Efficient local formulation for elasto-plastic corotational thin-walled beams

Abstract

International audienceA local elasto-plastic formulation, based on a low-order nonlinear strain expression using Bernoulli beam kinematics, is presented in this paper. This element, together with the corotational framework proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(17): 1755-1789) can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with arbitrary cross-section. The formulation captures both the Saint-Venant and warping torsional effects of open cross-sections. Numerical examples show that this local formulation is more efficient than the one proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(51):5811-5831) based on a Timoshenko beam assumption. Copyright (C) 2009 John Wiley & Sons, Ltd

Review of Nonlinear Analysis and Modeling of Steel and Composite Structures

“…Battini and Pacoste [79] developed both Euler-Bernoulli (EB) and Timoshenko elements for thinwalled frames based on the CR framework proposed by Pacoste and Eriksson [80]. The work in [79] was extended by Battini and Pacoste [81] and Alsafadie et al [82] to include material nonlinearities. Alsafadie et al [83] improved their previous work in [82] by including higher-order terms of bending curvature in the local formulation, and thus requiring a less number of elements in the modelling of structures.…”

“…The work in [79] was extended by Battini and Pacoste [81] and Alsafadie et al [82] to include material nonlinearities. Alsafadie et al [83] improved their previous work in [82] by including higher-order terms of bending curvature in the local formulation, and thus requiring a less number of elements in the modelling of structures. Battini [84] presented a CR element without rotational DOFs.…”

A comparative study of displacement and mixed‐based corotational finite element formulations for elasto‐plastic three‐dimensional beam analysis

“…Concerning the kinematic description employed in FE formulations for geometrically nonlinear structural analysis, existing three‐dimensional beam element formulations can be classified into three categories: the total Lagrangian formulation, the updated Lagrangian formulation and the corotational formulation (Felippa and Haugen, 2005). The corotational approach being the most recent (Alsafadie et al , 2010, 2011a, b, c; Felippa and Haugen, 2005; Battini and Pacoste, 2002a, b; Crisfield and Moita, 1996; Chen et al , 2006; Li, 2007a, b; Garcea et al , 2009) is also the least utilized and developed. Its main ideas can be summarized as:Define a local reference system attached to the element, which translates and rotates with the element overall rigid‐body motion, but does not deform with the element.Define nodal variables relative to this system, thus the element overall rigid‐body motion is excluded when computing the local internal force vector and element tangent stiffness matrix, resulting in an element‐independent formulation.The geometric nonlinearity induced by element large rigid‐body motion is incorporated into the transformation matrix relating local and global internal force vectors as well as local and global tangent stiffness matrices.In comparison with the total and the updated Lagrangian formulations, a corotational element formulation has two relative advantages (Felippa and Haugen, 2005; Battini and Pacoste, 2002a, b; Crisfield and Moita, 1996; de Ville de Goyet, 1989):the integration of the constitutive equation in the corotational formulation takes the same simple form as in the case of small deformation theory; andthe transformation matrix between the local and global nodal entities is independent of the assumptions made for the local element.Thus, many existing high‐performance elements for geometrically linear problems can be reused along with the corotational approach to solve large displacement and large rotation problems.…”

“…For the present element, the number of integration points within the cross‐section is arbitrary, which allows better representation of plastic deformations, whereas two Gauss points along the element length are found sufficient. Besides, it is well recognized indeed that explicit analysis of the spread of plasticity along the element length and within the cross‐section of framing members provides the most rigorous solution (Alsafadie et al , 2011a; Battini and Pacoste, 2002a, b). In fact, according to the proposed corotational formulation, distributed plasticity is captured within the local frame.…”