A path-following technique via an asymptotic-numerical method

A path-following technique is presented for the numerical solution of a class of elastic structural problems. The principle is to follow a non-linear solution branch by applying a perturbation technique in a stepwise manner. The solution is represented by a succession of local polynomial approximations. The perburbation technique used here is the asymptotic-numerical method proposed by Damil and Potier-Ferry. It is a combination of asymptotic expansions and finite element calculations which permits one to determine a large part of a non-linear branch by inverting only one stiffness matrix. The present continuation technique requires less computing time than the classical predictor-corrector schemes. Moreover, it is very robust and completely automatic, thanks to the analytical representation of the branch within each step. Various numerical examples are presented to evaluate the performance of the method.