A Numerical Approach to Static Deflection Analysis of an Infinite Beam on a Nonlinear Elastic Foundation: One-Way Spring Model

Abstract

A numerical procedure proposed by Jang et al. (2011) is applied for the numerical analyzing of static deflection of an infinite beam on a nonlinear elastic foundation. And one-way spring model is used for the modeling of fully nonlinear elastic foundation. The nonlinear procedure involves Green’s function technique and an iterative method using the pseudo spring coefficient. The workability of the numerical procedure is demonstrated through showing the validity of the solution and the convergence test with some external loads.

An efficient method for the static deflection analysis of an infinite beam on a nonlinear elastic foundation of one-way spring model

“…For the numerical results comparison, we listed here the iterative scheme proposed in [17] and we called it Jang's iterative method (JIM). The values of parameters are taken from [17].…”

“…It is also interesting to test the accuracy and speed of convergence for both iterative schemes for discontinuous loading function w(x) against different values of parameter k p and k. The rectangular loading function w 1 (x) and w 2 (x) are taken from [17]. In Figure 5 and 6 we depicted both discontinuous loading functions.…”

“…The author provided the convergence proof of his devised iterative scheme but did not discuss its order of convergence. Recently Park et al [17] proposed an iterative method with the inclusion of pseudo spring coefficient but numerical experimentation shows that the rapid convergence of iterative scheme depends on the careful selection of pseudo spring coefficient and authors did not advise about the selection of parameter. In both articles, the authors constructed fixedpoint iterative methods.…”

“…In the later author improved the convergence by the inclusion of a pseudo parameter. We also constructed a fixed-point iterative method based on the Newton-Raphson iterative method for the BVPs called the QLM which shows comparatively a better convergence relative to the work of [16,17] .…”

Numerical investigation of non-linear deflections of an infinite beam on non-linear and discontinuous elastic foundation

“…A new semi analytical approach to the identification of large deflection of Bernoulli-Euler-v. Karman beam was also proposed (Jang, 2013a). Nonlinear elastic foundation using an one-way spring model (Park et al 2013) and variable flexural and axial rigidities Bernoulli-Euler-v. Karman beam were also considered (Jang, 2014). Finally, iterative methods also have been successfully applied to problems in ocean engineering such as nonlinear water waves (Jang & Kwon, 2005;Jang et al, 2006;Jang et al, 2007a;Jang & Kwon, 2007b, Jang et al 2010a) and the simultaneous detection of the nonlinear restoring and nonlinear damping of a nonlinear oscillation (Jang, 2009;Jang et al 2010bJang et al , 2011bJang et al , 2011cJang et al , 2013b In numerical experiments section, the nonlinear deflection of an infinite beam on a non-uniform elastic foundation is successfully obtained, and they show the method is simple and straightforward.…”