Multi-resolution multi-scale topology optimization — a new paradigm

The purpose of this work is to present a new-concept multi-resolution multi-scale topology optimization. The key idea of the present strategy is that design optimization should be performed progressively from low to high resolution, not at a single resolution level. To achieve the multi-resolution strategy, design optimization is formulated in a wavelet-based variable space, not in a direct density variable space. The major advantages of the multi-resolution design optimization include: (1) topologically simple and close-to-the-global-optimum structures may be obtained without any explicit constraint, and (2) the convergence is not sensitive to mathematical programming methods. For the ecient numerical implementation of the multi-resolution approach, the side constraints imposed on the direct density variables are removed by mapping the density variables into intermediate variables. These intermediate variables are then wavelet-transformed to new design variables. It is addressed that the present multi-resolution topology optimization can resolve major numerical instability problems such as mesh- dependencies and local minima. The usefulness of the multi-scale nature of the wavelets in the present multi- resolution multi-scale optimization formulation is also discussed.