Finite element historical deformation analysis in piecewise linear plasticity by mathematical programming

In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. The aim is achieved through the mechanical interpretation of some phases of the algorithm, which leads to the characterization, for each pivotal step, of an elastic structure corresponding to the actual updated tableau. This allows to avoid the evaluation and updating of the whole PLPC matrix and allows to translate all the mathematical programming algorithm into a finite termination procedure which provides the complete deformation history of the structure along the given loading path through the elastic analysis of structures which are suitable modifications of the original one. This is shown to lead to a dramatic reduction of the variables to be handled and to a substantial simplification from the numerical and computational standpoint. The extension of the procedure to the historical deformation analysis under sequence of individually proportional loadings is also pointed out. Finally, the method is applied to several problems for some of which the solution is available by other iterative asymptotical or with finite termination solution procedures, so that comparisons become possible and are made