Techniques to suppress intermediate density in topology optimization of compliant mechanisms

Discrete topological problems are often relaxed with continuous design vari ables so that they can be solved using continuous mathematical programming. Such practice prevails because large-scale discrete 0-1 mathematical progr amming is not generally available. Although the relaxed problems become tra ctable, they may cause the appearance of intermediate density in the optimu m topologies, especially those of structures and compliant mechanisms. Vari ous penalty schemes have been proposed to suppress the intermediate density . Most of the past works assumed that the same penalty schemes could be eff ectively applied to both problems of stiffest structure design and complian t mechanism design. Differences in nature between the problems are generall y neglected. This work distinguished the two problems, and observed that co mplaint mechanism (CM) problem does not suffer intermediate density as seri ously as minimum compliance (MC) problem does. Besides allocating more mate rial, explicit and implicit penalties were pursued to suppress intermediate density. To ensure mesh-independence and not to complicate the nonconvex o bjective function in CM problem, a new technique using a constraint of expl icit penalty with variable bound is proposed to suppress intermediate densi ty in topology optimization of compliant mechanisms. Together with a perime ter constraint, the new technique is also applied to MC problem.