Adaptive topology optimization under suitably graded THB‐spline refinement and coarsening.

In the present work, we propose an adaptive topology optimization (TO) method under suitably graded truncated hierarchical B‐spline refinement and coarsening (SGTHB‐TO). A series of algorithms have been devised to implement admissible adaptivity of SGTHB‐TO by resorting to the definitions of suitably graded isogeometric hierarchical meshes. We apply the proposed SGTHB‐TO method to two‐dimensional and three‐dimensional TO problems of compliance and compliant mechanism. According to the numerical results, SGTHB‐TOs with or without admissible restriction share similar optimization processes, except that numerical artifact, such as edge blurring and islanding gray regions occurring in SGTHB‐TO without admissible restriction, can be eliminated by SGTHB‐TO with admissible parameter equaling to 2. Besides, the convergence rate can be largely accelerated by imposing an admissible constraint on SGTHB‐TO for TO problems with geometric nonlinearity existing in the design domain, which is attributed to the improved numerical accuracy by the admissible adaptive discretization scheme of isogeometric analysis (IGA). Therefore, the SGTHB‐TO method with the admissible parameter equaling to 2 is a more effective adaptive TO method than SGTHB‐TO without considering admissible restriction, in terms of both numerical stability and convergence rate. [ABSTRACT FROM AUTHOR]