移动可变形孔洞的显式拓扑优化方法来进行承受大变形的超弹性结构设计,材料本构采用常用的Mooney-Rivlin模型。首先,介绍了移动可变形孔洞方法的基本思想和可变形孔洞的显式描述方法;其次,构造了基于移动可变形孔洞方法的超弹性结构拓扑优化的数学列式,给出了相应的灵敏度结果;最后,通过数值算例验证了本方法的有效性。数值结果表明,该方法可以通过较少的设计变量和非常稳健的优化过程,给出边界由B样条曲线描述且可与CAD/CAE软件无缝连接的超弹性结构设计。

Existing implicit topology optimization methods have many issues in design of hyperelastic structures,such as the large number of design variables,convergence difficulties in finite element analysis of intermediate designs,inconsistency between the optimized designs and CAD/CAE systems.In order to overcome such issues,an explicit topology optimization method is proposed based on Moving Morphable Void(MMV)to design hyperelastic structures undergoing large deformation.The hyperelasticity is characterized by the widely-adopted Mooney-Rivlin material model.Firstly,both the basic idea underpinning the MMV-based approach and the explicit description of the morphable voids are introduced.Secondly,the mathematical formulation and the corresponding sensitivity results for the optimal design of hyperelastic structures are presented.Finally,a numerical example demonstrates the effectiveness of the proposed approach.It is verified that,by using fewer design variables,through a robust and stable optimization process,optimized hyperelastic structures with B-spline-described boundaries,which can be transferred to the CAD/CAE system directly,can be obtained by the proposed approach.