Solution method for beams on nonuniform elastic foundations

This technical note presents an analytical method, accompanied by a numerical scheme, to evaluate the response of beams on nonuniform elastic foundations, namely, when the foundation modulus is k = k(x). The method employs a Green's function formulation, which results in a system of nonsingular integral equations for the distributed reaction q(x). These equations can be discretized in a straightforward manner to yield a system of linear algebraic equations that can be solved by elementary numerical techniques.