A　geometrically　nonlinear　topology　optimization　method　for　continuum　structures　is　proposed　based　on　the　independent　continuous　mapping　method.　The　stress　constraint　problem　is　studied　due　to　the　importance　of　structural　strength　in　engineering　applications.　First,　a　topology　optimization　model　is　established　for　a　lightweight　structure　with　element　stress　as　constraints.　Second,　the　stress　globalization　method　is　adopted　to　convert　local　stress　constraints　into　strain　energy　constraints,　which　overcomes　the　difficulties　caused　by　local　stress　constraints,　such　as　model　establishment,　sensitivity　analysis,　and　massive　solution　calculations.　Third,　the　sensitivity　of　the　objective　function　and　constraint　function　is　analyzed,　and　the　method　of　moving　asymptotes　is　employed　to　solve　the　optimization　model.　In　addition,　the　additive　hyperelasticity　technique　is　utilized　to　solve　the　numerical　instability　induced　by　structures　undergoing　large　deformation.　Numerical　examples　are　given　to　validate　the　feasibility　of　the　proposed　method.　The　method　provides　a　significant　reference　for　geometrically　nonlinear　optimization　design.