limit_lo.m

ABAQUS is a general purpose finite element analysis program which is widely used to analyses mechani

function [pnd]=limit_load(rea,num,x,a);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The limit load is calculated for each geometry and each crack length
% using either the solution from Miller (1978) or the solution from a
% non hardening solution
%
alpa=a/W;
c=W-a;
if num==1 %  centre crack panels
	pl=2.3094*s0*(W-a)/2;
end;
if num==2 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Those limit load values was applied to fit displacement loaded
% sec-analysis. The data was obtained from the non-hardening sec.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%if a==100; pl=2.14e11;
%elseif a==200; pl=1.91e11;
%elseif a==300; pl=1.68e11;
%elseif a==400; pl=1.389e11;
%elseif a==500; pl=1.19e11;
%elseif a==600; pl=9.35e10;
%elseif a==700; pl=7.19e10;
%elseif a==800; pl=4.67e10;
%elseif a==900; pl=2.33e10;
%end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Limit load applied for sec-analysis, as sum of the reaction
% forces in the bottom for a force loaded model in non-hardening.
% ADK 12/1-95
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if a==100; pl=2.1352e11;
elseif a==200; pl=1.8656e11;
elseif a==300; pl=1.5376e11;
elseif a==400; pl=1.1393e11;
elseif a==500; pl=7.4994e10;
elseif a==600; pl=4.2781e10;
elseif a==700; pl=2.0736e10;
elseif a==800; pl=7.9079e9;
elseif a==900; pl=0.17111e10;
end

%pl=(3.6566*alpa^3-6.1261*alpa^2+1.4353*alpa+1.0922)*(W-a)*s0;
end;

if num==3;

%if alpa < 0.295
%ml=1.15*s0/4*W^2*(1.261-2.72*(0.31-alpa)^2)*(1-alpa)^2;
%else 
%ml= 1.15*s0*W^2*(1.2606*(1-alpa)^2)/4;
%end

     if a==100;	ml=5.310e13;
      elseif a==200; ml=4.5786e13;
       elseif a==300; ml=3.6178e13;
	elseif a==400; ml=2.6587e13;
	 elseif a==500; ml=1.8529e13;
	  elseif a==600; ml=1.1899e13;
	   elseif a==700; ml=6.7500e12;
	    elseif a==800; ml=2.9803e12;
	     elseif a==900; ml=7.4635e11;
	     


end;
end;
                 
if num==4;   % double edge crack
pl=2.3094*s0*(c)/2*(1+log((1-a/(2*W))/(1-a/W)));
end




[m,n]=size(rea);
	if num==3;
		for i=1:n;
                 M(i)=0.0;
                 for j=1:m;
                 M(i)= M(i)+(x(j)-c/2)*rea(j,i);
                 end;
                 end;  
		pnd=abs(M)/ml;

	else
		pnd=abs(sum(rea)/pl);
	end;