I am trying to do mechanics calculations for composite thin walled
tubes. It seems natural to use polar coordinates to enable generality.
This way a single function r[theta] can be used (vs. something like
f_top[x] & f_btm[x]) and vertical lines in the cross section are not a
problem. I have successfully done all of the calculations using a
circular cross section. Now I want to examine a rectangular section.
Naturally this will be defined as a piecewise function of theta.
At first I tried defining this function with a Which statement. This
will give a function that looks correct when plotted, but will not
behave correctly in the ensuing integrations.
Then I defined the piecewise function numerically as follows:
r[th] = r1[th]*Step[theta,a,b] + r2[th]*Step[theta,b,c] + .......etc
(where r1[th] is a horizontal line defining the top of the box, r2[th]
is a vertical line defining the left side, etc)
This should have worked swimmingly, but I get an Indeterminate result at
0, pi/2, pi, 3pi/2, and 2pi. For example at pi/2 only r1[th] should be
contributing, but r2[th] and r4[th] return ComplexInfinity at that value
and Mathematica doesn't know what to do with 0*Infinity.
Does anyone have any suggestions for fixing this? Is there some way to
temporarily define 0*Infinity as 0? Or is there any other way to get
the noncontributing functions to go to zero over a given interval?
Thanks in advance,
Composite Materials, Manufacture, and Structures Lab
Colorado State University