syms Px Mz1 Mz2 Mz3 Mz4 Mz5 Qz1 Qz2 Qz3 Qz4 Qz5 My1 My2 My3 My4 My5 Qy1...
Qy2 Qy3 Qy4 Qy5 Mx1 Mx2 Mx3 Mx4 Mx5 mx1 mx2 B1 B2 B3 B4 B5...
Kb1 Kt1 Kb2 Kt2 Kb3 Kt3 Kb4 Kt4
Mz=[Mz1 Mz2 Mz3 Mz4 Mz5]; Qz=[Qz1 Qz2 Qz3 Qz4 Qz5];Px=[Px];
My=[My1 My2 My3 My4 My5]; Qy=[Qy1 Qy2 Qy3 Qy4 Qy5];
Mx=[Mx1 Mx2 Mx3 Mx4 Mx4];
B=[B1 B2 B3 B4 B5];
ez=0; ey=0; z=0; y=0; z0=0; y0=0;
beta_y= 1/Iy*(z^3*area
beta_z= 1/Iz*(y^3*area
beta_w= 1/Cw*omega_n*(y^2+z^2)*area; %(3.21)
C0= rp_sequare
Cy=ey; Cz=ez-z0; %(3.27)
d=sym(zeros(7,7));e=sym(zeros(7,7));f=sym(zeros(7,7));K=sym(zeros(35,35));
m=0;
for i=1:4
%i is the number of nodes
j=i+1 ;
if i<=2
mx=Mx(1,2);
else
mx=Mx(1,4);
end
%2.1- d Matrix
d(6,2)=-0.1*Px;
d(6,4)=-1.1*Px*Cz-0.55*(My(1,i)-My(1,j))-0.1*Qz(1,i)*l-0.45*Qz(1,j)*l;
d(6,6)=d(5,5);
d(7,2)=-0.1*Px*Cz-0.05*(My(1,i)-My(1,j))-0.05*Qz(1,j)*l;
d(7,3)=0.1*Px*Cy+0.05*(Mz(1,i)-Mz(1,j))+0.05*Qy(1,j)*l;
d(7,4)=-0.1*Px*C0-(0.05*(My(1,i)-My(1,j))+0.05*Qz(1,i)*l)*beta_y...
-(0.05*(Mz(1,i)-Mz(1,j))+0.05*Qy(1,i)*l)*beta_z...
d;
%2.2- e matrix:
e(5,4)=0.1*Px*Cy+0.05*(Mz(1,i)-Mz(1,j))-0.05*Qy(1,i)*l+0.1*Qy(1,j)*l;
e(5,7)=Px*Cy*l/30+(Mz(1,i)-Mz(1,j))*l/60+Qy(1,i)*l^2/60;
e(6,2)=d(6,2);
e(6,4)=-0.1*Px*Cz-0.05*(My(1,i)-My(1,j))+0.05*Qz(1,i)*l-0.1*Qz(1,j)*l;
e(7,6)=-Px*Cz*l/30-(My(1,i)-My(1,j))*l/60-Qz(1,j)*l^2/60;
e;
%2.33 - f matrix
f(1,1)=0;f(2,2)=d(2,2);f(3,3)=d(3,3);f(4,4)=d(4,4);f(5,5)=d(5,5);
f(6,6)=d(6,6);
f(7,7)=2*Px*C0*l/15+((My(1,i)-My(1,j))*l/15+Qz(1,i)*l^2/20+Qz(1,j)*l^2/60)...
*beta_y+((Mz(1,i)-Mz(1,j))*l/15+Qz(1,i)*l^2/20+Qz(1,j)*l^2/60)*beta_z...
+(Kb1*(B(1,i)-B(1,j))*l+Kt1*mx*l^2)*beta_w;
f(4,2)=-e(4,2);f(2,4)=f(4,2);f(4,3)=-e(4,3);f(3,4)=f(4,3);f(5,3)=-d(5,3);
f(3,5)=f(5,3);
f;
KG=[d e;e f];
Kt=KE+KG
K=
I downsized it to 4 submatrices thinking that it will be easier, K matrix should be constructed from Kt, the first Kt(i=1) is the first 14x14 element of the K then Kt(i=2) starts at K(8,8) the overlaped elements should be Kt(i=1)+Kt(i=2) and so on....
