Topology uncertainty leads to different topology solutions and makes topology optimization ambiguous. Point connection and grey cell might cause topology uncertainty. They are both eradicated when hybrid discretization model is used for discrete topology optimization. A common topology uncertainty in the current discrete topology optimization stems from mesh dependence. The topology solution of an optimized compliant mechanism might be uncertain when its design domain is discretized differently. To eliminate topology uncertainty from mesh dependence, the genus based topology optimization strategy is introduced in this paper. The topology of a compliant mechanism is defined by its genus which is the number of holes in the compliant mechanism. With this strategy, the genus of an optimized compliant mechanism is actively controlled during its topology optimization process. There is no topology uncertainty when this strategy is incorporated into discrete topology optimization. The introduced topology optimization strategy is demonstrated by examples with different degrees of genus.

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