A virtual punching method for shape optimization of openings on curved panels using CAD-based Boolean operations

This paper aims at developing new methodologies for shape optimization of openings on three-dimensional curved panels that are used widely in aeronautical and aerospace engineering. To circumvent the difficulties associated with the hole boundary shape parameterization, a virtual punching method that exploits Boolean operations of the CAD modeler is proposed for the definition of shape design variables. Compared with the parametric mapping method developed previously, the virtual punching method is shown to be an implicit boundary representation for this specific kind of structure. Instead, the parametric mapping method is based on the explicit boundary representation. A zero-order genetic algorithm (GA) is correspondingly implemented into the design procedure of the virtual punching method to execute the optimization process for two reasons. First, it makes it possible to avoid sensitivity analysis that is relatively difficult due to the implicit boundary representation formulation and the use of an unstructured mesh. Second, the computing cost of the GA is practically affordable in shape optimization because often only a small number of design variables are involved. Numerical tests are carried out for typical examples of the stress concentration minimization around openings on the curved panels.