Modeling Deficiencies in the Eight-Node Mindlin Plate Finite Element Physically Explained

Filho, João Elias Abdalla; Dow, John O.; Belo, Ivan Moura

doi:10.1061/(asce)em.1943-7889.0001715

Cited by 1 publication

(2 citation statements)

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“…However, in Equation 7, two terms can be identified that are not related to shear strain. Such terms are (𝜀 𝑥,𝑦 ) 0 and (𝜀 𝑦,𝑥 ) 0 , which are flexural quantities, and are therefore interpreted as spurious in Equation 7 (Dow, 1999;Abdalla Filho et al, 2020). Four-node elements behave poorly in bending due to the presence of these terms, which are known as parasitic shear terms.…”

Section: Four-node Plane Element In Strain Gradient Notationmentioning

confidence: 99%

“…A comprehensive synthesis of these developing works on strain gradient notation has been presented (Dow, 1999). Since then, research involving strain gradient notation has continued to be developed by Mohamed, Byrd, and Dow (2005), Abdalla Filho, Fagundes, and Machado, (2006), Abdalla Filho, Belo, and Dow (2016), Abdalla Filho, Belo, and Dow (2017), and Abdalla Filho, Dow, and Belo (2020.…”

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

Bortoli,

Abdalla Filho

2024

Acta Sci Technol

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In this work, plane stress free vibration is performed using four-node elements formulated using strain gradient notation. Accurate results are sought, and the effects of parasitic shear are investigated. By applying strain gradient notation, which is a physically interpretable notation, parasitic shear terms are identified a priori in the shear strain expressions of the four-node plane element. Parasitic shear is the source of shear locking in that element, and the a priori removal of the parasitic shear terms corrects the element for locking. Several studies in the literature show that this modeling error causes improper behavior of the element in bending, which affects the computed results of stress and displacements of the structure. Based on this, this work applies strain gradient notation to examine the effects of parasitic shear on the natural frequencies and corresponding mode shapes of plane stress structures. The results are compared with literature results, and with the isoparametric FEM formulation modeled by ANSYS software. It is observed that parasitic shear has a higher preponderance in coarse meshes of flexural vibration modes. Furthermore, the deleterious effects are emphasized as bending deformation becomes more important in the model. Strain gradient notation shows advantages in the numerical aspect and successfully eliminates the parasitic shear terms from the four-node element. The problems studied here display accurate results.

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Section: Four-node Plane Element In Strain Gradient Notationmentioning

confidence: 99%