Extrapolation locking and its sanitization in Koiter's asymptotic analysis

Abstract This paper shows that the FEM implementation of Koiter's asymptotic method [W.T. Koiter, On the stability of elastic equilibrium, 1970, Ph.D. Thesis, Delft, 1945. English transl. NASA TT-F10, 883, 1967, AFFDL-TR70-25] outlined by Casciaro et al. [Finite element asymptotic analysis of slender elastic structures: a simple approach, Int. J. Num. Meth. Eng. 35 (1992) 1397–1426] provides accurate and reliable results in the critical and post-critical analysis of non-linear elastic structures. Care, however, does have to be taken in implementing (apparently) minor details to avoid locking effects which adversely affect accuracy and which can destroy the method reliability. As the effects related to the finite element interpolation have been discussed before this paper focuses on the non-linear locking due to the use, implicit in the method, of finite distance extrapolations. Within this scope, it is shown that perturbation algorithms based on compatible formulations can imply a strong critical and post-critical locking when analysing structures characterized by high stiffness ratios in the presence of moderate pre-critical rotations. On the contrary, perturbation algorithms based on independent extrapolations of displacements and stresses furnish reliable results in excellent agreement with those provided by step-by-step analysis, at a small fraction of its computational cost.

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