Asymptotic–numerical methods and Pade approximants for non‐linear elastic structures

Abstract In this paper, we apply asymptotic–numerical methods for computing non‐linear equilibrium paths of elastic beam, plate and shell structures. The non‐linear branches are sought in the form of asymptotic expansions, and they are determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can be easily computed by using recurrence formulas. In comparison with a more classical step‐by‐step procedure, the method is rapid and automatic. We show, with some examples, that the choice of the expansion's parameter and the use of Padé approximants play an important role in the determination of the size of the domain of convergence.