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1、%function[J1,J2,J3,r,x1,x2,x3]=ZZ8DPQ(A)%计算主、8面体、等效、偏、球应力，输入：A-应力矩阵%A=[1003;261;315]A=input('A=?')fori=1:3forj=1:3str=strcat('请输入A(',num2str(i),',',num2str(j),'):');A(i,j)=input(str);endend%A=[1003;261;315]%A=[50-5;0-50;-505]%A=[423;261;315]%A=[505080;500-75;80-75-30]%计算第一不变量J1=A(1,1)+A(2,2
2、)+A(3,3);%计算第二不变量J2=det(A(1:2,1:2))+det(A(2:3,2:3))+det(A([1,3],[1,3]));%计算第三不变量J3=det(A);%求主应力赋值rp=[1-J1+J2-J3]r=[roots(p)]S123=sort(r,'descend')%%%%%%%%应力矩阵主对角元素减主应力B=A;fori=1:3forj=1:3B(j,j)=A(j,j)-r(i);%pauseend%求主应力方向余弦[x1x2x3]=solve('(B(1,1)*x1+B(1,2)*x2+B(1,3)*x3)=0',...'(B(2,1)*x1+B
3、(2,2)*x2+B(2,3)*x3)=0',...'(x1*x1+x2*x2+x3*x3)=1',...'x1','x2','x3');%numeric(x1)lmn=[eval(x1);eval(x2);eval(x3)]end%求主切应力值t121323=[(abs(r(1)-r(2)))/2(abs(r(1)-r(3)))/2(abs(r(3)-r(2)))/2]%求最大切应力值tmax=max(max(t121323))%求8面体应力值FX=[1/sqrt(3);1/sqrt(3);1/sqrt(3)]C=[S123(1)00;0S123(2)0;00S123(3)
4、]%计算等倾面上全应力分量S=C*FX;%求全应力分量的平方赋值为S1S1=S.^2;%求等倾面全应力赋值为SQSQ=sqrt(sum(S1));%求等倾面正应力赋值为SZ8Sz8=S'*FX%求剪应力赋值为SJSj8=sqrt(SQ^2-Sz8^2)%求等效应力赋值为SJSdx=sqrt(((S123(1)-S123(2))^2+(S123(3)-S123(2))^2+(S123(1)-S123(3))^2)/2)%求应力球张量Sm=[J1/300;0J1/30;00J1/3]%求应力偏张量Sp=A-Sm%画莫尔圆alpha=0:pi/20:2*pi;%角度[0,2*pi]
5、R=(S123(1)-S123(3))/2;%半径x=(S123(1)+S123(3))/2+R*cos(alpha);y=R*sin(alpha);plot(x,y,'r-')fill(x,y,'r');%计算莫尔圆图面范围ifS123(3)>=0,XMIN=0,XMAX=S123(1)+1,YMIN=-R-1,YMAX=+R+1;elseifS123(1)<=0,XMIN=S123(3)-1,XMAX=0,YMIN=-R-1,YMAX=+R+1;elseXMIN=S123(3)-1,XMAX=S123(1)+1,YMIN=-R-1,YMAX=+R+1;endaxisequ
6、alholdonR=(S123(1)-S123(2))/2;%半径x=(S123(1)+S123(2))/2+R*cos(alpha);y=R*sin(alpha);plot(x,y,'k-')fill(x,y,'k');axisequalholdonR=(S123(2)-S123(3))/2;%半径x=(S123(2)+S123(3))/2+R*cos(alpha);y=R*sin(alpha);plot(x,y,'-')fill(x,y,'b');%line([0,0],[YMIN,YMAX])axisequalaxis([XMINXMAXYMINYMAX])%设定轴取值
7、范围%quiver(0,YMIN,0,YMAX,'r','filled','LineWidth',2);%line([0,0],[YMIN,YMAX],'Color','k','LineWidth',2)%annotation1=annotation(figure1,'arrow',[(S123(1)+S123(3))/20],[S123(1)+S123(2))/20]);%annotation1=annotation(figure1,'arrow',[0.250.75],[0.50960.5096])
