Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh

Lv, Yanhui; Zhang, Jin

doi:10.1016/j.amc.2021.126753

Cited by 1 publication

(2 citation statements)

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“…24 The convergence of stress solutions is frequently not as good as that of displacement solutions due to the inherent theoretical flaws of displacement-based element models. The discordant displacement modes, [25][26][27] the improved strain method, 28 the selectively reduced integration system, 29 the new spline FEM, 30 the unsymmetric interpolation technique, 31 and natural coordinate ways [32][33][34][35][36] have all been proposed in the last 50 years for developing strong finite element models that are insensitive to mesh distortion. Although the preceding methods can help to improve the FEM's robustness, it should be noted that most models will fail once the element form is sufficiently distorted.…”

Section: Introductionmentioning

confidence: 99%

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Representing capabilities of novel semi-analytical triangular plate elements

Pour

Farsangi

2023

The Journal of Strain Analysis for Engineering Design

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Two novel plate-bending elements are developed and investigated in this study. Elements with 13 and 15 degree-of-freedoms are named AT13 and AT15, respectively. These triangular elements are formulated in a semi-analytic way. For this aim, the basic elasticity function is employed with unknown parameters. Subsequently, the trial-and-error procedure is used to determine the unidentified constants. Besides, the achieved results are compared with those obtained by displacement-based triangular elements with the same degrees-of-freedom (TUBA13 and TUBA15). In this research, both stress and displacement responses of diverse structures are assessed. After performing extensive numerical studies, the findings clearly demonstrate the superiorities of the proposed elements.

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