A Statistical Approach for Error Estimation in Adaptive Finite Element Method

Moslemi, Hamid; Tavakkoli, Ali

doi:10.1080/15502287.2018.1558424

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…The AFEM is employed widespread in various fields of science including engineering, mathematics, physics, etc. Moslemi and Tavakkoli [28] could develop a static approach for error estimation in AFEM. Khoei et al [29] modeled cohesive crack propagation using AFEM and advanced this issue [30] by modeling of non-planar cohesive fracture crack growth via AFEM.…”

Section: Adaptive Finite Element Methodsmentioning

confidence: 99%

A New Nodal Stress Recovery Technique in Finite Element Method Using Colliding Bodies Optimization Algorithm

Kaveh

Seddighian

2019

Period. Polytech. Civil Eng.

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In Finite Element Method (FEM), the stress components are calculated within the elements firstly, and then these components are recovered to the nodes. For the recovery process, there are several well-known methods in which the increase of their accuracy imposes additional costs into the problem. In this paper, a new nodal stress recovery technique is proposed in which Colliding Bodies Optimization (CBO) Algorithm fits an appropriative function for nodal stress fields. The CBO employs this function to compute the stress components in the nodal coordinates. Therefore, a particular model to stress fields and its components will be available. It can be considered as a connection between analytical approaches and numerical methods, providing benefits of both categories. Finally, the accuracy, efficiency, and applicability of the new technique are investigated employing three diverse examples.

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Section: Adaptive Finite Element Methodsmentioning

confidence: 99%

A New Nodal Stress Recovery Technique in Finite Element Method Using Colliding Bodies Optimization Algorithm

Kaveh

Seddighian

2019

Period. Polytech. Civil Eng.

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“…𝐺𝐼𝑂𝑅 is the element's Gauss Integration Order Reduction numer. Furthermore, the Round-off error normalized to one can be calculated using Equation (11) where 𝜅̅ 𝑀 𝐾 is the condition number of the system inverted mass and stiffness matrices, and 𝜀 is the Machine Epsilon number.…”

Section: Pseudo-algorithmmentioning

confidence: 99%

“…The maximum permissible error determination has been a problem solved differently by other authors [11]. In this work, the problem identified was that the internal forces of some elements could tend to zero, so the related results of 𝜂̅ will tend to be infinitive, which will bring spurious outcomes.…”

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confidence: 98%

Complexity Adaptation Strategy for Order-Adaptive Elements

Mora,

Khaji

Proceedings of the Seventeenth International Conference On Civil, Structural and Environmental Engineering Computing

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Many studies have worked on reducing dynamic analysis convergence problems. Currently, there are some robust algorithms. However, they can fail when dealing with complex structures due to numerical and especially physical instabilities. Some of them can also be time-consuming procedures. On the other hand, the intrinsic truncated error in structural analysis decreases when the shape function order is raised (p-refinement). Nevertheless, this action will increase the complexity and, thus, structural convergence problems. Therefore, the solution proposed is to adapt the complexity when physical instabilities are predicted, and Hermite interpolation can be used to state well-posed results. The physical instability can be predicted by analyzing strain energy outliers and moment-curvature rule abnormalities. Moreover, to get more realistic results, nonlinear elements with plastic length were developed. Since no previous references have worked with these kinds of nonlinear high-order elements, using a set of sigmoid functions in the stiffness matrix integral was the solution to obtain generalized high-order Timoshenko beams. Another contribution of this work was establishing an appropriate manner of getting the maximum permissible error in p-adaptive methods. Finally, some examples were made to prove the formulation's robustness and show how influential the truncated error can be.

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