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

Abstract

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.

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

“…Vector λ contains the unknown temperature and flux coefficients corresponding to the NURBS basis functions. The (known) right hand side vector b contains not only the vector y but also the products of the terms in ũ and t that are prescribed boundary conditions and the corresponding columns of H and G. By solving the linear system in (43), all the unknown coefficients of temperature and heat flux can be obtained. The temperature and flux density distributions around the boundary can then be recovered from ( 23) and (24).…”

“…Since the initial IGA was based on NURBS [6] which contains a tensor product form, the uniform NURBS-based refinement scheme is difficult to capture local features of interest. In order to ameliorate this difficulty, the method has been extended to T-splines [41,42], THB-splines [43], hierarchical B-splines (HB) [15], LR-splines [44], hierarchical box splines [45] and Powell-Sabin B-splines [46].…”