Topolopy　optimization　design　of　continuum　structures　that　can　rake　account　of　stress　and　displacement　constraints　simultaneously　is　difficult　to　solve　at　present.　The　main　obstacle　lies　in　that,　the　explicit　function　expressions　between　topological　variables　and　stress　or　displacement　constraints　can　nor　be　obtained　using　homogenization　method　or　variable　density　method.　Furthermore,　large　quantities　of　design　variables　in　the　problem　make　it　hard　to　deal　with　by　the　formal　mathematical　programming　approach.　In　this　paper,　a　smooth　model　of　topology　optimization　for　continuum　structures　is　established　which　has　weight　objective　considering　stress　and　displacement　constraints　based　on　the　independent-continuous　topological　variable　concept　and　mapping　transformation　method　proposed　by　Sui　Yunkang　and　Yang　Deqing.　Moreover,　the　approximate　explicit　expressions　are　given　between　topological　variables　and　stress　or　displacement　constraints.　The　problem　is　well　solved　by　using　dual　programming　approach,　and　the　proposed　element　deletion　criterion　implements　the　inversion　of　topology　variables　from　the　discrete　to　the　continuous.　Numerical　examples　verify　the　validity　of　proposed　method.