Level set topology optimization of stationary fluid-structure interaction problems

Jenkins, Nicholas W.; Maute, Kurt

doi:10.1007/s00158-015-1229-9

Cited by 58 publications

(45 citation statements)

References 41 publications

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“…Note that this approach restricts the number an element edge can be intersected by the fluid-solid interface to at most one. Therefore, the geometry resolution is limited by the size of an XFEM element, and convergence issues have been observed if sub-element-size features tend to emerge in the optimization process [24].…”

Section: Parametrization Of the Level Set Functionmentioning

confidence: 99%

“…External and internal phase boundaries are described implicitly by the zero level set isosurfaces of a Level Set Function (LSF), φ (x), where x is the position vector [18,19,20]. LSMs are well-suited for topology optimization because smooth differentiable changes in the LSFs lead to changes in the topology of the body, such as holes merging or splitting [21,22,23]; however, these changes may lead to discontinuities in the physical response [24].…”

Section: Introductionmentioning

confidence: 99%

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CutFEM topology optimization of 3D laminar incompressible flow problems

Villanueva

Maute

2017

Computer Methods in Applied Mechanics and Engineering

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This paper studies the characteristics and applicability of the CutFEM approach [1] as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds number (Re < 200). CutFEM is a methodology for discretizing partial differential equations on complex geometries by immersed boundary techniques. In this study, the geometry of the fluid domain is described by an explicit level set method, where the parameters of a level set function are defined as functions of the optimization variables. The fluid behavior is modeled by the incompressible Navier-Stokes equations. Species transport is modeled by an advection-diffusion equation. The governing equations are discretized in space by a generalized extended finite element method. Face-oriented ghost-penalty terms are added for stability reasons and to improve the conditioning of the system. The boundary conditions are enforced weakly via Nitsche's method. The emergence of isolated volumes of fluid surrounded by solid during the optimization process leads to a singular analysis problem. An auxiliary indicator field is modeled to identify these volumes and to impose a constraint on the average pressure. Numerical results for 3D, steady-state and transient problems demonstrate that the CutFEM analyses are sufficiently accurate, and the optimized designs agree well with results from prior studies solved in 2D or by density approaches.

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Section: Parametrization Of the Level Set Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

CutFEM topology optimization of 3D laminar incompressible flow problems

Villanueva

Maute

2017

Computer Methods in Applied Mechanics and Engineering

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“…Better representations at the cost of a more involved implementations are achieved by remeshing or discontinuous enrichments like those provided by the extended FEM . For the particular case of design‐dependent loads, this last alternative was used in the works of Jenkins and Maute (fluid‐solid interaction) and Coffin and Maute (thermal conduction problems).…”

Section: Introductionmentioning

confidence: 99%

Level set topology optimization for design‐dependent pressure load problems

Emmendoerfer

Fancello

Silva

2018

Numerical Meth Engineering

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Summary This work presents a level set framework to solve the compliance topology optimization problem considering design‐dependent pressure loads. One of the major technical difficulties related to this class of problem is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction‐diffusion equation substitutes the classical Hamilton‐Jacobi equation to control the level set evolution. This choice has the advantages of allowing the nucleation of holes inside the domain and the elimination of the undesirable reinitialization steps. Moreover, the proposed algorithm allows merging pressurized (wet) boundaries with traction‐free boundaries during level set movements. This last property, allied to the simplicity of the level set representation and successful combination with the reaction‐diffusion based evolution applied to a design‐dependent pressure load problem, represents the main contribution of this paper. Numerical examples provide successful results, many of which comparable with others found in the literature and solved with different techniques.

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“…Topology optimisation for fluid systems began with the treatment of Stokes flow by Borrvall and Petersson [11] and has since been applied to Navier-Stokes flow [12], as well as passive transport problems [13,14], reactive flows [15], transient flows [16,17,18], fluid-structure interaction [19,20], amongst many others. The extension of topology optimisation to turbulent fluid flow is still in its infancy [21,22].…”

Section: Introductionmentioning

confidence: 99%

Design of passive coolers for light-emitting diode lamps using topology optimisation

Alexandersen

Sigmund

Meyer

et al. 2018

International Journal of Heat and Mass Transfer

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Topology optimised designs for passive cooling of light-emitting diode (LED) lamps are investigated through extensive numerical parameter studies. The designs are optimised for either horizontal or vertical orientations and are compared to a lattice-fin design. The different orientations result in significant differences in topologies. The optimisation favors placing material at outer boundaries of the design domain, leaving a hollow core that allows the buoyancy forces to accelerate the air to higher speeds. Investigations show that increasing design symmetry yields performance with less sensitivity to orientation with a minor loss in mean performance. The topology-optimised designs of heat sinks for natural convection yield a 26% lower package temperature using around 12% less material compared to the lattice-fin design, while maintaining low sensitivity to orientation. Furthermore, they exhibit several defining features and provide insight and general guidelines for the design of passive coolers for LED lamps.

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Level set topology optimization of stationary fluid-structure interaction problems

Cited by 58 publications

References 41 publications

CutFEM topology optimization of 3D laminar incompressible flow problems

CutFEM topology optimization of 3D laminar incompressible flow problems

Level set topology optimization for design‐dependent pressure load problems

Design of passive coolers for light-emitting diode lamps using topology optimisation

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