Development and Evaluation of Solution Procedures for Geometrically Nonlinear Structural Analysis

This paper presents a comparative study of the solution techniques which are applicable to the solution of the nonlinear algebraic or differential equations characterizing geometrically nonlinear structural behavior. After reviewing the currently available solution techniques, attention is focused at developing procedures which are computationally economical. The new solution procedures are compared numerically with some of the more conventional procedures such as the Newton-Raphson method, incremental methods, and iterational procedures. Application is made to highly nonlinear problems including a simple truss-spring problem and symmetrically and asymmetrically loaded shells of revolution. Results indicate that a new self-correcting initial-value formulation has possibilities as a powerful tool for nonlinear analysis.