Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem.

This study presents the incorporation of the effective gradient‐free proportional topology optimization algorithm into the framework of isogeometric analysis. The minimization of the compliance is considered, and the solid isotropic material with penalization method is used. The geometry, displacements, and density are all described by non‐uniform rational B‐spline (NURBS) basis functions. The density at an integration point is determined proportionally to its compliance. Then, the NURBS description of the density is constructed elementwise by deriving a relation between densities assigned to integration points and control points. The global NURBS description of the density for the whole domain is a blend of those from elements. Furthermore, a multiresolution scheme is presented by means of k$$ k $$‐refinement technique to enable the efficient performance for large‐scale problems. The accuracy and efficiency of the proposed approach are assessed through six numerical examples, including two‐ and three‐dimensional structures, with several rigorous tests and comparisons with the gradient‐based optimality criteria algorithm. [ABSTRACT FROM AUTHOR]