Shape optimization of structures with cutouts by an efficient approach based on XIGA and chaotic particle swarm optimization

Structural shape optimization is one important and crucial step in the design and analysis of many engineering applications as it aims to improve structural characteristics, i.e., reducing stress concentration and structural weight, or improving the stiffness, by changing the structural boundary geometries. The goal of this paper is to present an efficient approach, which goes beyond limitations of conventional methods, by combining extended isogeometric analysis (XIGA) and chaotic particle swarm optimization algorithm for shape optimization of structures with cutouts. In this setting, mechanical response of structures with cutouts is derived by the non-uniform rational B-spline (NURBS) and enrichment techniques. The computational mesh is hence independent of the cutout geometry, irrelevant to the cutout shape during the optimization process, representing one of the key features of the present work over classical methods. The control points describing the boundary geometries are defined as design variables in this study. The design model, analysis model, and optimization model are uniformly described with the NURBS, providing easy communication among the three aforementioned models, resulting in a smooth optimized boundary. The chaotic particle swarm optimization (CPSO) algorithm is employed for conducting the optimization analysis. Apart from that, the CPSO has some advantages as it includes: (i) its structure is simple and easy to implement; (ii) without the need for the complicated sensitivity analysis as compared with the traditional gradient-based optimization methods; and (iii) effectively escaping from the local optimum. The accuracy and performance of the developed method are underlined by means of several representative 2-D shape optimization examples.