Variational Approach to Beams on Elastic Foundations

Starting from an elastic-continuum hypothesis, the foundation model proposed by Vlasov and Leontev is modified by incorporating in the analysis the horizontal displacements in the elastic foundation, hence making the foundation model more general. Equations derived are applicable to foundations of both finite and infinite thickness. Bending theory of beams on elastic foundations is presented using the proposed foundation model. Method of initial parameters is developed for finite beams on elastic foundations. The application of method of initial parameters to beams having general configuration carrying arbitrary external loads and moments is described. Results are presented in nondimensional form and are compared with existing solutions.