Principal Stress Lines (PSLs)-guided discrete topology designs for self-similar porous infills in shell structures with fractal geometry

Abstract

Although the optimization design for engineering structures to improve mechanical performance has gained a wide of discussions in recent years, the potential in the industry design and the considerations of structural aesthetics are extensively limited. In the current work, the main intention is to propose a new design method for shell structures, where the generation of the Principal Stress Lines (PSLs) and the fractal geometry are seamlessly coupled to achieve self-similar porous infill designs. Firstly, the implementation algorithm for shell structures with the NURBS (Non-uniform Rational B-splines)-based isogeometric analysis (IGA) is developed to generate the dense distribution of the PSLs in the whole domain, and the main transmission paths of the imposed loads are extracted to be the discrete topology designs for shell structures, which are applied to determine the overall layout of the stiffeners, namely primarily bearing-load bars, in the domain to improve structural performance. Secondly, the fractal geometry with several principles is considered to develop the numerical flowchart of the self-similar porous infill designs in shell structures, where the above stiffeners determine the layout compactness of porous unit cells in unique local regions. The Variable Period Voronoi Tessellations (VPVT), which are the self-similar generation mechanisms using the iterated function system, are employed to maintain structural manufacturability and a higher aesthetic appeal. Finally, several numerical examples with multiple loads and conditions, particular the engineering structure of the satellite fairing, are discussed to demonstrate the effectiveness and superiority of the proposed design method.