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function [sigma_z]=boussinesq_lookup(q,a,b,z)
fmn= [0.1,0.02926,0.03007,0.03058
0.2,0.05733,0.05894,0.05994
0.3,0.08323,0.08561,0.08709
0.4,0.10631,0.10941,0.11135
0.5,0.12626,0.13003,0.13241
0.6,0.14309,0.14749,0.15027
0.7,0.15703,0.16199,0.16515
0.8,0.16843,0.17389,0.17739];
m = a/z;
n = b/z;
if (n>1.5)
n=1.6;
elseif (1.3<=n)
if (n<=1.5)
n=1.4;
end
elseif 1.3<=n
n=1.2;
end
c = ones(1,4);
d = ones(1,4);
for i=1:4
[~,p]=min(abs(m-fmn(:,1)));
M =fmn(p,1);
fmn(p,1)=0;
if n==1.2
t=fmn(p,2);
elseif n==1.4
t=fmn(p,3);
elseif n==1.6
t=fmn(p,4);
end
d(i) = M;
c(i) = t;
end
b1=c(1);
b2=(c(2)-c(1))/(d(2)-d(1));
b3=(((c(3)-c(2))/(d(3)-d(2)))-((c(2)-c(1))/(d(2)-d(1)))/(d(3)-d(1)));
b4=(((c(4)-c(3))/(d(4)-d(3)))-((c(3)-c(2))/(d(3)-d(2)))-((c(2)-c(1))/(d(2)-d(1))))/(d(4)-d(1));
f3=b1+(b2*(m-d(1)))+(b3*(m-d(1))*(m-d(2)))+(b4*(m-d(1))*(m-d(2))*(m-d(3)));
sigma_z=q*f3;
end
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