The　polish　mapping　and　the　filter　mapping　in　the　ICM　(independent　continuous　mapping)　method　for　topology　optimization　were　extended,　and　the　composite　function　was　used　to　coordinate　the　filter　function.　Due　to　the　superposed　discrete　effects　of　composite　functions,　the　composite　function　of　the　power　function　and　the　sine　function　was　introduced　to　identify　the　presence　and　absence　of　the　elements.　The　ICM　method　was　used　to　establish　the　topology　optimization　model　for　the　continuum　structure　with　the　minimum　weight　under　the　displacement　constraints,　which　was　solved　with　the　exact　dual　algorithm　of　the　quadratic　programming.　Then　based　on　the　dynamic　inversion　strategy,　the　rational　inversion　function　was　constructed　with　the　optimal　threshold　to　obtain　the　most　strict　discrete　solution.　Moreover,　the　2-stage　＂discrete-continuous＂　and　＂continuous-discrete＂　solution　method　was　established　for　topology　optimization.　Moreover,　a　calculator　program　was　developed　and　compiled　based　on　the　MATLAB　according　to　this　new　method.　The　results　show　that　the　proposed　method　has　the　advantages　of　higher　computational　efficiency,　less　optimal　gray　values　and　less　structural　weight　after　inversion,　and　gives　a　more　reasonable　structural　topology.　©　2018　Elsevier　B.V.　All　rights　reserved.