05-03-09

I have managed a working dynamic shear model from Antman's system of equations. The bending model is still in development.

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.

29-01-09

I have determined that d3 is not a departure from the "s" unit vector of the traditional kenematicians (everyone but Antman). d3 and "s" are identical.
The big question remaining---which Antman does not address at all---is how do we calculate shear deformation? D1s(r(s,t)---d3---is the slope in global coordinates and D2s(r(s,t)) is "u"; there is no method to calculate shear deformation.

22-01-09
I have settled in to the lab and I have made some progress on the Antman dynamic equations in chapter 8. I am stiff confused about the tensor "J" though.

13-01-09

I have restated my study of Antman; in particulat, chapter 8. I am planning to work through all of the derivations over the next week ( or two ).