SuperElement/CalcBqi2.m at master · mohammadtawfik/SuperElement · GitHub

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function Aqi=CalcBqi2(x,Xi,nn,qq)
    %This function evaluates the second derivativs
    % of B(x) function at all nodes
    %x  = x-position
    %Xi = coordinates of all nodes
    %nn = number of nodes
    %qq = elemenet continuity
    Aqi=zeros(nn,1);
    for ii=1:nn
        Temp1=0;
        for ll=1:nn
            if ll!=ii
                Temp0=1;
                for jj=1:nn
                    if and(jj!=ii,jj!=ll)
                        Temp0=Temp0*((x-Xi(jj))^(qq+1)) ...
                        /((Xi(ii)-Xi(jj))^(qq+1));
                    endif
                endfor
                if qq!=0
                  Temp1=Temp1+Temp0*(qq+1)*qq*((x-Xi(ll))^(qq-1))/ ...
                  ((Xi(ii)-Xi(ll))^(qq+1));
                endif
            endif
        endfor
        Temp2=0;
        for ll=1:nn
            if ll!=ii
                Temp21=0;
                for mm=1:nn
                  if and(mm!=ii,mm!=ll)
                    Temp0=1;
                    for jj=1:nn
                      if and(jj!=mm,and(jj!=ii,jj!=ll))
                        Temp0=Temp0*((x-Xi(jj))^(qq+1)) ...
                        /((Xi(ii)-Xi(jj))^(qq+1));
                      endif
                    endfor
                    Temp21=Temp21+Temp0*(qq+1)*((x-Xi(mm))^qq)/ ...
                    ((Xi(ii)-Xi(mm))^(qq+1));
                  endif
                endfor
                Temp2=Temp2+Temp21*(qq+1)*((x-Xi(ll))^qq)/ ...
                ((Xi(ii)-Xi(ll))^(qq+1));
            endif
        endfor
        Aqi(ii)=Temp1+Temp2;
    endfor
endfunction
    %Function will work on Octave, FreeMat, and Matlab
    %Create by Mohammad Tawfik
    %mohammad.tawfik@gmail.com
    %In assotiation with research paper published on
    %ResearchGate.Net
    %Title: In Search for the Super Element: Algorithms to Generate Higher-Order Elements
    %DOI: 10.13140/RG.2.2.24039.75682