Reanalysis of linear and nonlinear structures using iterated Shanks transformation Original Research Article

Reanalysis of structures is a common task in two important fields of structural engineering, namely optimization and reliability. It implies the solution of the kinematic equations for each new set of data. In order to simplify this task several approximate methods have been developed. In this paper a simple method for reanalysis, applicable to either linear or nonlinear structures, is proposed. It is based on the improvement of the Neumann resolvent series, which diverges beyond a certain radius, by means of the iterated Shanks transformation. The method is compared with two relevant proposals intended to improve the convergence of the Neumann series, namely the Padé series and the scaled approximation methods. The accuracy and simplicity of the proposed method is demonstrated through some examples concerning linear and nonlinear structures.