A modified Q4/Q4 element for topology optimization

By Glaucio H. Paulino, Chau H. Le. 2009

68 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ec9f05dae559fe6693b13a3a854ae83cf42c8746

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. Zhan Kang
2. Yiqiang Wang
3. Ramana V. Grandhi
4. Joshua D. Deaton
5. Zhen Luo
6. Qizhi He
7. Nong Zhang
8. Tam H. Nguyen

In Mechanics of Materials

1. Zhan Kang
2. Yiqiang Wang
3. Qizhi He
4. Zhen Luo
5. Nong Zhang
6. Ramana V. Grandhi
7. Joshua D. Deaton
8. Chau H. Le

Citations in the corpus

• Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, methodology): “Paulino and Le [27] suggested a modified Q4/Q4M interpolation scheme, and applied the internal averaging techniques to suppress the islanding effect.”
• A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, result): “The mechanisms at work in these multiresolution methods are similar to previous papers that effectively allow for variation of density within finite elements and are analogous to earlier work based on CAMD approaches (Rahmatalla and Swan 2004; Matsui and Terada 2004; Paulino and Le 2009).”
• Improving multiresolution topology optimization via multiple discretizations (2012, background): “Another option is to locate the nodal design variables at the midpoints of the four edges of the quadrilateral elements [17].”
• Topology optimization of structures using meshless density variable approximants (2013, background): “Paulino and Le [25] proposed a kind of hybrid low-order finite elements, in which the nodes of design variables are inconsistent with the nodes of the displacement vector.”
• Topology optimization using a continuous density field and adaptive mesh refinement (2018, unknown): “KH,ij = ∫Ωe r (2)[∇N̄i(x, y)]∇N̄j(x, y) + N̄i(x, y)N̄j(x, y)dΩe, (10)”
• Structural topology optimization based on non-local Shepard interpolation of density field (2011, methodology): “Even in some nodal design variable methods allowing for spatial density variation within each element, the density distribution is interpolated by only design variable values of those nodes belonging to the corresponding element [32–35].”
• A multi-resolution method for 3D multi-material topology optimization (2015, unknown): “By contrast, the nodal-based approaches [53–55] consider the densities at the finite element nodes as the design variables.”
• A nodal variable method of structural topology optimization based on Shepard interpolant (2012, methodology): “Certain filter techniques based on weighted average of design sensitivities [26], or the minimum length scale control techniques [22], can be applied for achieving designs that can be more easily implemented in engineering.”
• Adaptive topology optimization with independent error control for separated displacement and density fields (2014, background): “Since the work of [26], nodal design variable-based methods have attracted much attention [27–30].”