Abstract
This work deals with heat conduction problems formulation in the framework of a CAD-compatible topology optimization method based on a pseudo-density field as a topology descriptor. In particular, the proposed strategy relies, on the one hand, on the use of CAD-compatible Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field and, on the other hand, on the well-known Solid Isotropic Material with Penalization (SIMP) approach. The resulting method is then referred to as NURBS-based SIMP method. In this background, heat conduction problems have been reformulated by taking advantage of the properties of the NURBS entities. The influence of the integer parameters, involved in the definition of the NURBS hyper-surface, on the optimized topology is investigated. Furthermore, symmetry constraints, as well as a manufacturing requirement related to the minimum allowable size, are also integrated into the problem formulation without introducing explicit constraint functions, thanks to the NURBS blending functions properties. Finally, since the topological variable is represented by means of a NURBS entity, the geometrical representation of the boundary of the topology is available at each iteration of the optimization process and its reconstruction becomes a straightforward task. The effectiveness of the NURBS-based SIMP method is shown on 2D and 3D benchmark problems taken from the literature.
Highlights
The continuous downscaling of semi-conductor electronics in devices like smartphones and laptops, which require increasing power rates that need to be dissipated, calls for major challenges to design dedicated cooling systems [1]
As discussed in [32,33], some consequences of outstanding importance result from this approach: (1) the number of design variables is unrelated to the number of elements and a significant reduction of the design variables amount can be obtained with respect to the classical Solid Isotropic Material with Penalization (SIMP) approach; (2) the optimized topology is unrelated to the quality of the mesh of the finite element (FE) model; (3) the Non-Uniform Rational Basis Spline (NURBS) formalism allows taking advantage of an implicitly defined filter zone, whose size depends on the NURBS parameters
The results presented are obtained by means of the code SANTO (SIMP And NURBS for Topology Optimization) developed at the I2M laboratory in Bordeaux [32,33]
Summary
The continuous downscaling of semi-conductor electronics in devices like smartphones and laptops, which require increasing power rates that need to be dissipated, calls for major challenges to design dedicated cooling systems [1]. Yoon and Koo [26] developed a sensitivity analysis for TO of steady-state conductive thermal problems subject to design-dependent thermal loads using density gradients–based boundary detection, whilst Hu et al [25] presented an interesting application of TO dealing with heat transfer problems in microchannels in order to optimize their performances in terms of both heat dissipation and pressure drop. As discussed in [32,33], some consequences of outstanding importance result from this approach: (1) the number of design variables is unrelated to the number of elements and a significant reduction of the design variables amount can be obtained with respect to the classical SIMP approach; (2) the optimized topology is unrelated to the quality of the mesh of the FE model; (3) the NURBS formalism allows taking advantage of an implicitly defined filter zone, whose size depends on the NURBS parameters. Upper-case bold letters are used to indicate tensors and matrices, while lower-case bold letters indicate column vectors
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
