基于多点自由度约束的方向性保形拓扑优化设计方法

A Directional Shape-Preserving Topology Optimization Method With Multi-Point Constraints

保持飞行器气动面、功能面等型面的精确外形是飞行器刚度设计的重要内容.为控制飞行器结构局部区域的翘曲变形模式,抑制特定方向上有害的翘曲变形,提出考虑结构方向性保形约束的拓扑优化设计新方法.一方面,引入由保形区域内有限控制点生成的人工附加弱单元(artificial weak elements,AWEs),使控制点各自由度位移通过多点自由度约束(multi-point constraints,MPCs)传递到AWEs上,约束AWEs的变形能可以实现对保形区域翘曲变形的抑制;另一方面,合理配置多点自由度约束,将需要抑制的特定方向上自由度耦合到AWEs上,从而实现方向性保形优化设计.数值算例证明所提出的优化设计方法能在结构刚度拓扑优化设计的基础上实现对局部保形区域在特定方向上翘曲变形的有效控制,与已有约束所有自由度翘曲变形的保形拓扑优化设计相比,方向性保形优化设计在变形控制效果上更加具有灵活性.

Shape preservation of aerodynamic surfaces and functional surfaces was an important aspect in aircraft stiffness design. An extended topology optimization method was presented with directional shape-preserving constraints, which suppressed the warping deformation of structural local domains in particular directions and generated required deformation patterns. On the one hand, artificial weak elements （AWEs） were established with respect to the finite control points in local shape-preserving domains. Multi-point constraints （MPCs） were further applied to transfer nodal displacements at the control points to nodes of the AWEs. Strain energy of the AWEs was then constrained to suppress the warping deformation. On the other hand, the MPCs were properly defined to transfer only the displacements of the specified degrees of freedom to be suppressed. Directional shape preservation was in turn achieved. The numerical examples and optimized designs prove the validity of the proposed method in maintaining directional shape preservation based on the stiffness maximization topology optimization. Compared with the existing shape-preserving topology optimization design method, the proposed directional shape-preserving one brings more flexibility in controlling the local structural deformation.