A space-preserving data structure for isogeometric topology optimization in B-splines space

In this work, we put forward a space-preserving data structure for isogeometric topology optimization in B-splines space, exploiting the Bezier extraction operator of B-splines. According to the space-preserving nature of Bernstein basis function space within an individual isogeometric analysis element, we derive the standard elemental stiffness matrix for all Bezier elements. With the aid of Bezier extraction matrix obtained from the knot insertion algorithm, all the elemental stiffness matrices of B-spline elements can be equivalently expressed by the aforementioned standard Bezier stiffness matrix. The data processing arrays are put forward for B-spline and Bezier isogeometric analysis meshes, which constitute the space-preserving data structure for isogeometric topology optimization. Three numerical examples are used to validate the effectiveness of the proposed space-preserving data structures for isogeometric topology optimization, where the maximum memory burden is decreased by four orders of magnitude, and the maximum computational efficiency is improved by two orders of magnitude, involved in storing and computing the essential data for the stiffness matrices of all B-spline elements, in comparison with the conventional space-varying data structure. Therefore, the proposed space-preserving data structure is a promising way of implementing isogeometric topology optimization method.