Continuum　topology　optimization　usually　produces　results　similar　to　a　skeleton　structure.　In　addition,　material　utilization　in　the　optimized　structure　is　greatly　improved　compared　with　the　original　structure.　On　the　other　hand,　the　redundancy　of　the　structure　is　greatly　reduced　due　to　the　removed　material.　Partial　local　failure　in　the　optimized　structure　makes　it　more　difficult　for　the　entire　structure　to　meet　strength/stiffness　requirements.　Using　the　independent　continuous　mapping　(ICM)　method,　with　minimal　weight　as　the　objective　and　both　stress　and　displacement　as　the　respective　constraints,　continuum　topology　optimization　models　which　also　consider　damage　can　be　employed.　A　dual-sequence　quadratic　programming　(DSQP)　algorithm　was　used　in　this　work　to　solve　such　topology　optimization　models.　Numerical　examples　confirmed　the　effectiveness　and　feasibility　of　the　models.　The　results　indicated　that　both　good　load　path　and　weight　reduction　can　be　obtained.　In　addition,　compared　with　the　structure　obtained　using　conventional　topology　optimization,　redundancy　is　greatly　improved,　and　the　strength/stiffness　requirements　for　the　structure　can　be　satisfied　for　each　damage　scenario.　Furthermore,　the　results　indicate　that　the　strength/stiffness　of　the　structure,　after　topology　optimization,　is　only　slightly　sensitive　to　local　damage.