Implicit Corotational Method: analysis of slender panels assemblages

In some recent works, it has been shown that the Implicit Corotational Method (or simply ICM) is a powerful and consolidated approach for recovering nonlinear models starting from the corresponding linear ones both in the cases of continuum and discrete problems (see [1, 2, 3]). The method is based on the polar decomposition theorem and the corotational description of motion, which is directly applied at the continuum level. By referring to the linear stress solution as Biot tensor in corotational frame and using a mixed variational formulation, we obtain an automated way of using the information gained by the linear model in the nonlinear context. Since linearized model are always available it is easy to obtain, by this way, the corresponding nonlinear models in a form convenient for numerical implementations. A similar picture holds when the approach is directly applied to the finite element discretization. In this case, starting from a linear finite element, the methods give the corresponding nonlinear, frame indifferent, finite element interpolation. As good and accurate is the linear finite element as good will be the corresponding nonlinear one. On the other hand, in the last years high-performance plate finite elements, based on hybrid stress formulation and which exhibit a good behavior in the linear/elastic context, have been developed (see [4, 5, 6] and references therein) showing that they are in general simple, stable, locking–free. On the contrary, the developments of so good finite elements for the geometrically nonlinear case is in general more difficult. The idea of the present work is then to reuse these finite elements in a nonlinear context using the ICM. For this purpose, the format of the element has been rearranged to be suitable for ICM implementation and a specialized corotational algebra for the plate model has been developed [7]. The implementations are carried out in both contexts of path–following and asymptotic approaches, extending the FE codes KASP and RASP already available and aimed at asymptotic and path–following analysis, respectively, of slender panels assemblages (see [8] and related references).