Topology optimization in wavelet space

By Thomas A. Poulsen. 2002

74 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5f155af7378105101a567b2e816cfc1db54a81b4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Ole Sigmund
2. Glaucio H. Paulino
3. Xiaoping Qian
4. Boyan S. Lazarov
5. Ramana V. Grandhi
6. Joshua D. Deaton
7. Chau H. Le
8. Gengdong Cheng

In Mechanics of Materials

1. Glaucio H. Paulino
2. Ole Sigmund
3. Xiaoping Qian
4. Boyan S. Lazarov
5. Chau H. Le
6. Gengdong Cheng
7. Cameron Talischi
8. Shengli Xu

Citations in the corpus

• 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.”
• Morphology-based black and white filters for topology optimization (2007, methodology): “…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…”
• Topology optimization in B-spline space (2013, background): “Design parametrization in wavelet space has been explored in [29, 30].”
• 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).”
• A modified Q4/Q4 element for topology optimization (2009, background): “Note that high resolution for the final topology has been the objective of various methods, which attempt to suppress checkerboard patterns and direct corner contact (Pomezanski et al. 2005; Poulsen 2002, 2003; Sigmund and Petersson 1998).”
• Improving multiresolution topology optimization via multiple discretizations (2012, methodology): “Studies have been conducted to improve the manufacturability of the topology design and alleviate the numerical instability [33–36].”
• A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization (2002, methodology): “Recently the wavelet approach to checkerboard-removal (in Poulsen (2002) ) has been extended (in Yoon et al. (2002)) to a wavelet method that removes the onenode connected hinges.”
• Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach (2014, methodology): “2009), adaptive design variable fields (Guest and Genut 2010), density filters (Bourdin 2001; Burns and Tortorelli 2001; Sigmund 2007), wavelets (Poulsen 2002), NURBS basis functions (Azegami et al.”
• Honeycomb Wachspress finite elements for structural topology optimization (2009, methodology): “To achieve geometric control over the formation of checkerboard, Wavelet methods have also been applied to topology optimization ( Poulsen 2002b; Yoon and Kim 2005).”