An Approximate Nonuniform Bending Theory and Its Application to the Swept-Plate Problem

Differential equations and boundary conditions are derived, by means of the calculus of variations, for cylindrical bars in nonuniform bending. The resulting equations are used, together with similar nonuniform torsion equations, to obtain deflections and stresses in swept cantilever plates of uniform rectangular cross section. Comparisons are made with experimental results for plates with four different sweep angles. The theory predicts deflections quite close to those found experimentally. Stresses computed from the equations, however, are not in as close agreement. It is also noticed that the theory is less accurate for large sweep angles than for small ones.