Minimum thickness control at various levels for topology optimization using the wavelet method

Especially in microsystem design, maintaining the minimum thickness of each structural member at a certain scale is often as important as achieving the maximum system performance. Several successful methods to suppress one-point hinges or checkerboards in topology optimization have been developed, but an efficient method to control the minimum thickness at a desire scale remains to be developed. The objective of this investigation is to develop a wavelet-based minimum thickness controlling method applicable to topology optimization and to show the effectiveness of the proposed method in MEMS design. The idea behind the thickness controlling method is to extend the wavelet shrinkage method developed for one-point hinge control to any scale-level minimum thickness control. The major difficulties in implementing this idea are the development of an efficient algorithm to detect all undesirable patterns of different scales and the hierarchical application of the wavelet shrinkage method over multiple scales. Some techniques to overcome these difficulties are developed and applied to some MEMS design problems.