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

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.