Parametric structural optimization of 2D Complex shape based on isogeometric analysis

The geometric model and the analysis model can be unified together through the isogeometric analysis method, which has potential to achieve seamless integration of CAD and CAE. Parametric design is a mainstream and successful method in CAD field. This method is not continued in simulation and optimization stage because of the model conversion in conventional optimization method based on the finite element analysis. So integration of the parametric modeling and the structural optimization by using isogeometric analysis is a natural and interesting issue. This paper proposed a method to realize a structural optimization of parametric complex shapes by using isogeometric analysis. By the given feature curves and the constraints, a feature frame model is built. Based on the feature frame model, a parametric representation of complex shape is obtained. After adding some auxiliary curves, the feature frame model is divided into many box-like patches in three dimension or four-sided patches in two dimension. These patches are built into parametric patches by using volume interpolation methods such as Coons method. Based on the parametric patches, isogeometic analysis is applied. Thus, the relationships are constructed among the size parameters, the control points and the physical performance parameters. Then the sensitivity matrix could be derived based on the relationships. The size optimization is carried out in the first stage by taking the size parameters as variables. Based on the result of size optimization, shape optimization with the constraints of stress is carried out in the second stage by taking the control points as variables. Serval planar complex shapes are taken as example to verify our method. The results verify that the parametric modeling and structural optimization can be united together without model conversion. Benefit from this, the optimization design can be executed as a dark box operation without considering the concrete modeling and analysis by input of the sizes, constraints and loads.