A Q4/Q4 continuum structural topology optimization implementation

By Salam Rahmatalla, Colby Swan. 2004

168 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/621548ba93535fd912dbc103b07447331ddbf72d

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Topology optimization of continuum structures under buckling constraints (2015, methodology): “However, a ‘‘layering’’ or ‘‘islanding’’ phenomenon of black and white regions in the design domain may appear [24].”
Topology optimization of structures using meshless density variable approximants (2013, methodology): “Rahmatalla and Swan [23] presented a nodal variablebased topology optimization method to ensure C continuity of the design variables for suppressing checkerboards using finite elements.”
A modified Q4/Q4 element for topology optimization (2009, background): “For the CAMD options in that paper (Rahmatalla and Swan 2004), nodal design variables are always considered at the locations of displacement nodes.”
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].”
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].”
Stress-constrained topology optimization with design-dependent loading (2012, unknown): “…displacement interpolation with 4-node linear density interpolation) implementation, the design variables are guaranteed to be C0 continuous, thus preventing the checkerboarding phenomenon that often occurs with element-based design variables (Rahmatalla and Swan 2004; Sigmund and Petersson 1998).”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, background): “Rahmatalla and Swan (2004) and Matsui and Terada (2004) proposed nodal based design variables which allowed for a continuous approximation of material density (CAMD) that naturally alleviates checkerboards.”
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].”
Topology optimization using the finite cell method (2012, background): “For an overview of the huge body of literature, see, for example Ramière et al. (2007), Glowinski and Kuznetsov (2007).”
Topology optimization using B-spline finite elements (2011, background): “Even though this approach, naturally excludes checkerboard patterns, other shape irregularities such as “islanding” and “layering” have been observed ( Rahmatalla and Swan 2004 ).”