Modified Vlasov Model for Beams on Elastic Foundations

Abstract

Realizing the inadequacy of the classical Winkler model to represent an elastic continuum, Vlasov and Leont'ev developed a two‐parameter model for a beam on an elastic foundation. The Vlasov model required an estimation of a parameter, 7, that controls the decay of stresses in the continuum. Vallabhan and Das developed a unique iterative technique to determine a consistent value of the y parameter. Their model is called a “modified” or “refined Vlasov” model. Here, the finite different technique is employed to solve the fourth‐order differential equations. The results of sample problems obtained by using the modified Vlasov model are compared with more sophisticated finite element solutions.