t_stress.m

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

function [Tnd]=T_stress(a,rea,num,x);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The function tfac calculates the compressive T stress, by
% calculating K_I(a,b)=f_I*stress*Sqrt(pi*a)
% f_I, is given in  *)"Stress Intensity factore Handbook Vol 1."
% The Society of Materials Science, Japan, Pergamon Press 1987
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  INPUT :
%%%%%%%%%%%%%%%%
% 	a  	=	crack length 
%	rea	=	reaction forces in top nodes of panel
%
%  OUTPUT :
%%%%%%%%%%%%%%%
%	Tnd	=	non-dimesionailised T-stress.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                  Constants                                            %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	a=round(a);
	alpa=a/W
	c=W-a;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%		Main Routine						%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 		Center Crack Panels					%
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%
% Changes  for center crack panels was made the d. 30 April 1994, as
% the beta values, had to be corrected for the deeply crack panels    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
         if num==1;  
		fm=[1 1.006 1.025 1.058 1.109 1.187 1.303 1.488 1.816 ...
                   2.3118]; % *) 
		al=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]; % *)
	if alpa <= 0.6 
		Beta=-(1+0.085*(2*a/W));
	else 
                if alpa==0.7 
		Beta=-1.261;
		end
		if alpa==0.8
		Beta=-1.460;
		end
		if alpa==0.9
		Beta=-1.93;
		end
 	end



	 end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%		Singel Edge Crack- Tension (displacement loaded)        %
%  Changes in f_function	d. 18/8-94 		  		%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        
        if num==2; 
		beta=[-0.464 -0.434 -0.371 -0.278 -0.153 0.69e-2 ...
		0.21 0.501 0.103e1];
                al=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9];
% obs 19/8-94   f=1.12-0.23*alpa+10.55*alpa^2-21.72*alpa^3+30.39*alpa^4;
   		f=(2*tan(pi*alpa/2)/(pi*alpa))^0.5* ...
   		(0.752+2.02*alpa+0.37*(1-sin(pi*alpa/2))^3)/cos(pi*alpa/2);
        end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 		Single Edge Crack - Bending 				%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




       if num==3;  
 		beta=[-0.363 -0.229 -0.07344 0.0921 0.262 0.433 0.610 0.839 0.126e1];				                      		
		
		al=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9];
                f=1.122-1.40*alpa+7.33*alpa^2-13.08*alpa^3+14*alpa^4;
                 [m,n]=size(rea)
                 for i=1:n;
                 M(i)=0.0;
                 for j=1:m;
                 M(i)= M(i)+(x(j)-c/2)*rea(j,i);
                 end;
                 M=abs(M);
                 end; 
		end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%		   Double Edge Crack  					%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


	if num==4;
                 beta=[-0.436 -0.445 -0.458 -0.463 -0.471 -0.441 -0.411 ...
                 -0.33 -0.196];
                 al=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9];
                 f= 1.222-0.154*alpa+0.807*alpa^2-1.894*alpa^3+2.494*alpa^4;
                 end;  
 
[g,h]=size(al);

if num~=1 % for CCP Beta is given by a function rather than vector 

		for i=1:h
				if al(i)==alpa
				Beta=beta(i);				
				end;
		end;
else
		for i=1:h
				if al(i)==alpa
				f=fm(i);				
				end;
		end;
end;		

if num==3;
				for i=1:n;
				Tnd(i)=6*M(i)*f*Beta/(W^2*s0);
				end
		else
					[m,n]=size(rea);
					if m~=1
					p=sum(rea);  
					else 
					p=rea;
					end
				Tnd=Beta*f*abs(p)/(W*s0);
		end;