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Topic: Another question about coordinate transformation
Replies: 3   Last Post: Jan 14, 2013 12:37 AM

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Tang Laoya

Posts: 27
Registered: 11/21/12
Another question about coordinate transformation
Posted: Jan 13, 2013 10:38 PM
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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?

Tang Laoya

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