Achieving minimum length scale in topology optimization using nodal design variables and projection functions

By James K. Guest, Jean-Herve Prevost, Ted Belytschko. 2004

1,402 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/9b564abd01ac557e9bdb17073e6f6b736bc1b646

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Support Structures for Additive Manufacturing: A Review (2018, methodology): “They embed a projection step associated with the overhang angle constraint within the standard Heaviside Projection methodology (HPM) [94].”
Topological Optimization of Compliant Adaptive Wing Structure (2009, methodology): “This includes the incorporation of filter functions, for example the Heaviside step function [23], in the optimization scheme.”
Improving multiresolution topology optimization via multiple discretizations (2012, methodology): “The latter two approaches have some similarity; the density filter method in [38] uses the finite element density design variables, while the projection method in [14] uses the finite element nodal design variables.”
A general formulation of structural topology optimization for maximizing structural stiffness (2011, methodology): “Some of the density filter techniques choices are Heaviside function (Guest et al. 2004), modified density filter with a Heaviside function (Sigmund 2007), volume preserving nonlinear density filter based on Heaviside functions (Xu et al. 2010).”
Interior value extrapolation: a new method for stress evaluation during topology optimization (2015, methodology): “Many methods have been proposed, among the most used are sensitivity filtering [11] and density filtering [12, 13, 14, 15].”
Reducing dimensionality in topology optimization using adaptive design variable fields (2010, methodology): “In fact, savings were less significant when applying this approach to the more difficult compliant inverter design problem described in Reference [19].”
Imposing maximum length scale in topology optimization (2009, methodology): “The reader is referred to Guest et al. (2004) for details.”
Topology optimization of structures using meshless density variable approximants (2013, methodology): “It is noted that the problem formulation may be functionally similar to the filtering [9–11] or projection methods [20,24].”