Geometrical and material nonlinear analysis of structures under static and dynamic loading based on quadratic path

The Newton-Raphson method, which is based on the Taylor series expansion, and which uses the tangent stiness matrix, has been extensively used to solve nonlinear problems. This traditional method, especially for the large-scale, is time consuming. Consequently, iterative algorithms cannot be eective for analyzing the process. In the incremental-iterative analysis of elastic nonlinear structures, great saving in computation can be achieved if distinction is made between the predictor and corrector phases. This paper shows how a simple assumption can improve the computational eciency of the nonlinear analysis of structures. It is shown that very high computational eciency may be obtained by assuming the pursuit of each Degree Of Freedom (DOF) by a quadratic curve. Through examples, it is demonstrated how this eciency signicantly decreases the computing time of analysis compared with time taken to deploy the Newton-Raphson, modied Newton-Raphson and Conjugate Gradient (CG) methods.