A pseudo-equilibrium finite element for limit analysis of Reissner-Mindlin plates

Cavalcante, Eric Luis Barroso; Neto, Eliseu Lucena

doi:10.1016/j.apm.2021.03.004

Cited by 3 publications

(6 citation statements)

References 38 publications

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“…Table 3 shows the collapse load for the

32\times 32

mesh in clamped boundary conditions for varying through‐the‐thickness IPs and using MISS‐4. The collapse load results influenced by the number of IPs and it converges to the value given in the last column of Table 3 which is evaluated using a yielding function in terms of generalized stresses 52 . This last value is much closer to that provided by Cavalcante and Neto 52 …”

Section: Numerical Resultssupporting

confidence: 75%

“…The collapse load results influenced by the number of IPs and it converges to the value given in the last column of Table 3 which is evaluated using a yielding function in terms of generalized stresses 52 . This last value is much closer to that provided by Cavalcante and Neto 52 …”

Section: Numerical Resultssupporting

confidence: 75%

“…The collapse load results influenced by the number of IPs and it converges to the value given in the last column F I G U R E 2 Square plate: Convergence of the limit load of Table 3 which is evaluated using a yielding function in terms of generalized stresses. 52 This last value is much closer to that provided by Cavalcante and Neto. 52 The equilibrium paths are shown in Figure 3 for a 4 × 4 mesh and for different positions and numbers of the plastic admissibility IPs.…”

Section: Square Platesupporting

confidence: 80%

“…52 This last value is much closer to that provided by Cavalcante and Neto. 52 The equilibrium paths are shown in Figure 3 for a 4 × 4 mesh and for different positions and numbers of the plastic admissibility IPs. In the simply supported case the collapse load is almost insensitive to this choice, while a high number of IP smooths out the curve.…”

Section: Square Platesupporting

confidence: 80%

“…The good convergence properties of MISS‐4 are highlighted in Figure 2 which shows that for both the boundary conditions it gives lower error than Abaqus S4. For the clamped case, it is possible to observe how the collapse load predicted by MISS‐4 with the finest mesh is slightly different from the one provided by Cavalcante and Neto 52 and higher than the UB provided by Bleyer and De Buhan 51 . Conversely, good accordance is found with the collapse load predicted by Abaqus.…”

Section: Numerical Resultsmentioning

confidence: 82%

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A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

Liguori

Madeo

Garcea

2022

Numerical Meth Engineering

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Mixed assumed stress finite elements (FEs) have shown good advantages over traditional displacement‐based formulations in various contexts. However, their use in incremental elasto‐plasticity is limited by the need for return mapping schemes which preserve the assumed stress interpolation. For elastic‐perfectly plastic materials and small deformation problems, the integration of the constitutive equation furnishes a closest point projection (CPP) involving all the element stress parameters. In this work, a dual decomposition strategy is adopted to split this problem into a series of CPPs at the integration points level and in a nonlinear system of equations over the element, in order to simplify its solution. The strategy is tested with a four nodes mixed shell FE, named MISS‐4, characterized by an equilibrated stress interpolation which improves the accuracy. Two decomposition strategies are tested to express the plastic admissibility either in terms of stress resultants or point‐wise Cauchy stresses. The recovered elasto‐plastic solution preserves all the advantages of MISS‐4, namely it is accurate for coarse meshes in recovering the equilibrium path and evaluating the limit load showing a quadratic rate of convergence, as demonstrated by the numerical results.

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“…Table 3 shows the collapse load for the