Nonlinear Winkler-based beam element with improved displacement shape functions

Abstract

This paper presents a Winkler-based beam element capable of representing the nonlinear interaction mechanics between the beam and the foundation. The element is derived based on a displacement-based formulation using improved displacement shape functions. The improved displacement shape functions are analytically derived based on the homogeneous solution to the governing differential equilibrium equation of the problem, thus enhancing the model accuracy. An iterative technique is used to determine the length-scale parameter needed in evaluating the displacement shape functions. Two numerical examples are used to verify the accuracy and the efficiency of the proposed Winkler-based beam model.