The contact problem for bending of a two-leaf spring with variable thicknesses of leaves

The unbonded contact problem for bending of a two-leaf spring under arbitrary loading is considered. The thickness of each leaf is variable. In the absence of loading, the leaves are right-lined and fit each other closely. The leaves are modeled as Bernoulli–Euler cantilever beams. The problem is reduced to finding the density of the leaves' interaction forces. This density consists of a piecewise continuous part and concentrated forces. A rigorous problem statement is formulated, the uniqueness of solution is established, and analytical solutions of the problem for some special cases are constructed. It is established that the classification of particular cases is determined by the sign of some function that depends on the given loading and variable thicknesses of the leaves. It is shown that the leaves may contact at one point on the tip of the short leaf, over the whole short leaf, or over a part of the short leaf and at its tip.