A contact finite element algorithm for the multileaf spring of vehicle suspension systems

This paper presents an innovative finite element (FE) algorithm for the contact problem of the multileaf spring in vehicles. The well-established classic beam theory is adopted to construct the complementary strain energy variational. A piecewise contact stress pattern is approximated to the real contact state between two layered beams. The vector of nodal contact stresses is taken to represent primary state variables. To implement the principle of the least complementary energy, a quadratic programming (QP) problem with equality and unilateral constraints is formulated. The corresponding Kuhn-Tucker condition is equivalent to the linear complementary problem. In this study, Lemke's algorithm is applied to solve for the nodal stress vector and subsequently to determine the contact stress distribution over the contact surfaces between the layered beams. The algorithm is verified against experimental stress analysis, and it is found that the computation and test correlate well.