Multi-resolution multi-scale topology optimization — a new paradigm

By Yoon Young Kim, Gil Ho Yoon. 2000

133 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/b9316c1baee336b209fa4e88145ac77562ed49e4

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In Civil and Structural Engineering

In Computational Theory and Mathematics

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Citations in the corpus

A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “Regularization was also suggested by design parameterization in wavelet space (Kim and Yoon 2000; Poulsen 2002), and Pomezanski et al. (2005) proposed an extension of SIMP to penalize corner contact directly.”
Deep learning for determining a near-optimal topological design without any iteration (2018, background): “Kim and Yoon (2000) proposed a multi-level strategy in which topology optimization is progressively performed from low to high resolution.”
Topology optimization in B-spline space (2013, background): “Design parametrization in wavelet space has been explored in [29, 30].”
Morphology-based black and white filters for topology optimization (2007, methodology): “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, 1997; Sigmund and Petersson, 1998) and density filters (Bruns and Tortorelli, 2001; Bourdin, 2001”
Improving multiresolution topology optimization via multiple discretizations (2012, methodology): “Kim and Yoon [28] utilized wavelet space to perform the design optimization progressively from low to high resolution while using the same finite element mesh.”
Topology optimization in wavelet space (2002, methodology): “‡Note added at revision: After this paper was submitted, Kim and Yoon have published similar work in Reference [9].”
Filters in topology optimization based on Helmholtz‐type differential equations (2011, background): “Recently, projection schemes that build on density ﬁltering [8, 9] and wavelet parameterization [10, 11] have also been proposed for preventing smeared designs and for imposing minimum length scale in the design.”
Volume preserving nonlinear density filter based on heaviside functions (2010, methodology): “There are also other restriction methods such as level-set method (Sethian and Wiegmann 2000; Wang et al. 2003; Allaire et al. 2004), wavelet parameterization ( Kim and Yoon 2000; Poulsen 2002) and phase-field approach (Bourdin and Chambolle 2003; Wang and Zhou 2004).”