A simple checkerboard suppression algorithm for evolutionary structural optimization

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Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method (2007, background): “In a continuum structure which is discretized using low-order bilinear (2D) or trilinear (3D) finite elements, the above sensitivity numbers could become C0 discontinuous across element boundaries and result in checkerboard patterns in topology by definition [20,21].”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “…number of element i, ui is the displacement vector and Ki is the stiffness matrix for element i. αei = 1 2 uTi Kiui (4) Since ESO is susceptible to checkerboarding similar to density-based methods, Li et al. (2001a) introduced a simple algorithm to alleviate these numerical difficulties.”
Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials (2009, methodology): “Therefore these “void” elements can be totally removed from the design domain except that the removal causesthesingularityofglobalstiffnessmatrixoranychange of boundary conditions [ 22 ,23].”
Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review (2016, background): “[77] solved the checkerboard problem by averaging the sensitivity number of an element with the neighboring elements; Yang et al.”