Non-linear analysis of structures using two-point method

Non-linear algebraic equations must be solved by an iterative method, the non-linear equations being linearized by evaluating the non-linear terms with the known solution from the preceding iteration. The Newton–Raphson method, which is based on the Taylor series expansion and uses the tangent stiffness matrix, has been extensively used to solve non-linear problems. In this paper, a new Newton–Raphson algorithm is developed for analyses involving non-linear behavior. Our method, here named as a two-point method, is constructed as a predictor–corrector one, most frequently taking Newton's method in the first iteration. It should be noted that our concern in this research ignores the problem of passing 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, it offers a strategy that can be deployed to reduce both the number of the iterations and the computing time involved in non-linear analysis of structures.