Checkerboard instabilities in topological shape optimization algorithms

@inproceedings{BonnetierCheckerboardII,
  title={Checkerboard instabilities in topological shape optimization algorithms},
  author={Eric Bonnetier and François Jouve}
}
Checkerboards instabilities for an algorithm of topological design are studied on a simple example. The algorithm uses orthogonal rank-2 laminates as design variables, which need to be regularized as the associated Hooke’s laws are degenerate. When the displacements are approximated by Q1 or Q1-bubble elements, the discrete operator is linearized, and its eigenvalues are computed in terms of the regularization parameter. 

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