Discrete parameterization using full or partial ground structures of truss/frame elements is not appropriate for domain representation as they do not map all points in the continuum and can lead to dangling or overlapping elements in the optimal topology. Existing continuum parameterization using units cells with holes, ranked microstructures or penalized Young’s modulus (SIMP model) mainly have problems like the appearance of checkerboard patterns and stiffness singularity regions. This is probably due to point-contact between diagonally placed cells and such regions can be avoided by using higher order elements, perimeter constraints or filtering schemes which result in additional computational load on the optimization procedures. An edge connectivity throughout is ensured when using a honeycomb representation with staggered regular hexagonal cells. In this paper, such a parameterization is employed for topology synthesis of compliant mechanisms with flexibility-stiffness and flexibility-strength multi-criteria formulations. The material connectivity is well-defined, and checkerboard and zero-stiffness singularities are not seen in numerous examples solved with honeycomb parameterization.

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