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 oneway 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.
Accurate modeling of nonlinear deflection of an infinite beam on a nonlinear elastic foundation is crucial for material and structural engineering. The research can be applied to strength analysis and practical engineering design application, say, to curved plate manufacturing. Therefore, many theoretical and experimental studies have been carried out on the nonlinear modeling of an infinite beam on a nonlinear elastic foundation.
The closedform solutions for the static and dynamic response of a uniform beam resting on a linear elastic foundation can be found in several references [
Recently, Jang et al. [
From the existing literature, a number of studies have analyzed a beam on an elastic foundation; however, they just use linear plus a nonlinear term of spring force, that is, linearcubic model. And they are related to the static analysis of nonuniform beams which is resting on a nonlinear elastic foundation, and the recovered solution is not accurate or has many limits. Few studies have fully adopted the nonlinear elastic foundation model, whose spring force is based on oneway spring model, as shown in Figure
Nonlinear elastic foundation model: a nonlinear spring model (one way) and a conventional one (two way).
An infinite beam on a nonlinear elastic foundation: a nonlinear spring model.
Although there are many researches, fully nonlinear elastic foundation was not considered. Beaufait and Hoadley [
In this paper, the nonlinear spring force is fully analyzed by the
The wellknown classical
The boundary
Timoshenko [
In this study, the main idea of the present study is proposed by Jang et al. [
Therefore, (
From (
To examine the nonlinear iterative procedure in (
In this section, numerical experiments are performed to determine the validity of the iterative method. This study assumes a nonlinear spring force
For simplicity, the present study considers an infinite beam on a nonlinear elastic foundation, whose spring force is derived as follows:
To determine if the iterative method converges to an exact solution, the 3 cases of exact solutions listed in Table
Three cases of the exact solution.
Case  Exact solution 

a 

b 

c 

Exact solutions in Table
Applied loading conditions corresponding to the exact solution in Table
Numerical solutions compared to the exact solutions.
Convergence behaviors of the iterative solutions.
Errors between the exact solutions and iterative solutions.
The accuracy of the applied iterative method for the nonlinear spring model is proven in Section
The locally distributed rectangulartype loadings in Figure
Applied loading.
Convergence behavior of the applied iterative method
In Figure
Validity of the solution.
Another loading condition in Figure
Applied loading conditions.
Convergence behavior of the solutions
Validity of the solution in Figure
Finally, the validity and accuracy of the applied iterative procedure are investigated. The nonlinear spring force is considered, and the iterative procedure is applied successfully for the solution. Convergence of the deflections according to the external loading conditions is observed for the effects of the pseudo
In this work, we succeeded in applying the numerical method proposed by Jang et al. [
This work was supported by a 2year research grant of Pusan National University.