%%%%?A?99?LINE?TOPOLOGY?OPTIMIZATION?CODE?BY?OLE?SIGMUND?JANUARY?2000?%%%
%%%%?CODE?MODIFIED?FOR?INCREASED?SPEED?September?2002?BY?OLE?SIGMUND?%%%
function?top（nelxnelyvolfracpenalrmin）;
%?INITIALIZE
x（1:nely1:nelx）?=?volfrac;?
loop?=?0;?
change?=?1.;
%?START?ITERATION
while?change?>?0.01??
??loop?=?loop?+?1;
??xold?=?x;
%?FE-ANALYSIS
??[U]=FE（nelxnelyxpenal）;?????????
%?objectIVE?FUNCTION?AND?SENSITIVITY?ANALYSIS
??[KE]?=?lk;
??c?=?0.;
??for?ely?=?1:nely
????for?elx?=?1:nelx
??????n1?=?（nely+1）*（elx-1）+ely;?
??????n2?=?（nely+1）*?elx???+ely;
??????Ue?=?U（[2*n1-1;2*n1;?2*n2-1;2*n2;?2*n2+1;2*n2+2;?2*n1+1;2*n1+2]1）;
??????c?=?c?+?x（elyelx）^penal*Ue‘*KE*Ue;
??????dc（elyelx）?=?-penal*x（elyelx）^（penal-1）*Ue‘*KE*Ue;
????end
??end
%?FILTERING?OF?SENSITIVITIE