Isogeometric Size Optimization Design Based on Parameterized Volume Parametric Models

Abstract

Traditional structural optimization design methods are based on the finite element analysis(FEA), which makes it difficult to construct a direct relationship between the design parameters and the design objective parameters in the structural design process. The FEA method needs to convert the models back and forth between the design model and the analysis or optimization model during the design process. It is a cumbersome and time-consuming work and also affects the analysis accuracy. We propose an integrated design method that seamlessly integrates process of design, simulation and optimization based on uniformity of design models, analysis models and optimization models by benefiting the advantages of volume parameterization and isogeometric analysis(IGA). The size parameters are input as high-level parameters, then the middle parameters are obtained through hierarchical mapping. Based on these parameters, the semantic feature framework composes of feature points, feature curves and feature surfaces and even feature volume is gradually constructed. By extracting paths and sections, the geometric feature framework is generated. The paths and sections are segmented to form the volume parametric sub-patches through volume parametric mapping. These sub-patches are merged into a whole volume parametric model that can be used for IGA and size driven deformation. Based on volume parametric model, a mathematical relationship is constructed between the design objective parameters and the size design parameters. Through the mathematical relationship, the sensitivity equations are derived for sensitivity analysis. Finally, an isogeometric size optimization process is complete. Thus, an integration of design process including geometric modeling, performance analysis, and structural optimization is achieved. Taking the maximum stiffness and the minimum stress as the size optimization objectives, the integrated design examples fall into four groups including single size optimization, multi sizes non-coupled optimization, multi sizes coupled optimization, and complex mechanical structure optimization. The optimization results prove that our method is effective, and it can be applied on complex mechanical parts. The designed results do not require reconstruction, thus achieving the integrated and optimized design of mechanical structures.