Multiobjective and multi-physics topology optimization using an updated smart normal constraint bi-directional evolutionary structural optimization method

Abstract

To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.

Multi-physics bi-directional evolutionary topology optimization on GPU-architecture

“…The initial and final structure is shown in Figure 2. The final design obtained using the CPU code has been validated in previous numerical studies (Munk et al (2017(Munk et al ( , 2018a). The compliance of the initial structure is 5.13 × 10 9 Nm, whereas the final structure has a compliance of 2.281 × 10 9 Nm.…”

“…For a more in-depth overview of the LBM, interested readers should seek out the textbook by Succi (2001). For details on how the LBM and FEA are coupled, the reader is advised to seek out the previous works by the authors on this topic (Munk et al (2017(Munk et al ( , 2018a).…”

“…2(a)) has a symmetry about the x-and y-axis, which is lost with the use of the single-precision GPU code. Further, it is known that the optimal structure for this particular problem should be symmetric, since the physics of the problem does not contain any unsymmetrical behavior (Munk et al (2017(Munk et al ( , 2018a). Secondly, there is clear evidence of numerical errors in the topology (Fig.…”

“…This may be because Computational Fluid Dynamics (CFD) is a much more computationally intensive task compared with FEA. Recent studies have shown the potential of LBM methods in multi-physics topology optimization (Pingen et al (2007(Pingen et al ( , 2009; Makhija et al (2012); Laniewski-Wollk and Rokicki (2016); Munk et al (2017Munk et al ( , 2018a). Further, since the LBM operates on a finite difference grid, is explicit in nature and requires only next neighbor interaction, it is very suitable for implementation on GPUs (Tölke and Krafczyk (2008)).…”

On the effect of fluid-structure interactions and choice of algorithm in multi-physics topology optimisation

“…Most recently, Munk et al (2017a) coupled a BESO algorithm to a LBM for the design of micro fluidic mixers with the fluid-structural coupling present. They then extended this method to include multiple objective topology optimisation problems with design-dependent pressure loads (Munk et al (2018)).…”