Abstract
Designs obtained with topology optimization (TO) are usually not safe against damage. In this paper, density-based TO is combined with a moving morphable component (MMC) representation of structural damage in an optimization problem for fail-safe designs. Damage is inflicted on the structure by an MMC which removes material, and the goal of the design problem is to minimize the compliance for the worst possible damage. The worst damage is sought by optimizing the position of the MMC to maximize the compliance for a given design. This non-convex problem is treated using a gradient-based solver by initializing the MMC at multiple locations and taking the maximum of the compliances obtained. The use of MMCs to model damage gives a finite element-mesh-independent method, and by allowing the components to move rather than remain at fixed locations, more robust structures are obtained. Numerical examples show that the proposed method can produce fail-safe designs with reasonable computational cost.
Highlights
Topology optimization (TO) has gained increasing popularity since the first article by Bendsoe and Kikuchi (1988) and the research is constantly evolving (Deaton and Grandhi 2014)
In this article we propose a method to obtain fail-safe designs by using so-called moving morphable components (MMCs) (Guo et al 2014) to model damage in the structure while using density-based TO to obtain an optimized material layout of the structure
This procedure is known as a robust formulation (Wang et al Topology optimization with MMCs is an alternative to the density-based approach which was introduced by Guo et al (2014) and Zhang et al (2016)
Summary
Topology optimization (TO) has gained increasing popularity since the first article by Bendsoe and Kikuchi (1988) and the research is constantly evolving (Deaton and Grandhi 2014). Ambrozkiewicz and Kriegesmann (2018) examined how well the algorithm by Zhou and Fleury (2016) performed and found that it was sensitive to damage zones which weren’t included in the optimization They proposed their own method where they used the stress-state in the structure to divide the structure into knots and beams and each knot and beam was removed one at at time to simulate a damage to that particular place. In this article we propose a method to obtain fail-safe designs by using so-called moving morphable components (MMCs) (Guo et al 2014) to model damage in the structure while using density-based TO to obtain an optimized material layout of the structure. In the present work, socalled damage maps are used just to show that the optimized structures are fail-safe
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