Convergence Properties of an Algorithm for the Large-Displacement Analysis of Elastic-Plastic Space Structures

The paper deals with convergence properties of an iterative procedure, which is suitable for the structural analysis of elastic-plastic space structures in the presence of large displacements (a case in which the equilibrium equations must be written with reference to the eformed configuration). The proposed algorithm is based on the backward difference concept and leads to a numerical solution, which coincides with the minimum point of a convenient objective function. As typically happens with elastic-plastic problems, the load history is subdivided into a finite number of time-steps, during which the material response is assumed to be nonlinear elastic. Then, it is shown that the iterative rocedure, applied at each time-step, tends to reduce the value of the objective function, iteration by iteration. In consequence, it converges toward the correct solution of the given problem. Finally, some numerical tests (including a sample problem concerned with a tensile structure) are considered, in order to check the performance of the approach presented here.