Examples in Symbolic Programming using MATLAB
by P. Venkataraman
Airy Stress Function (cantilevered beam)

A cantilever beam of unit thickness, of length L, and depth 2h, is loaded with uniform distributed load (q per unit length) on the top surface.  It is in plane stress and is rigidly supported at x = L.  Show that the following stress function is valid and find the values for A, B, C, D

    Airy cantilever
    airy function

Symbolic programming is used to
(i) Check the satisfaction of the biharmonic equation
(ii) Solving for constants using the boundary conditions