MODIFIED VLASOV MODEL FOR BEAMS ON ELASTIC FOUNDATIONS

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, gamma, that controls the decay of stresses in the continuum. Vallabhan and Das developed a unique iterative technique to determine a consistent value of the gamma 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.