Topology optimization of elastic continua using restriction

Borrvall, Thomas

doi:10.1007/bf02743737

Cited by 100 publications

(58 citation statements)

References 53 publications

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“…In order to obtain a more discrete (black and white) solution than for the original sensitivity filter (16), Borrvall (2001) suggests the following modification…”

Section: Alternative Sensitivity Filtermentioning

confidence: 99%

“…Restriction methods for density based topology optimization problems can roughly be divided into three categories: 1) mesh-independent filtering methods, constituting sensitivity filters (Sigmund, 1994(Sigmund, , 1997Sigmund and Petersson, 1998) and density filters (Bruns and Tortorelli, 2001;Bourdin, 2001); 2) constraint methods such as perimeter control (Ambrosio and Buttazzo, 1993;Haber et al, 1994), global gradient control (Bendsøe, 1995;Borrvall, 2001), local gradient control (Niordson, 1983;Petersson and Sigmund, 1998;Zhou et al, 2001), regularized penalty methods (Borrvall and Petersson, 2001) and integral filtering (Poulsen, 2003); and 3) other methods like wavelet parameterizations (Kim and Yoon, 2000;Poulsen, 2002), phase-field approaches (Bourdin and Chambolle, 2003;Wang and Zhou, 2004) and level-set methods (Sethian and Wiegmann, 2000;Wang et al, 2003;Allaire et al, 2004) 1 . The filtering methods in group 1 are probably the most popular ones due to their ease of implementation and their efficiency.…”

Section: Introductionmentioning

confidence: 99%

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Morphology-based black and white filters for topology optimization

Sigmund

2007

Struct Multidisc Optim

1,415

801

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In order to ensure manufacturability and mesh-independence in density-based topology optimization schemes it is imperative to use restriction methods. This paper introduces a new class of morphology based restriction schemes which work as density filters, i.e. the physical stiffness of an element is based on a function of the design variables of the neighboring elements. The new filters have the advantage that they eliminate grey scale transitions between solid and void regions. Using different test examples, it is shown that the schemes in general provide black and white designs with minimum length-scale constraints on either or both minimum hole sizes and minimum structural feature sizes. The new schemes are compared with methods and modified methods found in the literature.

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“…In order to obtain a more discrete (black and white) solution than for the original sensitivity filter (16), Borrvall (2001) suggests the following modification…”

Section: Alternative Sensitivity Filtermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Morphology-based black and white filters for topology optimization

Sigmund

2007

Struct Multidisc Optim

1,415

801

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“…The filtered design is calculated from an essentially non-physical "unfiltered" design variable ξ that becomes the independent variable of the optimization problem. Note that while ρ is defined on the potential structural domain only, the variable ξ may be defined on the whole space, see [4]. However, a simplified treatment, discussed, e.g., in [21], is to use a ξ-variable that is defined in the structural domain only and that is what is used in the sequel.…”

Section: Restriction Methodsmentioning

confidence: 99%

Dynamical systems and topology optimization

Klarbring

Torstenfelt

2010

Struct Multidisc Optim

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This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm.A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling.Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented.

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“…1 Filter Scheme Sensitivity filter formula is defined by Sigmund. In order to obtain clearer topology optimization boundary, Borrvall [11] proposed a modified sensitivity filter formula. In the topology optimization of multi-physics fields [12], the density in the formula is always leave out.…”

Section: Find X I Nementioning

confidence: 99%

An Improved Method for Decreasing Intermediate Density Elements in Topology Optimization

Jiang¹,

Zhang²,

Wan³

et al. 2017

Proceedings of the 2nd International Conference on Computer Engineering, Information Science &Amp; Application Technology (ICCI

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Abstract. The instability phenomenon of numerical solution usually exists in topology optimization of continuum structure. The sensitivity filter method is used to solve this instability phenomenon of numerical solution generally, but many intermediate density elements still exist in the result of topology optimization. Intermediate density elements are difficult to manufacture in the industry, so it is urgent to form an efficient method to decrease them. This paper proposes a improved method-considering density gradient message and elements numbers in the filter radius. It sets up a model which focus on modifying the weighting function and the elements' density within the filter radius. It is based on Solid Isotropic Material with Penalization (SIMP). The optimality criteria method (OC) is used to solve this model. Finally a widely studied example is used to demonstrate the availability and advantage of the proposed filter method.

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Topology optimization of elastic continua using restriction

Cited by 100 publications

References 53 publications

Morphology-based black and white filters for topology optimization

Morphology-based black and white filters for topology optimization

Dynamical systems and topology optimization

An Improved Method for Decreasing Intermediate Density Elements in Topology Optimization

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