Efficient finite element formulation for the analysis of localized failure in beam structures

Abstract

SUMMARYThis paper presents a finite element formulation for the analysis of localized failures in beam structures. Each member is considered to be a prismatic body that, in case of a localized failure, is divided by a singular surface into two elastic bulks. The fracture process on this surface is described by the cohesive crack concept using a traction-separation law. A plane cross section is assumed, which implies a link between the continuous and the structural (classical beam theory) description of the beam. For the numerical treatment of the model a finite beam element exhibiting an internal interface is proposed, whereas the strong discontinuities are approximated by means of additional degrees of freedom that are placed at the centroid of the singular surface. Hence, each bulk can be described individually by a common beam element with the normal set of nodal degrees of freedom, whereas the singular surface is described layer-wise. The residuum vector and the symmetric stiffness matrix of the resulting element are obtained by assembling the contributions of the two bulks and the singular surface and afterwards by eliminating the additional degrees of freedom by a static condensation. The formulation, which does not change the global degrees of freedom, is numerically very efficient, especially in the case of extensive beam structures, and can easily be implemented in any conventional finite element code. Several numerical examples are provided to demonstrate the effectiveness and the robustness of the proposed method. The equilibrium iterations show an optimal convergence rate, even if many cracks emerge simultaneously. The results do not exhibit any artificial mesh dependencies or artificial stress-locking effects.

Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling

“…In the case of a = −0.0718 the structure fails when the first hinge forms at 336 kN. In Table 3 we compare our results with the results obtained by Darvall and Mendis [22], Armero and Ehrlich [7] and Wackerfuss [11]. beam model for the entire structure, and on another side, a refined representation of localized instability effects (both geometric and material) by meso-scale effects based upon the geometrically nonlinear elastoplastic shell formulation.…”

“…We consider the clamped portal frame under vertical loading first studied by Darvall and Mendis [22] and later examined by Armero and Ehrlich [7] and Wackerfuss [11]. The geometry of the frame is presented in Figure 22.…”

“…The most frequently used regularization nowadays is so-called embedded (strong) discontinuity approach; see e.g. Jirasek [5], Armero and Ehrlich [6], [7], [8], Ibrahimbegovic et al [9], [10], and Wackerfuss [11] for implementation of embedded discontinuity approach for beam and bar finite elements. The key point is introduction of localized energy dissipation.…”

“…Moreover, the spreading of plasticity over the entire frame and the appearance of the softening plastic hinges in the frame is consistently accounted for in the course of the nonlinear analysis. With respect to the existing embedded discontinuity beam finite elements, see Armero et al [6], [7], [8], and Wackerfuss [11], we use more complex material models: stressresultant elastoplasticity with hardening to describe beam material behavior and stress-resultant rigid-plastic softening to describe material behavior at the discontinuity.…”

Corotational Formulation for Bonded Joint Finite Elements

“…Tthe limitations and abilities of the joint element in modeling nonlinear adherends are shared by beam elements in general, and more in-depth discussion on these limitations and how to overcome them are dealt with extensively in literature [26][27][28][29][30][31][32][33] . The example of adherend material nonlinearity is the single lap joint shown in Figure 10, but with elasticperfectly plastic adherends.…”