boussinesq_spline.m

function sigma_z=boussinesq_spline(q,a,b,z)
 % function that determines stress under corner of an a by b rectangular platform
  % z-meters below the platform. The calculated solutions are in the fmn data
  % m=fmn(:,1)
  % in column 2, fmn(:,2), n=1.2
  % in column 3, fmn(:,2), n=1.4
  % in column 4, fmn(:,2), n=1.6
  % this funciton uses spline interpolation
  % outputs : sigma_z is the stress  under the corner
  
  %fmn is the data table given
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];
%fmn1 is a new data table that removes the first column of n values to be
%used in interp2 function
    fmn1=fmn(:,2:4);
    
  %  these lines calculate m and n 
  m=a/z;
  n=b/z;
  
  %these lines convert the m and n values into there coordinates on the new
  %data table
  m=m*10;
  n=(n-1)/.2;
  
  %these lines create the cordinates of the fmn1 table
  y=1:8;
  x=1:3;
  
  % interp2 is a built in function that in this cases uses cubic spline to
  % solve for the interpolated value.  
  value=interp2(x,y,fmn1,n,m,'spline');
  
  %calculates the stress
  sigma_z=q*value;
end