9 Elastic Beam Problems
9.1 A Simple 2D Beam Problem
Approximate solutions can be developed for two-dimensional boundary value problems in plane stress or plane strain by representing the Airy stress function as a polynomial in x1 and x2. This general methodology is developed via several specific examples.
To begin, recall the general form of the biharmonic equation for the case of plane strain,
or, for plane stress,
Recall also the connections between and the stresses, viz.,
To illustrate how an approximate ...