基于光滑变形隐式曲线的模型重构、应力分析与优化设计一体化方法

An Integrated Approach of Model Reconstruction, Stress Analysis and Optimization Design via Smoothly Deformable Implicit Curves

为克服传统计算机辅助结构优化设计方法中几何建模、力学性能分析和优化设计3个阶段相互割裂和模型转换耗时费力的不足,提出一种基于光滑变形隐式曲线的一体化优化设计方法.首先借鉴扩展超二次曲线的构建思想,定义一种参数少且变形能力强的隐式光滑曲线,并结合R函数对待优化结构进行模型重构;然后利用有限胞元分析方法,在固定网格下对所重构的隐式模型进行高精度应力分析;最后建立起包含von Mises应力约束的以体积最小化为目标的结构优化模型,并推导出相应的灵敏度解析计算公式.通过对典型支架结构实施模型重构、应力分析和优化设计,验证了文中方法的有效性.

In conventional computer aided optimization design methods, the three processes including geometric modeling, mechanical analysis and optimization design are independent of each other, and consequently the model transformation among them takes lots of time and effort. To overcome this deficiency, an integrated opti- mization design framework is proposed based on smoothly deformable implicit curves. Firstly, the smoothly de- formable implicit curve, which is characterized by very few parameters and high deformation capacity, is formu- lated according to the construction idea of extended superquadrics, and it is further combined with R-functions for implicit model reconstruction. Secondly, finite cell method is utilized to predict the stress response of the recon- structed implicit model with high precision within an extended, regular and fixed Eulerian mesh. Thirdly, the mathematic model of structure optimization is established by taking yon Mises stress as constraint and volume minimization as the objective, and the corresponding calculation formulas of analytical sensitivities are deduced. Finally, the validity of the proposed method is verified with the geometric modeling, stress analysis and optimiza- tion design of a classical bracket structure.