Topology optimization using the p-version of the finite element method

Nguyen, Tam H.; Le, Chau H.; Hajjar, Jerome F.

doi:10.1007/s00158-017-1675-7

Cited by 21 publications

(25 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As per our investigations, the filter radii choices for various MTO configurations, as described in Nguyen et al (2017), seem to result in reasonably correct designs. However, it is of considerable interest to explore the full potential of MTO, which motivates us to investigate whether filter radii smaller than those proposed in Nguyen et al (2017) can also be used. As mentioned earlier, a limiting factor is the occurrence of QR-patterns ( Fig.…”

Section: Introductionsupporting

confidence: 70%

“…In MTO approaches, the design and analysis discretizations are decoupled, such that a finer density field can be expressed on a coarse analysis mesh (Nguyen et al 2010(Nguyen et al 2017Parvizian et al 2012). Figure 2 shows an MTO element that uses 4 analysis nodes and 9 design voxels.…”

Section: Mto Conceptmentioning

confidence: 99%

“…Since then, various variants have been proposed (e.g. Nguyen et al 2012Nguyen et al , 2017Parvizian et al 2012;Wang et al 2014), and these have been used on several TO problems, e.g. for 3D TO in interactive handheld devices (Nobel-Jørgensen et al 2015), and designing thermoelectric generators (Takezawa and Kitamura 2012), phononic materials (Vatanabe and Silva 2013), patientspecific 3D printed craniofacial implants (Sutradhar et al 2016), etc.…”

Section: Introductionmentioning

confidence: 99%

“…However, this solution comes with the same disadvantages as discussed previously for low-order MTO. Application of a minimal filter radius is often preferred, and values have been suggested based on full-scale numerical tests by previous studies (Groen et al 2017;Nguyen et al 2017).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

QR-patterns: artefacts in multiresolution topology optimization

Gupta

Langelaar

Keulen

2018

Struct Multidisc Optim

View full text Add to dashboard Cite

Recent multiresolution topology optimization (MTO) approaches involve dividing finite elements into several density cells (voxels), thereby allowing a finer design description compared to a traditional FE-mesh-based design field. However, such formulations can generate discontinuous intra-element material distributions resembling QR-patterns. The stiffness of these disconnected features is highly overestimated, depending on the polynomial order of the employed FE shape functions. Although this phenomenon has been observed before, to be able to use MTO at its full potential, it is important that the occurrence of QR-patterns is understood. This paper investigates the formation and properties of these QR-patterns, and provides the groundwork for the definition of effective countermeasures. We study in detail the fact that the continuous shape functions used in MTO are incapable of modeling the discontinuous displacement fields needed to describe the separation of disconnected material patches within elements. Stiffness overestimation reduces with p-refinement, but this also increases the computational cost. We also study the influence of filtering on the formation of QR-patterns and present a low-cost method to determine a minimum filter radius to avoid these artefacts.

show abstract

Section: Introductionsupporting

confidence: 70%

Section: Mto Conceptmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

QR-patterns: artefacts in multiresolution topology optimization

Gupta

Langelaar

Keulen

2018

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…As a result, the optimized designs are often suffered from blurred boundaries and may not contain structural details with small feature sizes, although high-resolution density meshes are employed. Nevertheless, recent works (Nguyen et al, 2017;Groen et al, 2017) have shown that, such drawback can be overcome by introducing higher-order finite elements for structural analysis and advanced filter techniques (Guest et al, 2004;Sigmund, 2007;Xu et al, 2010 andWang et al, 2011). In those contributions, optimized designs with fine structural features and distinct boundaries are obtained successfully in SIMP-based multi-resolution topology optimization framework.…”

Section: Introductionmentioning

confidence: 99%

An efficient moving morphable component (MMC)-based approach for multi-resolution topology optimization

Liu

Zhu

Sun

et al. 2018

Struct Multidisc Optim

View full text Add to dashboard Cite

In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, highresolution optimization results can be obtained with much less numbers of degrees of freedoms (DOFs) and design variables since the topology optimization model and the finite element analysis model are totally decoupled in the MMC-based problem formulation. This is achieved by introducing hyper-elements for structural response analysis and adopting a design domain partitioning strategy to preserve the topological complexity of optimized structures. Both two-and three-dimensional numerical results demonstrate that substantial computational efforts can be saved for large-scale topology optimization problems with the use of the proposed approach.

show abstract

Design and analysis adaptivity in multiresolution topology optimization

Gupta

Keulen

Langelaar

2019

Numerical Meth Engineering

View full text Add to dashboard Cite

Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO method can be approximately 3 and 30 times faster than the traditional topology optimization method for 2D and 3D problems, respectively. To further exploit the potential of decoupling analysis and design, we propose a dp-adaptive MTO method, which involves locally increasing/decreasing the shape function orders (p) and design resolution (d). The adaptive refinement/coarsening is performed using a composite refinement indicator which includes criteria based on analysis error, presence of intermediate densities as well as the occurrence of design artefacts referred to as QR-patterns. While standard MTO must rely on filtering to suppress QR-patterns, the proposed adaptive method ensures efficiently that these artefacts are suppressed in the final design, without sacrificing the design resolution. The applicability of the dp-adaptive MTO method is demonstrated on several 2D mechanical design problems. For all the cases, significant speed-ups in computational time are obtained. In particular for design problems involving low material volume fractions, speed-ups of up to a factor of 10 can be obtained over the conventional MTO method.

show abstract

Topology optimization using the p-version of the finite element method

Cited by 21 publications

References 50 publications

QR-patterns: artefacts in multiresolution topology optimization

QR-patterns: artefacts in multiresolution topology optimization

An efficient moving morphable component (MMC)-based approach for multi-resolution topology optimization

Design and analysis adaptivity in multiresolution topology optimization

Contact Info

Product

Resources

About