An adaptive volume constraint algorithm for topology optimization with a displacement-limit

This paper proposes a novel adaptive volume constraint algorithm (AVC) to replace the fixed volume constraint (FVC) in the traditional topology optimization method, such that a minimum-compliance optimal structure that simultaneously meets the additional displacement limit can be searched. Optimal minimum-compliance structures are subject to the limit of a predetermined amount of material in traditional calculation methods, and often fail to meet practical stress and displacement constraints, or become unnecessarily strong. Without displacement sensitivities, the AVC algorithm iteratively adjusts allowable material usage based on the difference between the actual displacement, and the allowable displacement limit. In this way, topology optimization can efficiently construct a minimum-compliance structure that meets the allowable displacement limit. The regular volume constraint algorithm (RVC), which slightly changes the volume constraint each time at the end of FVC, is also executed in order to demonstrate the advantages of the AVC algorithm. The effectiveness of the AVC algorithm is demonstrated by two illustrative 2-D design problems: a cantilever beam and a simple beam.