Flexibility-based large increment method for analysis of elastic–perfectly plastic beam structures

Abstract

This paper presents the derivation and implementation of a flexibility-based large increment method (LIM) for solving nonlinear structural problems. The finite element displacement and force approaches have been developed for solving nonlinear structural problem. The displacement-based finite element method requires a step-by-step approach for material nonlinear analysis that depends on flow theory. Furthermore, significant mesh refinement is often required in plastic zones. The main advantage of the LIM is that it separates the usage of the three-system equation into two stages, global linear stage and local nonlinear stage. Here LIM formulations are developed for two-dimensional beam elements controlled by an elastic–fully plastic material model. These new formulations are demonstrated using simple nonlinear problems and the results are compared to those obtained from the displacement method. The examples highlight the accuracy and the computational efficiency of the flexibility-based large increment method for this class of structural problems.