Subject: More questions about Maxima's tensor functions
From: Glenn Ramsey
Date: Wed, 16 Nov 2005 12:34:49 +1300
Hi,
I have some more questions about using the the tensor functions in Maxima.
The calculations I want to do don't seem to be covered in the examples
and I'm wondering if this isn't an appropriate way to be attempting to
use it.
What I want to do is to define an function of the form:
W(E_11, E_12, E_13, ...) := c1 *exp(c2*(E_11)^2 + c2*(E_22)^2 +....)
where the function is defined in terms of the individual components of a
tensor for which numerical values are known. (This is a strain energy
function used in finite deformation elasticity and E is the Green's
strain tensor.)
Then I want to calculate a stress tensor S_ij = del(W)/del(E_ij) by
taking the partial derivatives this function with respect to each
component of E, from which I can calculate a force to be used in a
minimisation routine to estimate the parameters c1, c2, ... .
Is it possible define the function as a tensor and then have Maxima
generate the tensor of partial derivatives?
I could do this by creating a matrix where each element is defined
individually eg: matrix([diff(W,E_11,1),diff(W,E_12,1), ... ]), but it
would be nice to be able to do it without having to define each element,
since that would be less error prone and less tedious if I want to try a
number of different W functions.
Glenn
--
Glenn Ramsey 07 8627077
http://www.componic.co.nz