Spacecraft　in　the　aerospace　field　and　military　equipment　in　the　military　field　are　at　risk　of　being　impacted　by　external　objects,　which　can　cause　local　damage　to　the　structure.　The　randomness　of　local　damage　is　a　new　challenge　for　structural　design,　and　it　is　essential　to　take　random　damage　into　account　in　the　conceptual　design　phase　for　the　purpose　of　improving　structure’s　resistance　to　external　shocks.　In　this　article,　a　random　damaged　structure　is　assumed　to　have　damages　of　the　same　size　and　shape　at　random　locations,　and　the　random　damage　is　considered　as　multiple　damage　conditions　of　the　structure.　In　order　to　improve　the　randomness　and　comprehensiveness　of　the　multiple　damage　conditions,　the　stacking　strategy　is　used　to　generate　the　distribution　of　the　damage　area.　Following　this　strategy,　the　topology　optimization　design　of　the　random　damaged　structure,　which　is　to　minimize　the　weight　of　the　structure　with　a　constraint　on　the　stress　of　the　structure　under　multiple　damage　conditions,　is　formulated　based　on　the　independent　continuous　mapping　(ICM)　method.　The　dual　sequence　quadratic　programming　(DSQP)　algorithm　combined　with　the　stress　globalization　method　is　adopted　to　solve　the　optimization　problem.　The　numerical　examples　demonstrate　the　effectiveness　and　applicability　of　the　proposed　method　in　the　topology　optimization　of　strength-safe　continuum　structures.　©　2023　Tech　Science　Press.　All　rights　reserved.