A STUDY OF VARIABLE STEP-LENGTH INCREMENTAL ITERATIVE METHODS FOR NONLINEAR FINITE-ELEMENT EQUATIONS

A deep study is carried out on the variable step-length incremental/it erative methods of nonlinear finite element equations in static struct ural analysis. Simple interpretations are presented for the convention al incremental/iterative method, single characteristic displacement co ntrolling method and arc-length controlling method from their geometri c characteristic in the load-deformation space. Based on the concept o f structural equilibrium, three constraint equations (i.e. zero increm ental displacement norm, zero residual force norm and zero incremental work) are established for controlling the iteration path. The automat ic selection method of initial load increment in each increment is dis cussed. The suitability and efficiency of the aforementioned methods a re studied and compared through tracing the snap through and snap back responses of two cylindrical shells.