I am trying to calculate the airy stress function for a cantilever beam with a uniform load acting downward on its upper surface.
I am attempting a solution using an Airy function of polynomial degree
The beam has a rectangular cross section.
I know that if either simgaxx, sigmayy or sigmaxy are symetrical about any axis, the stress function derivative along the axis of symmetry can be reduced to an even function, and odd polynomial coefficients along the perpendicular axis can be eliminated.
I'm just a little unsure which stresses are symmetrical about which axes.
The only one I can imagine would be sigmaxx is symetrical about the x- axis, so that would mean odd polynomial coefficients of y can be eliminated.
Am I right, and are there any other symmetrical distributions that I have missed?
Any help would be greatly appreciated.