Density and level set-XFEM schemes for topology optimization of 3-D structures

Villanueva, Carlos H.; Maute, Kurt

doi:10.1007/s00466-014-1027-z

Cited by 76 publications

(53 citation statements)

References 46 publications

(56 reference statements)

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“…Nguyen et al (2012) obtained an open-walled frame-like structure which must be attributed to the coarse mesh used for the study. Villanueva and Maute (2014) studied the same problem and found that with mesh refinement the optimized structure goes from being frame-like to being closed-walled -fully in agreement with the findings of the present paper.…”

Section: D Torsion Rodsupporting

confidence: 89%

On the (non-)optimality of Michell structures

Sigmund

Aage

Andreassen

2016

Struct Multidisc Optim

144

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Optimal analytical Michell frame structures have been extensively used as benchmark examples in topology optimization, including truss, frame, homogenization, density and level-set based approaches. However, as we will point out, partly the interpretation of Michell's structural continua as discrete frame structures is not accurate and partly, it turns out that limiting structural topology to frame-like structures is a rather severe design restriction and results in structures that are quite far from being stiffness optimal. The paper discusses the interpretation of Michell's theory in the context of numerical topology optimization and compares various topology optimization results obtained with the frame restriction to cases with no design restrictions. For all examples considered, the true stiffness optimal structures are composed of sheets (2D) or closed-walled shell structures (3D) with variable thickness. For optimization problems with one load case, numerical results in two and three dimensions indicate that stiffness can be increased by up to 80% when dropping the frame restriction. For simple loading situations, studies based on optimal microstructures reveal theoretical gains of +200%. It is also demonstrated how too coarse design discretizations in 3D can result in un-

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Section: D Torsion Rodsupporting

confidence: 89%

On the (non-)optimality of Michell structures

Sigmund

Aage

Andreassen

2016

Struct Multidisc Optim

144

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“…The simplest way is using the concept of ersatz material on the elements cut by the zero level curve (see, for example, the works of Allaire et al and Wang et al). 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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“…In this study we adopt a Lagrange multiplier approach, similar to the one of Geniaut et al (2007), for modeling sliding contact problems assuming a linear elastic material behavior and infinitesimal strains. The particular framework for integrating the explicit LSM and the generalized formulation of the XFEM used in this study are described in detail in Makhija and Maute (2014) and Villanueva and Maute (2014).…”

Section: Introductionmentioning

confidence: 99%

Level set topology optimization of problems with sliding contact interfaces

Lawry

Maute

2015

Struct Multidisc Optim

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This paper introduces a topology optimization method for the design of two-component structures and two-phase material systems considering sliding contact and separation along interfaces. The geometry of the contact interface is described by an explicit level set method which allows for both shape and topological changes in the optimization process. The mechanical model assumes infinitesimal strains, a linear elastic material behavior, and a quasi-static response. The contact conditions are enforced by a stabilized Lagrange multiplier method and an active set strategy. The mechanical model is discretized by the extended finite element method which retains the crispness of the level set geometry description and allows for the convenient integration of the weak form of the contact conditions at the phase boundaries. The formulation of the optimization problem is regularized by introducing a perimeter penalty into the objective function. The optimization problem is solved by a nonlinear programming scheme computing the design sensitivities by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in two dimensions. Consideration of contact leads to the formation of barb-type features that increase the interface stiffness. The numerical results further demonstrate the significant difference in the optimized geometries when assuming perfect bonding versus considering contact.

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Density and level set-XFEM schemes for topology optimization of 3-D structures

Cited by 76 publications

References 46 publications

On the (non-)optimality of Michell structures

On the (non-)optimality of Michell structures

Level set topology optimization for design‐dependent pressure load problems

Level set topology optimization of problems with sliding contact interfaces

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