Cellular level set in B-splines (CLIBS): a method for modeling and topology optimization of cellular structures

In this work, we develop a level set modeling technique for designing and optimization of solid/cellular structures, called cellular level set in B-splines (CLIBS). In this technique, the entire design domain for the solid/cellular structure in question is subdivided into a set of connected volumetric cells in three dimensions. In the level set scheme for representing the structural geometry, an implicit trivariate B-spline function is defined on each subdomain cell. This parameterization scheme allows us to impose constraints on the relevant B-spline coefficients for naturally maintaining geometric continuities at the connection faces between neighboring cells. Benefiting from the intrinsic properties of the trivariate B-spline functions, the method offers several useful properties and powerful functionalities to build and modify a solid/cellular structure in the modeling process and to conduct topology optimization. These processes are directly dealt with in terms of the B-spline coefficients with great numerical efficiency. While the model construction can be carried out in a use of the fast B-spline interpolation, the topology optimization may involve a sequence of discrete B-spline convolutions. Several 3D modeling and optimization examples are presented, including single-scale solid structures, periodic cellular structures and layered cellular structures. The proposed method is highly scalable, potentially leading to high definition modeling and optimization applications on a large-scale computing platform.