Filters in topology optimization

By Blaise Bourdin. 2001

1,292 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4ebdcc6d4ec451f221c2be20b9f61983dc7627ca

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Benchmarking optimization solvers for structural topology optimization (2015, methodology): “(Bourdin 2001) is used to ensure existence of solutions and to avoid checker board patterns in the final design.”
Topology optimization with finite-life fatigue constraints (2017, methodology): “2 Density filtering Density filtering is applied to the design variables [34, 35] to avoid the so-called checkerboard patterns [36–38], which present an artificial high stiffness of the model.”
On some fundamental properties of structural topology optimization problems (2010, background): “Filters ( Bourdin 2001; Sigmund 2007) and perimeter constraints (Ambrosio and Buttazzo 1994; Haber et al. 1996) are omitted from the problem formulations since our intention is to provide analytical solutions to some small-scale problem instances.”
Topology optimisation for natural convection problems (2014, methodology): “ers do not provide enough resistance to effectively inhibit the ﬂow when using the Brinkman approach [32,48], so imposing a minimum lengthscale can help on this issue. In this work, the density ﬁlter [49,50] is used, but there exists other methods to ﬁx the complications listed above [13,51]. The ﬁl”
Morphology-based black and white filters for topology optimization (2007, methodology): “The ﬁltered density measure is where the weighting function w ( x i ) is given by the linearly decaying (cone-shape) function as suggested in Bruns and Tortorelli (2001); Bourdin (2001).”
Topological design of structures and composite materials with multiobjectives (2007, methodology): “This technique was originally used in image processing for domain identification (Weickert, 1997; Aubert and Kornprobst, 2000; Charbonnier et al., 1997) and later was successfully introduced to structural topology optimization in Bourdin (2001) and Wang et al. (2004).”
Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials (2009, methodology): “A variety of restriction methods have been developed, for example, by perimeter control [18], gradient constraint [19] or blurring filters [20, 21 ].”
A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization (2005, methodology): “The advantage of filtering the design is that the optimization problem is consistent and regularized (Bourdin 2001).”
On projection methods, convergence and robust formulations in topology optimization (2011, methodology): “Here the mesh independent density filtering (Bruns and Tortorelli 2001; Bourdin 2001 ) is used as a basis to ensure existence of solutions.”
Topology optimization using regularized intermediate density control (2001, background): “In fact, proofs of existence as well as FEconvergence are given in [12].”
Polygonal finite elements for topology optimization: A unifying paradigm (2010, methodology): “According to the analysis by Bourdin [42], this convolution removes the ill-posedness of the continuum problem and mesh dependency of the discrete problem.”