An asymptotic approach for the evaluation of errors resulting from estimations of stability limits in nonlinear elasticity (Q1384796)

The determination of stability limits -- bifurcation and limit points -- of thin-walled elastic structures undergoing finite deformation involves substantial numerical effort. To reduce the latter, the nonlinear problem can be approximated by linear or quadratic eigenvalue problems. The aim of this paper is to assess the error connected with higher-order estimations of critical loads with the help of an asymptotic approach. Furthermore, the type of stability is identified by the angle between increment of displacement and load vector. Finally, the results are applied to two similar circular arch problems.