Large Deformation of Structures by Sequential Limit Analysis

Although most structures are designed to function under small deformation, their large deformation behavior can be used to estimate reliability and safety for survivorship from an accident or a natural disaster. Structures such as buildings, bridges, ships, vehicles and machinery are designed with a safety factor to protect certain assets from the unexpected and unknot elements. The large deformation analysis provides the rational basis for a safety factor. In this paper, the method of sequential limit analysis is used to compute large deformation solutions of truss and frame problems. Differing from the incremental method of plasticity, the limit analysis method is numerically stable, more effecient and requires simpler input data. A duality theorem serves as the foundation of an algorithm for computing the complete static and kinematic solutions simuhaneously and for establishing their accuracy in each step of a deformation sequence. The phenomena encountered in large deformation such as loading-unloading under monotone deformation, bifurcation (more generally, loss of uniqueness) of solutions, and internal contact of structural members are revealed by the sequential limit analysis presented in this paper.