On minimum length scale control in density based topology optimization

Abstract

This is the published version of a paper published in Structural and multidisciplinary optimization (Print). Citation for the original published paper (version of record):Hägg, L., Wadbro, E. (2018) On minimum length scale control in density based topology optimization AbstractThe archetypical topology optimization problem concerns designing the layout of material within a given region of space so that some performance measure is extremized. To improve manufacturability and reduce manufacturing costs, restrictions on the possible layouts may be imposed. Among such restrictions, constraining the minimum length scales of different regions of the design has a significant place. Within the density filter based topology optimization framework the most commonly used definition is that a region has a minimum length scale not less than D if any point within that region lies within a sphere with diameter D > 0 that is completely contained in the region. In this paper, we propose a variant of this minimum length scale definition for subsets of a convex (possibly bounded) domain. We show that sets with positive minimum length scale are characterized as being morphologically open. As a corollary, we find that sets where both the interior and the exterior have positive minimum length scales are characterized as being simultaneously morphologically open and (essentially) morphologically closed. For binary designs in the discretized setting, the latter translates to that the opening of the design should equal the closing of the design. To demonstrate the capability of the developed theory, we devise a method that heuristically promotes designs that are binary and have positive minimum length scales (possibly measured in different norms) on both phases for minimum compliance problems. The obtained designs are almost binary and possess minimum length scales on both phases.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

“…Based on the threefield SIMP method, a robust formulation considering corrosion and expansion operations as well as a geometric constraint method without additional finite element analysis were proposed [44,45]. Meanwhile, the minimum length scale control of the topology design can be imposed using a structural skeleton [46] and an image morphology operator [47]. It is worth noting that the length scale control was not applied to the topology optimization of harmonic excitation structures in previous studies.…”

A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems

“…Numerical methods for the design optimization of technical systems are of great interest in science and engineering. Applications include the optimization of mechanical structures [ 2 , 29 ], electromagnetic devices [ 5 , 19 ], fluid flow [ 21 ], heat dissipation [ 20 ] and many more. There exist several different approaches to computational design optimization.…”

Inverse Design of Photonic Devices with Strict Foundry Fabrication Constraints

“…In contrast, topology optimization strategies open up a much larger design landscape by parametrizing a design as a pixelated image, which is typically transformed by a sequence of convolutional filters and pixel-wise nonlinear functions. ,− These so-called density or three-field parametrizations allow a gradient-based optimization algorithm (e.g., LBFGS or MMA) to modify any pixel within the design and apply arbitrary changes to the topology. In practice, however, there is often a trade-off between maintaining design feasibility (binarization of the pixels and feature size constraints) and attaining high performance.…”