STATEMENT AND ANALYTICAL SOLUTION OF THE CONTACT PROBLEM OF THREE-LEAF SPRING BENDING

Abstract

Theunbondedcontactproblemofthree-leafspringbendingisconsidered. This problem consists in finding the contact forces in the system of three Bernoulli-Euler cantilever beams. The system is loaded by the force concentrated at the tip of the longest beam. In the absence of loading the beams are straight and fit each other closely. There is no friction between the beams. The rigorous problem statement is formulated, the uniqueness of solution is proved and the analytical solution of the problem for the arbitrary lengths of the leaves is constructed. This construction simultaneously proves the existence of the solution. The obtained solution generalizes the known solutions for the special cases. It is shown that only two contact patterns are possible: the forces at the tips of the leaves and the same with the additional force between the long leaves. The new integral representations for the nearest leaves distances are used for the validation of the analytical solution. The obtained results can be used for the leaf springs design.