Application of cubic spline on large deformation analysis of structures

Abstract

This paper presents a new method for non-linear analysis of structures using an iterative method originated from quadrature rule based on spline function. At first, the above-mentioned method is developed for solving systems of non-linear algebraic equations and then it is implemented on structural problems. In this procedure like many other state of the art methods, the non-linear equations are linearized by evaluating the non-linear terms with the known solution from the preceding iteration. The proposed method is constructed as a predictor-corrector one, must frequently taking Newton’s method in the first iteration. For this method, a simple step-by-step algorithm was implemented and presented to calculate non-linear analysis of structures. It should be noted that currently, the proposed method is incapable of tracing the equilibrium curve after passing the limit points. The presented method incorporates the known information at each stage of the loading process to determine the subsequent unknown variables. Compared with the classic Newton-Raphson algorithm and a recently proposed two-point method, it offers a strategy that can be deployed to reduce the number of the iterations to trace the equilibrium path in non-linear analysis of structures.