An efficient nonlinear analysis of 2D frames using a Newton-like technique

The Newton–Raphson method, which is based on the Taylor series and uses the tangent stiffness matrix, has been widely used to solve nonlinear problems. In this paper, a Newton-like algorithm is used for analyses involving geometric nonlinearity. This iterative technique that requires two initial guesses is known as two-point iterative method. In this method, a real function is assumed to approximate the tangent stiffness matrix of the structure. This paper, proposes an efficient function for reducing the computing time and, number of iterations in the Newton–Raphson method coupled with the two-point methodology. The computational nonlinear analysis on planar frames shows that the proposed strategy can reduce the computing time up to around 40%. Compared with the classic Newton–Raphson algorithm, the presented method proposes a methodology which also can reduce the number of iterations.