Abstract: To address the issue of yielding mechanisms while using the minimum compliance with a volume constraint(MCVC) model,the minimum weight with a displacement constraint(MWDC) model is used to find safe robust thresholds of physical and performance parameters for the MCVC model avoiding mechanisms. The 99-line and 120-line topology optimization codes are used to solve the MCVC and MWDC models,respectively. A large number of morbid examples with mechanisms appearance are studied.Resultsshow that the mechanism occurs when the maximum strain energy ratio is larger than a threshold,or when the volume ratio is less than a threshold. However,the two thresholds are problem dependent. They vary for different structures and/or loading cases,but for those examples that were tested,the range of the threshold of the maximum strain energy ratio turns out to be between 4.59 and 12 38,and the range of the threshold of the volume ratio is between 0.15 and 0.26.