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

Abstract

Topology optimization is typically used for suitable design suggestions for objectives like mean compliance, mean temperature, or model analysis. Some modern modeling technics in topology optimization require a nodal based material interpolation. Therefore this article is referred to a continuous material interpolation in topology optimization. To cover a smooth and differentiable density field, we address trigonometric shape functions which are infinitely differentiable. Furthermore, we extend a so-known global criteria method with a sharpening function based on binary cross-entropy, so that sharper solutions results. The proposed material interpolation is applied to different applications such as heat transfer, elasto static, and potential flow. Furthermore, these different objectives are together optimized using a multi-objective criterion.

Truss Parametrization of Topology Optimization Results with Curve Skeletons and Meta Balls

“…The presented parameterization can be applied to the optimization results of thermal or fluid mechanical topology optimization presented (Dede, 2009;Denk et al, 2021d). In particular, considering the minimization of thermal compliance can lead to more complex design proposals than the minimization of elastostatic compliance (Denk et al, 2020).…”

“…In particular, considering the minimization of thermal compliance can lead to more complex design proposals than the minimization of elastostatic compliance (Denk et al, 2020). Figure 9 shows such minimization of thermal compliance with (Denk et al, 2021d) for different use-caes and furthermore their skeletonization, segmentaiton and polyline simplification. The main dissatvantage of this curve skeletonization is that each shape is treated as an object that can be constructed by extruding a circular cross section.…”

Irradiation-dependent topology optimization of metallization grid patterns and variation of contact layer thickness used for latitude-based yield gain of thin-film solar modules

“…In order to perform a continuous optimization, the Solid Isotropic Material with Penalization (SIMP) approach with exponential functions is used [21][22][23][24]. Depending on the location of the evaluated element, the loss function can be sensitive up to one percent in PCE by reversing the binary grid density.…”