Multi-Objective Topology Optimization of Heat Conduction and Linear Elastostatic using Weighted Global Criteria Method

Abstract

Multi-Objective Topology Optimization is a tool for finding lowweight solutions using a discretized geometry of several objective functions. In this contribution, the coupling of heat conduction and elastostatics is covered using the global criteria method. For the comparison of the different objectives and objective distributions typically the single target optimized solutions are selected as normalization criteria [1], [2]. The use of these optimized results requires additional calculation effort, so that this work uses the objective distribution of full material properties instead. For the normalization, the objective distributions will be standardized, and quantile normalized. The normalization strategies are compared to each other by the number of iterations and the resulting objective value.

Nodal Cosine Sine Material Interpolation in Multi Objective Topology Optimization With the Global Criteria Method for Linear Elasto Static, Heat Transfer, Potential Flow and Binary Cross Entropy Sharpening

“…The use of topology optimization is applied in many different areas, such as elasto static (Denk et al, 2020;Proos et al, 2001;Zolfagharian et al, 2020bZolfagharian et al, , 2020a, heat conduction (Dede, 2009;Denk et al, 2020;Gersborg-Hansen et al, 2006;Kim et al, 2006;Rodríguez and Pavanello, 2015), fluid mechanics (Dede, 2009), electrostatic (Gupta et al, 2015) or structural dynamics (Kim et al, 2006;Proos et al, 2001). The authors of (Alberto and Sigmund, 2004) summarize several physic types such as electrostatic fields, potential flow, or heat conduction described by the Poisson equation for topology optimization.…”

“…Figure 1: Multiobjective optimization with the ratio weighted sum of (Denk et al, 2020) Most of the multiobjective optimizations (Dede, 2009;Denk et al, 2020;Kim et al, 2006;Proos et al, 2001;Rodríguez and Pavanello, 2015) are applied on element based material interpolation. So nodebased material interpolation strategies required in (Gupta et al, 2015) cannot be used.…”

“…To summarize our contribution, our research addresses nodal-based material interpolation. We applied the nodal interpolation method on different tasks such as fluid flow, heat transfer, and elasto static by extending the global criteria method proposed in our recent work (Denk et al, 2020). Additionally, we use a new continuous material interpolation based on the cosine/sine function and compare that approach with several material interpolation methods in the literature.…”

“…This work addresses the multiobjective topology optimization using a continuous material interpolation, which extends our previous approach presented in (Denk et al, 2020). Despite recent publications, we choose an interpolation shape function method based on trigonometric functions.…”

Euclidian Distance Transformation, Main Axis Rotation and Noisy Dilitation Supported Cross-Section Classification With Convolutional Neural Networks

“…These curve skeletons serve as a reasonable shape descriptor for tube-like organic geometries (Tagliasacchi et al, 2016). Such geometries can be derived in topology optimization for linear elastic static, heat transfer, or considering both (Denk et al, 2020b). These skeletonization methods in reverse engineering are often applied to organic and tube-like shapes leading to circular cross-sections (Denk et al, 2020a;Kresslein et al, 2018;Nana et al, 2017).…”