I have a question concerning a 3d theory to calculate forces, stresses, deflections, etc. I am calculating a simply supported beam (a cylindrical pile). The theory is build up cylindrical coordinates; x and theta.
solving the theory gives me deflection in 3 directions; ur (radial), ux (length), utheta (along the surface). To plot a the deflection of the pile I convert all to cartesian coordinates:
> xcart := unapply(x+ux(x, theta), [x, theta])
> ycart := proc (x, theta) -> -(a+ur(x, theta))*cos(theta)+`uθ`(x, theta)*sin(theta)
> zcart := proc (x, theta) options operator, arrow; (a+ur(x, theta))*sin(theta)+`uθ`(x, theta)*cos(theta)
Then I can make a 3d plot of the deflection:
plot3d([xcart(x, theta), ycart(x, theta), zcart(x, theta)], x = 0 .. L, theta = 0 .. 2*Pi, axes = boxed, scaling = constrained)
I also calculated the stress distribution over the pile. I can plot this on a (undeformed) pile:
plot3d(a, 0 .. 2*Pi, 0 .. L, coords = cylindrical, axes = normal, scaling = constrained, color = sigvm)
with a= radius of the pile.
What I would like to do is plot the deflection of the pile with the colors of the stresses. Problem is that the coordinates of the stress do not match the coordinates of the deformed beam. I can change the coordinates of the stress from (x,theta) to (xcart,ycart,zcart), but that will mean it will take the values of the deformed beam.
I need to find a way to let Maple read the sigvm in 'normal' (x,theta) and plot them on (xcart,ycart,zcart) the deflected pile.
Does anyone know a way how to do it?