obtaining large numbers while using syms

Hello, I have a matrix which vontains symbols:

kesi_eta=[1/sqrt(3)    1/sqrt(3)
          -1/sqrt(3)   1/sqrt(3)
          -1/sqrt(3)   -1/sqrt(3)
          1/sqrt(3)    -1/sqrt(3)];
Kij_new=0;
for i=1:4
    kesi=kesi_eta(i,1);
    eta=kesi_eta(i,2);
    B=(1/4).*[1+eta   0       -1-eta   0       -1+eta  0        1-eta   0
          0       1+kesi  0        1-kesi  0       -1+kesi  0       -1-kesi
          1+kesi  1+eta   1-kesi   -1-eta  -1+kesi -1+eta   -1-kesi 1-eta];
J=[Lx/2   0
   0      Ly/2];
Bhat=(1/(2*Lx*Ly)).*[Ly*(1+eta)  0            -Ly*(1+eta)  0           -Ly*(1-eta)   0            Ly*(1-eta)   0
                     0           Lx*(1+kesi)  0            Lx*(1-kesi) 0             -Lx*(1-kesi) 0            -Lx*(1+kesi)
                     Lx*(1+kesi) Ly*(1+eta)   Lx*(1-kesi)  -Ly*(1+eta) -Lx*(1-kesi)  -Ly*(1-eta)  -Lx*(1+kesi) Ly*(1-eta)];
D_red=[1/E -v/E    0;
       -v/E 1/E    0;
       0     0   1/G];
C=D_red^-1;

Kij=Bhat.'*C*Bhat*h*det(J);
    Kij1=Kij;
    Kij_old=Kij_new+Kij1;
    Kij_new=Kij_old;
end

and the out put gives me very large numbers without simplification.even when I use function simplify(), I face these numbers:

[                                  (72115234146317045769238718114163*E*h*(9*v - 17))/(2596148429267413814265248164610048*(v^2 - 1)),                                           -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),     (3*E*h*(13521606402434444180830355908725*v + 10516804979671237742249216795996))/(324518553658426726783156020576256*(v^2 - 1)),                               -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),                                   -(4507202134144814726943451969575*E*h*(9*v - 17))/(324518553658426726783156020576256*(v^2 - 1)),                                            (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)), -(3*E*h*(216345702438951137307716154342489*v - 120192056910528423132922512324889))/(2596148429267413814265248164610048*(v^2 - 1)),                                (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1))]
[                                             -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                (72115234146317045769238718114163*E*h*(2*v - 11))/(1298074214633706907132624082305024*(v^2 - 1)),                                  (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),  -(3*E*h*(24038411382105681923079572704721*v + 30048014227632094800241850930179))/(649037107316853453566312041152512*(v^2 - 1)),                                              (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                 -(4507202134144814726943451969575*E*h*(2*v - 11))/(162259276829213363391578010288128*(v^2 - 1)),                                 -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)), (3*E*h*(24038411382105678543698410504400*v + 192307291056845458764017743838089))/(1298074214633706907132624082305024*(v^2 - 1))]
[     (3*E*h*(13521606402434444180830355908725*v + 10516804979671237742249216795996))/(324518553658426726783156020576256*(v^2 - 1)),                                (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),                                  (72115234146317045769238718114163*E*h*(9*v - 17))/(2596148429267413814265248164610048*(v^2 - 1)),                                            (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)), -(3*E*h*(216345702438951137307716154342489*v - 120192056910528423132922512324889))/(2596148429267413814265248164610048*(v^2 - 1)),                               -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),                                   -(4507202134144814726943451969575*E*h*(9*v - 17))/(324518553658426726783156020576256*(v^2 - 1)),                                           -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1))]
[                                 -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),  -(3*E*h*(24038411382105681923079572704721*v + 30048014227632094800241850930179))/(649037107316853453566312041152512*(v^2 - 1)),                                              (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                (72115234146317045769238718114163*E*h*(2*v - 11))/(1298074214633706907132624082305024*(v^2 - 1)),                                  (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)), (3*E*h*(24038411382105678543698410504400*v + 192307291056845458764017743838089))/(1298074214633706907132624082305024*(v^2 - 1)),                                             -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                 -(4507202134144814726943451969575*E*h*(2*v - 11))/(162259276829213363391578010288128*(v^2 - 1))]
[                                   -(4507202134144814726943451969575*E*h*(9*v - 17))/(324518553658426726783156020576256*(v^2 - 1)),                                            (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)), -(3*E*h*(216345702438951137307716154342489*v - 120192056910528423132922512324889))/(2596148429267413814265248164610048*(v^2 - 1)),                                (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),                                  (72115234146317045769238718114163*E*h*(9*v - 17))/(2596148429267413814265248164610048*(v^2 - 1)),                                           -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),     (3*E*h*(13521606402434444180830355908725*v + 10516804979671237742249216795996))/(324518553658426726783156020576256*(v^2 - 1)),                               -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1))]
[                                              (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                 -(4507202134144814726943451969575*E*h*(2*v - 11))/(162259276829213363391578010288128*(v^2 - 1)),                                 -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)), (3*E*h*(24038411382105678543698410504400*v + 192307291056845458764017743838089))/(1298074214633706907132624082305024*(v^2 - 1)),                                             -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                (72115234146317045769238718114163*E*h*(2*v - 11))/(1298074214633706907132624082305024*(v^2 - 1)),                                  (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),  -(3*E*h*(24038411382105681923079572704721*v + 30048014227632094800241850930179))/(649037107316853453566312041152512*(v^2 - 1))]
[ -(3*E*h*(216345702438951137307716154342489*v - 120192056910528423132922512324889))/(2596148429267413814265248164610048*(v^2 - 1)),                               -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),                                   -(4507202134144814726943451969575*E*h*(9*v - 17))/(324518553658426726783156020576256*(v^2 - 1)),                                           -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),     (3*E*h*(13521606402434444180830355908725*v + 10516804979671237742249216795996))/(324518553658426726783156020576256*(v^2 - 1)),                                (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),                                  (72115234146317045769238718114163*E*h*(9*v - 17))/(2596148429267413814265248164610048*(v^2 - 1)),                                            (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1))]
[                                  (324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)), (3*E*h*(24038411382105678543698410504400*v + 192307291056845458764017743838089))/(1298074214633706907132624082305024*(v^2 - 1)),                                             -(324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                 -(4507202134144814726943451969575*E*h*(2*v - 11))/(162259276829213363391578010288128*(v^2 - 1)),                                 -(324518553658426690754359001612289*E*h*(3*v - 1))/(2596148429267413814265248164610048*(v^2 - 1)),  -(3*E*h*(24038411382105681923079572704721*v + 30048014227632094800241850930179))/(649037107316853453566312041152512*(v^2 - 1)),                                              (324518553658426690754359001612289*E*h)/(2596148429267413814265248164610048*(v - 1)),                                (72115234146317045769238718114163*E*h*(2*v - 11))/(1298074214633706907132624082305024*(v^2 - 1))]
 
 

Can someone pleaaase help me? I have even used vpa() and still the problem has not been fixed

thank you

[Walter Roberson]

Sqrt = @(x) sqrt(sym(x)) ;

kesi_eta=[1/Sqrt(3)    1/Sqrt(3)
        -1/Sqrt(3)   1/Sqrt(3)
        -1/Sqrt(3)   -1/Sqrt(3)
        1/Sqrt(3)    -1/Sqrt(3)];

Answer 1

[Ameer Hamza]

Specify the number of digits in vpa() to

vpa(x, 4)

[mojtaba najafi]

thank you for your answer.but now I reach something like this:

vpa(ans,4)
 
ans =
 
[  (1.541e-33*(7.569e+31*v - 8.053e+31))/(v^2 - 1.0),                                 -0.02083/(v - 1.0),   (7.704e-34*(4.056e+31*v - 3.09e+31))/(v^2 - 1.0), -(7.704e-34*(4.154e+31*v - 2.704e+31))/(v^2 - 1.0), -(7.704e-34*(4.056e+31*v - 7.662e+31))/(v^2 - 1.0), -(7.704e-34*(8.643e+31*v - 1.009e+32))/(v^2 - 1.0), -(3.081e-33*(3.785e+31*v - 2.883e+31))/(v^2 - 1.0),  (3.081e-33*(3.875e+31*v - 2.523e+31))/(v^2 - 1.0)]
[                                 -0.02083/(v - 1.0),  (7.704e-34*(4.831e+30*v - 3.076e+32))/(v^2 - 1.0),  (3.852e-34*(1.227e+32*v - 1.449e+31))/(v^2 - 1.0),  -(7.704e-34*(4.831e+30*v + 7.63e+31))/(v^2 - 1.0),  (3.852e-34*(3.892e+32*v + 1.449e+31))/(v^2 - 1.0), -(1.541e-33*(9.014e+30*v - 4.958e+31))/(v^2 - 1.0), -(1.541e-33*(1.144e+32*v - 1.352e+31))/(v^2 - 1.0),  (3.081e-33*(4.507e+30*v + 7.119e+31))/(v^2 - 1.0)]
[   (7.704e-34*(4.056e+31*v - 3.09e+31))/(v^2 - 1.0),  (3.852e-34*(1.227e+32*v - 1.449e+31))/(v^2 - 1.0),  (1.926e-34*(4.348e+31*v - 8.212e+31))/(v^2 - 1.0),                                 0.005582/(v - 1.0), -(1.926e-34*(4.348e+31*v + 1.008e+32))/(v^2 - 1.0), -(7.704e-34*(4.154e+31*v - 2.704e+31))/(v^2 - 1.0), -(7.704e-34*(4.056e+31*v - 7.662e+31))/(v^2 - 1.0),                                 -0.02083/(v - 1.0)]
[ -(7.704e-34*(4.154e+31*v - 2.704e+31))/(v^2 - 1.0),  -(7.704e-34*(4.831e+30*v + 7.63e+31))/(v^2 - 1.0),                                 0.005582/(v - 1.0),  (3.852e-34*(9.662e+30*v - 5.314e+31))/(v^2 - 1.0),  (3.852e-34*(1.227e+32*v - 1.449e+31))/(v^2 - 1.0),   (3.852e-34*(3.606e+31*v + 7.42e+30))/(v^2 - 1.0),                                 -0.02083/(v - 1.0), -(1.541e-33*(9.014e+30*v - 4.958e+31))/(v^2 - 1.0)]
[ -(7.704e-34*(4.056e+31*v - 7.662e+31))/(v^2 - 1.0),  (3.852e-34*(3.892e+32*v + 1.449e+31))/(v^2 - 1.0), -(1.926e-34*(4.348e+31*v + 1.008e+32))/(v^2 - 1.0),  (3.852e-34*(1.227e+32*v - 1.449e+31))/(v^2 - 1.0),  (1.926e-34*(4.348e+31*v - 5.818e+32))/(v^2 - 1.0),                                 -0.02083/(v - 1.0),    (7.704e-34*(4.056e+31*v + 9.4e+31))/(v^2 - 1.0), -(1.541e-33*(1.144e+32*v - 1.352e+31))/(v^2 - 1.0)]
[ -(7.704e-34*(8.643e+31*v - 1.009e+32))/(v^2 - 1.0), -(1.541e-33*(9.014e+30*v - 4.958e+31))/(v^2 - 1.0), -(7.704e-34*(4.154e+31*v - 2.704e+31))/(v^2 - 1.0),   (3.852e-34*(3.606e+31*v + 7.42e+30))/(v^2 - 1.0),                                 -0.02083/(v - 1.0),   (3.852e-34*(1.346e+32*v - 1.78e+32))/(v^2 - 1.0),  (3.081e-33*(3.875e+31*v - 2.523e+31))/(v^2 - 1.0), -(1.541e-33*(3.364e+31*v + 6.923e+30))/(v^2 - 1.0)]
[ -(3.081e-33*(3.785e+31*v - 2.883e+31))/(v^2 - 1.0), -(1.541e-33*(1.144e+32*v - 1.352e+31))/(v^2 - 1.0), -(7.704e-34*(4.056e+31*v - 7.662e+31))/(v^2 - 1.0),                                 -0.02083/(v - 1.0),    (7.704e-34*(4.056e+31*v + 9.4e+31))/(v^2 - 1.0),  (3.081e-33*(3.875e+31*v - 2.523e+31))/(v^2 - 1.0),  (3.081e-33*(3.785e+31*v - 7.149e+31))/(v^2 - 1.0),                                  0.07775/(v - 1.0)]
[  (3.081e-33*(3.875e+31*v - 2.523e+31))/(v^2 - 1.0),  (3.081e-33*(4.507e+30*v + 7.119e+31))/(v^2 - 1.0),                                 -0.02083/(v - 1.0), -(1.541e-33*(9.014e+30*v - 4.958e+31))/(v^2 - 1.0), -(1.541e-33*(1.144e+32*v - 1.352e+31))/(v^2 - 1.0), -(1.541e-33*(3.364e+31*v + 6.923e+30))/(v^2 - 1.0),                                  0.07775/(v - 1.0),  (6.163e-33*(8.411e+30*v - 4.626e+31))/(v^2 - 1.0)]
 

As you can see it is not a reaconable answer.

[Ameer Hamza]

What type of simplification do you want? The polynomials in numerators or denominators cannot be further simplified.

Answer 2

[Walter Roberson]

%variables user did not define. Give them a definite value.
h = sym(5/3); E = sym(10000); v = sym(123); Lx = sym(28); Ly = sym(18); G = sym(42); 

%proceed

Sqrt = @(x) sqrt(sym(x)) ;

kesi_eta=[1/Sqrt(3)    1/Sqrt(3)
        -1/Sqrt(3)   1/Sqrt(3)
        -1/Sqrt(3)   -1/Sqrt(3)
        1/Sqrt(3)    -1/Sqrt(3)];
Kij_new=0;
for i=1:4
    kesi=kesi_eta(i,1);
    eta=kesi_eta(i,2);
    B=(1/4).*[1+eta   0       -1-eta   0       -1+eta  0        1-eta   0
          0       1+kesi  0        1-kesi  0       -1+kesi  0       -1-kesi
          1+kesi  1+eta   1-kesi   -1-eta  -1+kesi -1+eta   -1-kesi 1-eta];
J=[Lx/2   0
   0      Ly/2];
Bhat=(1/(2*Lx*Ly)).*[Ly*(1+eta)  0            -Ly*(1+eta)  0           -Ly*(1-eta)   0            Ly*(1-eta)   0
                     0           Lx*(1+kesi)  0            Lx*(1-kesi) 0             -Lx*(1-kesi) 0            -Lx*(1+kesi)
                     Lx*(1+kesi) Ly*(1+eta)   Lx*(1-kesi)  -Ly*(1+eta) -Lx*(1-kesi)  -Ly*(1-eta)  -Lx*(1+kesi) Ly*(1-eta)];
D_red=[1/E -v/E    0;
       -v/E 1/E    0;
       0     0   1/G];
C=D_red^-1;
Kij=Bhat.'*C*Bhat*h*det(J);
    Kij1=Kij;
    Kij_old=Kij_new+Kij1;
    Kij_new=Kij_old;
end
simplify(Kij_new)

ans =