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 uses the tangent stiffness 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 effective for analyzing of 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 efficiency of the nonlinear analysis of structures. It is shown that very high computational efficiency may be obtained by assuming the pursuit of each degree of freedom (DOF) by a quadratic curve. Through examples it is demonstrated how this efficiency significantly, decreases the computing time of analysis compared with time taken to deploy the Newton-Raphson, modified Newton-Raphson and conjugate gradient (CG) methods.