Heaviside projection based topology optimization by a PDE-filtered scalar function

By Atsushi Kawamoto, Tadayoshi Matsumori, Shintaro Yamasaki, Tsuyoshi Nomura, Tsuguo Kondoh, Shinji Nishiwaki. 2011

305 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/3e7f498892eec847b44e00ef06fb5618eee860da

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Length scale and manufacturability in density-based topology optimization (2016, methodology): “An alternative to the convolution integral formulation, based on the solution of a partial differential equation (PDE), has been proposed first for sensitivity filtering in [87] and later extended to density filtering in [93] and [79].”
Undercut and overhang angle control in topology optimization: A density gradient based integral approach (2017, methodology): “Heaviside projection of density To alleviate the grayscale transition between the black and white density in the optimized designs, density projection schemes have been used in the past [19, 35, 32].”
General topology optimization method with continuous and discrete orientation design using isoparametric projection (2015, background): “Also, 2 ambiguity that stems from the periodic nature of the angular representation is potentially problematic and prevents application of filtering schemes [26, 27], which may help to yield better solutions or control manufacturability.”
Topology optimization approaches (2013, background): “Consequently, consistent derivatives have to be derived using the chain rule (Bruns and Tortorelli 2001; Bourdin 2001; Lazarov and Sigmund 2011; Kawamoto et al. 2011; Andreassen et al. 2011).”
Topology optimization in B-spline space (2013, methodology): “Thus, the B-spline filter provides an efficient filtering scheme similarly as partial differential equation (PDE) based filter [14, 15, 16], but without the need to solve the PDE.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “To combat this for situations where crisp boundary definition is important, several schemes have recently been developed to project the filtered densities into 0/1 (void/solid) space via a relaxed Heaviside function (Guest et al. 2004, 2011; Kawamoto et al. 2011) and morphology-based operators (Sigm”
On projection methods, convergence and robust formulations in topology optimization (2011, background): “Sigmund 1997). Recently, a number of projection schemes that alleviate the gray transition problem have been proposed by Guest et al. (2004), Sigmund (2007), Xu et al. (2010) and Kawamoto et al. (2010 ) a nd combinations of the former two were suggested for a multiprojection strategy by Guest (2009”