The　topology　optimization　of　continuum　structures　is　investigated　to　obtain　an　optimized　topology　satisfying　the　fail-safe　design　principle　with　suitable　redundancy　components.　An　optimization　model　with　a　nonlinear　objective　and　linear　constraints　is　established　by　defining　the　reciprocal　topology　variable　as　design　variables　and　linearly　approximating　the　structural　performance.　The　model　is　solved　by　a　dual　sequential　quadratic　programming　(DSQP)　algorithm.　Topology　optimization　with　displacement　constraints　is　used　as　an　example.　The　presented　optimization　model　and　solution　approach　offers　the　following　advantages.　(1)　A　volume　constraint,　which　makes　determining　reasonable　values　difficult,　need　not　be　specified.　(2)　Weighted　coefficients,　which　combine　multiple　compliances　under　different　load　cases　into　a　combined　compliance,　need　not　be　specified　as　well.　(3)　The　presented　optimization　model　is　a　type　of　single-objective　programming　and　thus　avoids　the　challenges　in　the　min-max　model.　(4)　The　proposed　method　shows　a　strong　capability　of　finding　optimum　solutions.