26-02-09

Two minor epiphanies; 1) the expression Partial wrt "s" of d(k)=u x d(k) is a restatement that "d" follows "u" and 2) the compatibility equation is the long sought after nonlinear coupling of torsional and transverse moments. I therefore know that in uniplanar responses w= Partial wrt "t" of the Integral (u) wrt "s".

19-01-09

The difference between r(i,j,k,t) and r(s,t) is the current sticking point. The partial of r(i,j,k,t) wrt "k" is the angle Phi. Phi is the total angle from the "k" coordinate in the global frame. Phi is the sum of the shear angle Beta and the rotation angle Theta. The partial of r(s,t) wrt "s" is the shear angle "nu" (Beta) and the partial of the directors "d" wrt "s" is the flexure "u" (Theta).

When the basis for r(0) is {ijk} then partials wrt k and partials wrt "s" have the same meaning as r(s)=sk. Therefore D1(ijk)r(ijk)-->r(0) and D2(ijk)r(ijk)-->D1(s)r(s). If this theory is sound then the planned "pure" shear test should work.