Mixed formulation in Koiter analysis of thin-walled beams
The paper extends the asymptotic mixed formulation proposed in (G. Garcea, G. Salerno, Sanitizing of locking in Koiter perturbation analysis through mixed formulation, Fourth World Congress on Computational Mechanics, Buenos Aires, Argentina, 1988; G. Garcea, G. Salerno, R. Casciaro, Comput. Methods. Appl. Mech. Engrg. 180 (12) (1999) 137167) to structures composed of an assemblage of flat slender elastic panels. The same type of structure has already been investigated in (A.D. Lanzo, G. Garcea, R. Casciaro, Int. J. Numer. Methods Engrg. 38 (1995) 23252345; A.D. Lanzo, G. Garcea, Int. J. Numer. Methods Engrg. 39 (1996) 30073031) with a compatible formulation and using the usual hypothesis of negligible precritical rotations in order to avoid the extrapolation locking (see also (G. Garcea, G.A. Trunfio, R. Casciaro, Comput. Methods. Appl. Mech. Engrg. 165 (14) (1998) 137167) produced by the high axial to flexural stiffness ratio of the panels. The use of a mixed formulation provides a consistent way of eliminating the extrapolation locking without introducing ad hoc approximations. It is thus both reliable and accurate. When combined with a quadratic straindisplacement relationship, as presented here, it gives zero fourth-order energy variations, further computational simplifications and a `natural' linearization of the eigenvalue problem required by the buckling analysis. An extensive numerical testing shows the effectiveness and robustness of the proposed approach.
thin-walled beams reliability nonlinear elasticity asymptotic methods multimodal buckling mixed finite elements accuracy