Dear all,
>From the below given script I can get the mass matrix correctly(I mean in a
matrix format in some column output), but I could not get the stiffness like
the mass matrix.
Can someone comment on this?
Rgds,
n1:(1/8)*(1-eta)*(1-eta)*(2-ksi-eta-ksi^2-eta^2)$
n2:(-1/8)*a*(1-eta)^2*(-1-ksi)*(1-eta)$
n3:(-1/8)*b*(1-eta)^2*(-1-eta)*(1-eta)^2$
n4:(1/8)*(1+eta)*(1-eta)*(2+ksi-eta-ksi^2-eta^2)$
n5:(1/8)*a*(1+eta)^2*(ksi-1)*(1-eta)$
n6:(-1/8)*b*(1+eta)^2*(-1-eta)*(1-eta)^2$
n7:(1/8)*(1+eta)*(1+eta)*(2+ksi+eta-ksi^2-eta^2)$
n8:(1/8)*a*(1+eta)^2*(ksi-1)^2*(eta+1)$
n9:(1/8)*b*(1+eta)^2*(eta-1)*(1+eta)^2$
n10:(1/8)*(1-eta)*(1+eta)*(2-ksi+eta-ksi^2-eta^2)$
n11:-(1/8)*a*(1-eta)*(-ksi-1)*(eta+1)$
n12:(1/8)*b*(1-eta)^2*(eta-1)*(eta+1)^2$
N:matrix([n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12])$
mass_integrand:transpose(N).N$
mass:ro*t*a*b*integrate(integrate(mass_integrand,ksi,-1,1),eta,-1,1);
bc1:diff(N,ksi,2);
bc2:diff(N,eta,2);
bc3:diff(N,ksi,eta);
B:matrix([bc1],
[bc2],
[bc3]);
D:E*t^3/(12*(1-nu^2))$
C:matrix([1, nu, 0],[ nu, 1, 0],[0, 0, (1-nu)/2])$
stiffness_integrand:transpose(B).C.B$
stiffness:D*a*b*integrate(integrate(stiffness_integrand,ksi,-1,1),eta,-1,1)$