331423959

Topology Design

Theorem

The topological derivative ofthe shape functional 4>(Q) is given by

_m*x {•.§:«!;

where v is solution to the adjoint semi-coupled eęuation, namely:

Findcp andv, such that —di v(kVcp) + cw<p    =    b_a    in    ft,

ip    =    0    on    <9ft,

—Av — k²v    =    o u<p    in    Q,

d_nv + \kv    =    0    on    <9ft,

^{ba =} ~W\ ^tv +    ■

J. Sokołowski (IECL) Topological Derivatives October 6, 2015    33 / 101