GBT-based structural analysis of elastic–plastic thin-walled members

Abstract

Structural systems made of high-strength and/or high-ductility metals are usually also rather slender, which means that their structural behavior and ultimate strength are often governed by a combination of plasticity and instability effects. Currently, the rigorous numerical analysis of such systems can only be achieved by resorting to complex and computationally costly shell finite element simulations. This work aims at supplying to designers/researchers an efficient and structurally clarifying alternative to assess the geometrically and/or materially non-linear behavior (up to and beyond the ultimate load) of prismatic thin-walled members, such as those built from cold-formed steel. The proposed approach is based on Generalized Beam Theory (GBT) and is suitable for members exhibiting arbitrary deformation patterns (e.g., global, local, distortional, shear) and made of non-linear isotropic materials (e.g., carbon/stainless steel grades or aluminum alloys). The paper begins by providing a critical overview of the physically and geometrically non-linear GBT formulation recently developed and validated by the authors (Abambres et al. 2012a), which is followed by the presentation and thorough discussion of several illustrative numerical results concerning the structural responses of 4 members (beams and columns) made of distinct (linear, bi-linear or highly non-linear) materials. The GBT results consist of equilibrium paths, modal participation diagrams and amplitude functions, stress contours, displacement profiles and collapse mechanisms  some of them are compared with values obtained from ABAQUS shell finite element analyses. It is shown that the GBT modal nature makes it possible (i) to acquire in-depth knowledge on the member behavioral mechanics at any given equilibrium state (elastic or elastic-plastic), as well as (ii) to provide evidence of the GBT computational efficiency, which is achieved by excluding from the analyses all the deformation modes that do not play any role in a particular member structural response.

A high performance flexibility-based GBT finite element

“…(27), (28), (37) inter-element equilibrium conditions. It can be easily verified that the stationary conditions of P C are the compatibility equations, Eqs.…”

“…Moreover, an effective equilibrium-based procedure for the reconstruction of the three-dimensional stresses has been presented in [23], the study of perforated members in [24], an improved beam element based on semi-analytical solutions in [25] and a discussion on the constitutive assumptions and consistency in the framework of the GBT in [26]. Other interesting developments of GBT are the formulation for the elastic-plastic analyses of thin-walled members experiencing arbitrary deformations and made of non-linear materials [27,28], and the study of the post-buckling behavior of thin-walled steel members in presence of non-standard support conditions [29]. In the GBT literature, much attention has also been devoted to the shear deformability [30][31][32].…”

A novel approach to analyze beam-like composite structures using mechanics of structure genome

“…Generalized beam theory is introduced to analyze various problems in thin-wall beam structures, such as non-linear, elastoplastic [1,2] and buckling problems [3] . Vidal et al [4] developed a finite element based on the Proper Generalized Decomposition, which expresses the displacement as a separated representation of two one-dimensional (1D) space functions to simplify original three-dimensional (3D) problems.…”

Load carrying capacity of functionally graded columns with open cross-sections under static compression

“…These two alternative modal approaches to analyze the elastic buckling behavior have been compared in [29][30][31]. For the latest trends in the development of the GBT, see for example [32][33][34][35][36][37][38]. In these papers special attention is focused on an effect of global and local distortional modes on the load carrying capacity of structures.…”