
Another question about coordinate transformation
Posted:
Jan 13, 2013 10:38 PM


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

