Formulations and solution procedures for nonlinear structural analysis

Abstract

This paper presents a survey of the formulations and solution procedures for nonlinear static and dynamic structural analysis. The formulations covered include the pseudo force method, the total Lagrangian method, the updated Lagrangian method, and the convected coordinate method. The relationship of each principle to the basic principle of virtual work is presented. For static analysis, the solution by direct minimization of the total potential, Newton-Raphson and modified Newton-Raphson, and the first and second order self correcting method are reviewed and put in proper perspective. It is concluded that the most efficient methods for static problems are the modified Newton-Raphson and the first order self correcting methods. For dynamic nonlinear analysis, a new method based on modal analysis using the pseudo force method is presented. Numerical results for the highly nonlinear dynamic response of a shallow cap ( λ = 6) under a step load at the apex shows the method to be 5 times faster than the Houbolt solution procedure. Other methods surveyed include the Newmark β method, the Wilson method, central differences, and the stiffly stable solution procedure of Park.