Combining shell and GBT-based finite elements: large-displacement elastoplastic analysis

It is widely accepted that Generalized Beam Theory (GBT) constitutes a very efficient and "structurally enlightening" tool to analyze thin-walled bars undergoing cross-section in-plane and out-of-plane (warping) deformation, due to its unique kinematic description of the beam, based on hierarchical and structurally meaningful "cross-section deformation modes". In particular, the computational efficiency of GBT is most remarkable in linear and linear stability (bifurcation) analyses of prismatic members. For complex geometries and physically non-linear problems, as previously proposed by the authors, it is more efficient to combine shell and GBT finite elements, a strategy that enables modeling, e.g., joints or tapered members. This paper extends the authors' previous work to the large displacement range, including plasticity, allowing an accurate calculation of collapse loads of members and systems with a small computational cost (with respect to a similarly accurate shell model). In this approach, a new large-displacement beam element is used in the prismatic and elastic parts, whereas shell elements are assigned to the geometrically complex and/or plastic zones. The beam element can handle small co-rotational cross-section deformation, to enable detecting the onset of local/distortional buckling and plasticity, and subsequently adaptively re-mesh the model using shell elements. Moreover, the unique modal decomposition features of GBT are recovered from the shell zone results using a new post-processing procedure. To show the capabilities of the proposed approaches, several illustrative examples are presented and discussed. For validation purposes, full shell finite element model solutions are provided.

Learning Objectives:
Recognize that the proposed approach is the most computational efficient to model the collapse behavior of thin-walled members.

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