Abstract In this paper an exact analytical solution of effective conductivity in a two-phase material with the generalized chequer-board geometry is obtained. They are
In(σe/σ2)=In(R+s2/R+1),
Where
R=s(1+ s2)[2+ε(ηs2 -1)]+ s2 (s2-1)T(ε,η)/s(1+ s)2 ε(1-η)-(s-1)T(ε,η)
And T(ε,η)=Σ H(n)sinh[√λna(1-η)tan([√λnbε)/h sinh([√λna ) tan ([√λnb)
Some calculated results for a=b, n=l and s=50, 7.14 are also shown.
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