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.　Results　show　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.