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 reso lution, not at a single resolution level. To achieve the multi-resolution s trategy, design optimization is formulated in a wavelet-based variable spac e, not in a direct density variable space. The major advantages of the mult i-resolution design optimization include: (1) topologically simple and clos e-to-the-global-optimum structures may be obtained without any explicit con straint, and (2) the convergence is not sensitive to mathematical programmi ng methods. For the efficient numerical implementation of the multi-resolut ion approach, the side constraints imposed on the direct density variables are removed by mapping the density variables into intermediate variables. T hese intermediate variables are then wavelet-transformed to new design vari ables. It is addressed that the present multi-resolution topology optimizat ion can resolve major numerical instability problems such as mesh-dependenc ies and local minima. The usefulness of the multi-scale nature of the wavel ets in the present multiresolution multi-scale optimization formulation is also discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.