Improved nonlinear displacement-based beam element on a two-parameter foundation

Abstract

This paper presents a nonlinear beam element on a two-parameter foundation. A set of governing differential equations of the problem (strong form) is first derived. The displacement-based beam-foundation element with improved displacement shape functions (weak form) is then formulated based on virtual displacement principle. The improved functions are analytically derived based on homogeneous solution to the governing differential equilibrium equation of the problem and are employed to enhance the model accuracy. Tonti's diagrams are used to conveniently represent the equations that govern both the strong and weak forms of the problem. An averaging technique previously proposed by the authors is employed to determine system parameters needed in evaluating the displacement shape functions. Finally, two numerical simulations are used to verify the accuracy and the efficiency of the proposed beam model. The first simulation is used to perform convergence studies of the proposed model and to show its accuracy in representing both global and local responses. The second simulation is used to address effects of the two-parameter foundation model on system responses when compared to the Winkler foundation model.