Application of pseudo-parameter iteration method to nonlinear deflection analysis of an infinite beam with variable beam cross-sections on a nonlinear elastic foundation

Abstract

In this study, the nonlinear deflection of an infinite beam with variable beam cross-sections on a nonlinear elastic foundation was analyzed using the pseudo-parameter iteration method (PIM), which is a novel iterative semi-analytic method for solving ordinary/partial differential equations. To do this, we set six types of infinite beams with concave and convex shapes under static loading conditions. To calculate the nonlinear deflection of the infinite beam with variable cross-sections, the Bernoulli-Euler beam equation (fourth-order ordinary differential equation) considering changing beam flexural rigidity was introduced, and the PIM was adopted to this equation. Through the numerical experiment, it was confirmed that the nonlinear deflections calculated via the PIM are quite close to the exact solution within a few iterations. In addition, the graph of error quickly reaches the steady state error for all cases as the number of iterations increases.