There　are　three　difficulties　in　topology　optimization　of　continuum　structures.　1)　The　topology　under　multiple　load　case　is　more　difficult　to　be　optimized　than　under　single　load　case,　because　the　former　becomes　a　multiple　objective　based　on　compliance　objective　functions.　2)　With　local　constraints,　such　as　an　elemental　stress　limit,　the　topology　is　more　difficult　to　be　solved　than　with　global　constraints,　such　as　the　displacement　or　frequency　limits,　because　the　sensitivity　analysis　of　the　former　has　very　expensive　computation.　3)　With　the　phenomenon　of　load　illness,　which　is　similar　with　stiffness　illness　in　the　structural　analysis,　it　is　not　easy　to　get　the　reasonable　final　topological　structure,　because　it　is　difficult　to　consider　different　influences　between　the　loads　with　small　forces　and　big　forces,　and　some　topology　paths　of　transferring　small　forces　may　disappear　during　the　iteration　process.　To　overcome　difficulties　above,　four　measures　are　adopted.　1)　Topology　optimization　model　is　established　by　independent　continuous　mapping　(ICM)　method.　2)　Based　on　the　von　Mises　strength　theory,　all　elements＇　stress　constraints　are　transformed　into　a　structural　energy　constraint.　3)　The　phenomenon　of　load　illness　is　divided　to　classify　into　three　cases.　4)　A　strategy　based　on　strain　energy　is　proposed　to　adopt　ICM　method　with　stress　globalization,　and　the　problems　of　the　above　mentioned　three　cases　of　load　illness　are　solved　in　terms　of　different　complementary　approaches.　Several　numerical　examples　show　that　the　topology　path　of　transferring　forces　can　be　obtained　more　easily　by　substituting　global　strain　energy　constraints　for　local　stresses　constraints,　and　the　problem　of　load　illness　can　be　solved　well　by　the　weighting　method　that　takes　the　structural　energy　as　a　weighting　coefficient.　©　2010　Higher　Education　Press　and　Springer-Verlag　Berlin　Heidelberg.