In this study, a patch removing based Isogeometric analysis (PR-IGA) method is proposed to conduct the holed structural analysis with only one parametric domain, in which there are also no trimmed elements. The theoretical foundation of this novel patch removing approach is that any holed structure can be obtained by removing sub-patches (i.e., the holes) from an intact base patch. Since the parametric domains of these patches are all meshed by rectangular grids, the elements in the resulted holed structural parametric domain could all be untrimmed rectangles under certain mapping conditions. To achieve the special condition, a systematic technique consisting of T-spline local refinement and control points substitution/adjustment is provided. Due to the intactness of parametric elements, the analysis procedure of holed structures based on the proposed PRIGA is quite simplified and efficient compared to traditional multi-patch and trimming schemes. Moreover, after the deduction of analytical sensitivities related to structural mass and mechanical responses, the PR-IGA is directly employed in the holed structural shape optimization to successfully eliminate the need for model transformation during modeling, analysis and optimization processes. Numerical examples involving analysis and shape optimization of complex holed structures are presented to demonstrate the effectiveness of the proposed method.

Isogeometric analysis; patch removing; shape optimization; holed structure