syms X EI A P R S CM L
E=71.7e9;R=2810;Rp=7800;Gc=1e7;e31=-16;EP=5e10;ta=0.46e-3;tb=2e-3;b=0.035;alfa=0.216;beta=6.044e-4;d31=-320e-12;
I=(1/12)*b*tb^3;
Ip=(1/12)*b*ta^3+(b*ta)*((ta+tb)/2)^2;
a=b*tb;
z=(ta+tb)/2;
zc=(tb/2)+ta;
s=a*R;
EI=E*I;
S1=b*(R*tb+2*Rp*ta);
EI1=EI+2*EP*Ip;
Ne=6;
F=[1,X,X^2,X^3];
Tv=[1 0 0 0 ; 0 1 0 0 ; -3/L^2 -2/L 3/L^2 -1/L ; 2/L^3 1/L^2 -2/L^3 1/L^2;];
N= F*Tv;
n1=diff(N);
n2=diff(N,2);
M=s*int((transpose(N)*N),0,L);
Mp=S1*int((transpose(N)*N),0,L);
K=EI*int((transpose(n2)*n2),0,L);
KP=EI1*int((transpose(n2)*n2),0,L);
L=55.3e-3;
plas=2;
hf=EP*d31*b*z*int((transpose(n1)),0,L);
hff=((Ne*2)-(plas*2));
hf2=zeros(hff,1);
hf1=zeros((Ne*2-4)-hff,1);
h14=[hf1;hf;hf2];
whos hf hf1 hf2
Notice that hf2 is size hff, and hf1 is size (Ne*2-4)-hff, so put the two together like you do in h14, and the total is going to be Ne*2-4 rows. In this case N2 = 6 so that would be 6*2-4 = 8. So h14 is going to be size number of rows in hf, plus 8. Meanwhile,with F and Tv both having length 4, F*Tv is going to have 4 rows, so N has 4 rows, and that leads to n1 having 4 rows, and since hf has the integral of something with 4 rows, hf is going to have 4 rows. At this point we have 4 rows in hf and add another (N2*2-4) = 8 rows, for a total of 12 rows in h14. A couple of mostly-useless transformations later, that becomes h
temp=sym(h14)
h4=sym(temp);
h=subs(h4);
p=Gc*zc*e31*b*int((transpose(n2)),0,L);
cp2=[hf1;p;hf2];
cp=transpose(cp2);
cp4=sym(cp);
cp1=subs(cp4);
m=(Ne*4)-2*(Ne-1);
disp([m, Ne])
Now Ne*4 - 2*(Ne-1) is Ne*4 - Ne*2 + 2 = (Ne*2) + 2. With Ne being 6, that gives 14, and that is the size you use to create several matrices.
Me=sym(M);
Melem=subs(Me);
Kh=sym(K);
Kelem=subs(Kh);
syms Ko1 Ko2 Ko3 Ko4 Ko5 Ko6
Ko1= zeros(m);
Ko2=zeros(m);
Ko3= zeros(m);
Ko4 = zeros(m);
Ko5 = zeros(m);
Ko6 = zeros(m);
Ko1 = sym(Ko1);
Ko2 = sym(Ko2);
Ko3 = sym(Ko3);
Ko4 = sym(Ko4);
Ko5 = sym(Ko5);
Ko6 = sym(Ko6);
for i1 = 1:4
for j1 = 1:4
Ko6(i1+10,j1+10)=subs( K(i1,j1));
Ko5(i1+8,j1+8)= subs (K(i1,j1));
Ko4(i1+6,j1+6)= subs( K(i1,j1));
Ko3(i1+4,j1+4)= subs (K(i1,j1));
Ko2(i1+2,j1+2)=subs (KP(i1,j1));
Ko1(i1,j1)= subs (K(i1,j1));
end
end
Ko1;
Ko2;
Ko3;
Ko4;
Ko5;
Ko6;
Ksys=Ko1+Ko2+Ko3+Ko4+Ko5+Ko6;
Ksys
Ksy=sym(Ksys);
Ksyst=subs(Ksys);
syms mo1 mo2 mo3 mo4 mo5 mo6
mo1 = zeros(m);
mo2 = zeros(m);
mo3 = zeros(m);
mo4 = zeros(m);
mo5 = zeros(m);
mo6 = zeros(m);
mo1 = sym(mo1);
mo2 = sym(mo2);
mo3 = sym(mo3);
mo4 = sym(mo4);
mo5 = sym(mo5);
mo6 = sym(mo6);
for i1 = 1:4
for j1 = 1:4
mo6(i1+10,j1+10) = M(i1,j1);
mo5(i1+8,j1+8) = M(i1,j1);
mo4(i1+6,j1+6) = M(i1,j1);
mo3(i1+4,j1+4) = M(i1,j1);
mo2(i1+2,j1+2) = Mp(i1,j1);
mo1(i1,j1) = M(i1,j1);
end
end
mo1;
mo2;
mo3;
mo4;
mo5;
mo6;
Msys=mo1 + mo2 + mo3 + mo4 + mo5 + mo6;
Msys
Mss=sym(Msys);
Msyst = subs(Mss);
cm=alfa*Msyst+beta*Ksyst;
ccm=Msyst\cm;
MMo=Msyst\Ksyst;
aaz=eye(m-2,m-2);
cc=-1*ccm;
M2=-1*MMo;
tot=(Ne*4);
a1=zeros(tot);
a2=zeros(tot);
a3=zeros(tot);
a1=sym(a1);
a2=sym(a2);
a3=sym(a3);
Nee=Ne*2;
for i1 = 1:Nee
for j1 = 1:Nee
a1(i1+Nee,j1) = M2(i1,j1);
a2(i1,j1+Nee) = aaz(i1,j1);
a3(i1+Nee,j1+Nee) = cc(i1,j1);
end
end
a1;
a2;
a3;
At=a1+a2+a3;
Att=sym(At);
A=subs(Att);
bm = zeros(1,Nee);
whos Msyst h
We can see here that h did indeed arrive with 12 rows as described. But Msyst is based on size m, which is 14. And you are trying to do an operation between those 14 rows of Msyst and the 12 rows of h, which is going to fail.
Bm =Msyst/h;
B=[bm ,Bm];
cm=zeros(1,Nee);
Cii=[cm,cp1];
Ci=sym(Cii);
C=subs(Ci);
A=double(A);
B=double(B);
C=double(C);
