Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning, Peter D.

doi:10.1007/s00158-017-1883-1

Cited by 20 publications

(8 citation statements)

References 48 publications

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“…Besides eliminating the issue of numerical oscillations, length scale control can also ensure the mesh is sufficiently fine with respect to the design's features to properly describe its physical behavior. Methods for length scale control in parametrized level set methods have recently been proposed (Dunning 2018;Jansen 2019).…”

Section: Fig 15mentioning

confidence: 99%

An interface-enriched generalized finite element method for level set-based topology optimization

Boom

Zhang

Keulen

et al. 2020

Struct Multidisc Optim

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During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

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Section: Fig 15mentioning

confidence: 99%

An interface-enriched generalized finite element method for level set-based topology optimization

Boom

Zhang

Keulen

et al. 2020

Struct Multidisc Optim

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“…For instance, length-scale constraints can be formulated by monitoring the distance from the boundary to the skeleton of the structure [6,88,53] or by comparing the areas enclosed by a boundary offset and by a level set offset [87]. Approaches that parametrize the level set with an explicit representation utilize the length-scale constraints introduced in structural topology optimization methods [59,43]. Another contributor to the erratic convergence is attributed to the current linear interpolation of the heaviside function H • φ in elements where φ changes sign.…”

Section: Numerical Examplesmentioning

confidence: 99%

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

Troya¹,

Tortorelli²,

Beck³

2021

14th WCCM-ECCOMAS Congress

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We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

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“…Limiting both phases results in a minimum local feature size and, accordingly, to a limitation of the local surface curvature. The length-scale control has been implemented for density-based methods (Amir and Lazarov 2018;Lazarov et al 2016;Schevenels et al 2011;Wang et al 2011;Zhou et al 2015) as well as for level setbased methods (Dunning 2018;Guo et al 2014b;Jansen 2019;Liu et al 2016). Explicit geometric constraints in 2D considering area and curvature were presented in the study of Yoely et al (2018Yoely et al ( , 2020.…”

Section: Related Workmentioning

confidence: 99%

Density-based shape optimization of 3D structures with mean curvature constraints

Bartz¹,

Franke²,

Fiebig³

et al. 2021

Struct Multidisc Optim

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This paper presents a density-based shape optimization using an interface motion scheme as in level set methods. The aim is to generate optimal material distributions with high-quality interfaces within a uniform geometric representation for topology and shape optimization. This reduces the effort for post-processing and facilitates an automated conversion to CAD models. By using a density function, the proposed method can seamlessly adopt density-based topology optimization results as the initial design. Finite element analyses are performed using the same mesh and density field as for optimization. The interface motion is based on an advection equation and shape derivatives without a penalization of intermediate densities. This prevents the formation of large grey transition regions while avoiding mesh-dependent spatial oscillations of the interface. Thus, boundary-fitted meshes with smooth surfaces and sufficiently retained stiffness and volume can be extracted. In addition, an optional constraint for the mean curvature of the surface as well as the necessary shape derivative is introduced. Thus, the surface curvature can be limited to a technically justifiable value, which improves, for instance, the manufacturability and fatigue strength. The evaluation is carried out using a two-dimensional example starting from a topology-optimized design as well as four three-dimensional examples starting from a trivial design. The considered optimization objective is to minimize the volume with respect to compliance constraints and, partially, additional mean curvature constraints.

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Minimum length-scale constraints for parameterized implicit function based topology optimization

Cited by 20 publications

References 48 publications

An interface-enriched generalized finite element method for level set-based topology optimization

An interface-enriched generalized finite element method for level set-based topology optimization

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

Density-based shape optimization of 3D structures with mean curvature constraints

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