Higher-order multi-resolution topology optimization using the finite cell method

This article presents a detailed study on the potential and limitations of performing higher-order multi-resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high-contrast topologies, a length-scale is applied on the solution using filter methods. The relations between stiffness overestimation, the analysis system, and the applied length-scale are examined, while a high-resolution topology is maintained. The computational cost associated with nested topology optimization is reduced significantly compared with the use of first-order finite elements. This reduction is caused by exploiting the decoupling of density and analysis mesh, and by condensing the higher-order modes out of the stiffness matrix.