Continuous approximation of material distribution for topology optimization

By Kazumi Matsui, Kenjiro Terada. 2004

221 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/76f51725a515559370ac54469d0843e9b7ed5668

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Large‐scale topology optimization using preconditioned Krylov subspace methods with recycling (2007, methodology): “The Solid Isotropic Material with Penalization (SIMP) method [13] [14] uses one design variable to represent the density in each element, while the recent method of Continuous Approximation of Material Distribution (CAMD) [15] [16] uses multiple variables per element.”
Polygonal finite elements for topology optimization: A unifying paradigm (2010, background): “Alternatively, a continuous variation of density can be obtained by sampling the density at the nodal locations and interpolating it with the shape functions [38, 39].”
Topology optimization using a continuous density field and adaptive mesh refinement (2018, unknown): “They use ηe = ∫Ωeρ(x, y)dΩe |Ωe| , (6)”
A modified Q4/Q4 element for topology optimization (2009, background): “Several approaches based on nodal design variables have been developed (Rahmatalla and Swan 2004; Matsui and Terada 2004; Guest et al. 2004).”
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].”
Improving multiresolution topology optimization via multiple discretizations (2012, background): “The design variables can be located at the centers, at the nodes, or at the midpoints of the edges of the finite elements [14–17].”
Topology optimization of structures using meshless density variable approximants (2013, background): “Matsui and Terada [22] were the first who studied the nodal density approximant for topology optimization problems by using finite element shape functions.”
Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes (2006, methodology): “In this section, we briefly discuss a new type of HDM in which continuous material distributions are assumed, using a continuous interpolation function at each node [41].”
Topology optimization using B-spline finite elements (2011, methodology): “This approach has since been used in conjunction with homogenization method and named continuous approximation of material distribution (CAMD) by Matsui and Terada (2004) .”
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].”
Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach (2014, methodology): “For more details, the interested reader is referred to (Almeida et al., 2010; Matsui and Terada, 2004).”
Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, methodology): “Matsui and Terada [25] introduced a continuous distribution model of material densities into the homogenization method by employing bi-linear shape functions to interpolate the material density field.”
A nodal variable method of structural topology optimization based on Shepard interpolant (2012, methodology): “Islanding phenomenon In some existing works on nodal density variable-based topology optimization methods, the shape functions for the Q4 element are used for discretizing both the displacement field and the relative density distribution of the artificial material [11, 20, 21, 25, 26].”
Honeycomb Wachspress finite elements for structural topology optimization (2009, methodology): “In one approach (Matsui and Terada 2004; Rahmatalla and Swan 2004), the continuity of the material field is enforced by using finite element shape functions to interpolate the density throughout the design domain from nodal densities.”
Multiscale isogeometric topology optimization for lattice materials (2017, background): “For example, whereas checkerboards appearing in FEA can be easily relieved with higher order elements [43,44], their use often requires high computational power [45].”