Date: Jan 13, 2013 10:38 PM
Author: Tang Laoya
Subject: Another question about coordinate transformation

Dear all,

In isoparameteric finite element of second order tetrahedron element, the original coordinate (x,y,z) would be transformed to standard coordinate (xi, eta, zeta) by shape function. As a result, for any (xi_i, eta_i, zeta_i) in the element, the original coordinate (x_i,y_i,z_i) can be calculated:
x_i=sum(N(i)*x(i), i=1,..,10)
y_i=sum(N(i)*y(i), i=1,..,10)
z_i=sum(N(i)*z(i), i=1,..,10)

Now my question is: if I give a rotation to the original element, the (x_i, y_i, z_i) is transformed to (x_ii, y_ii, z_ii), which can be calculated from (xi_ii, eta_ii, zeta_ii), what's the relationship between (xi_i, eta_i, zeta_i) and (xi_ii, eta_ii, zeta_ii)? are they just the same? how to prove this relationship?


Thanks,
Tang Laoya