A new flat shell finite element for the linear analysis of thin shell structures

Hamadi, Djamal; Ayoub, Ashraf; Ounis, Abdelhafid

doi:10.1080/17797179.2016.1153401

Cited by 11 publications

(4 citation statements)

References 25 publications

(20 reference statements)

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“…In short, many researchers have presented new formulations for the strain-based elements that satisfy both compatibility and equilibrium conditions [20] , [21] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] . However, only a handful of them (such as [20] , [21] , 25 , 33] ) have described the techniques used to obtain the functions that satisfy both conditions, causing the techniques used in the remainder to be left unknown.…”

Section: Introductionmentioning

confidence: 99%

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

Perumal

Koh

2023

MethodsX

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Section: Introductionmentioning

confidence: 99%

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

Perumal

Koh

2023

MethodsX

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“…(2016a) and the results obtained are very significant. Also, another flat shell element is developed to analyze this shell structures with different geometrical shapes, and good results can be obtained (Djamal et al ., 2016b). For plates bending problems, more elements have also been formulated by Belarbi and Charif (1999), Belounar and Guenfoud (2005), Himeur and Guenfoud (2011) and Sifeddine et al .…”

Section: Introductionmentioning

confidence: 99%

A four-node rectangular plate finite element using Airy functions with transverse shear

Abderrahmani

2023

IJSI

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PurposeAmong different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular, quadrangular or sector plate elements, owing to the intricate geometrical shapes and applied loads. The scope of this study is the development of a new rectangular finite element for thin plate bending based on the strain approach using Airy's function. It is called a rectangular plate finite element using Airy function (RPFEUAF) and has four nodes. Each node had three degrees of freedom: one transverse displacement (w) and two normal rotations (x, y).Design/methodology/approachEquilibrium conditions are used to generate the interpolation functions for the fields of strain, displacements and stresses. The evolution of the Airy function solutions yielded the selection of these polynomial bi-harmonic functions. The variational principle and the analytical integration approach are used to evaluate the basic stiffness matrix.FindingsThe numerical findings for thin plates quickly approach the Kirchhoff solution. The results obtained are compared to the analytical solution based on Kirchhoff theory.Originality/valueThe efficiency of the strain based approach using Airy's function is confirmed, and the robustness of the presented element RPFEUAF is demonstrated. Because of this, the current element is more reliable, better suited for computations and especially intriguing for modeling this kind of structure.

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“…In 1970, Ahmad et al proposed this approach, for the first time, to analyze thin and thick curved shell structures [1]. After that, this method was developed by many other researchers using different types of shell element [2][3][4][5][6][7]. To improve this approach, some studies were performed by using strain interpolation.…”

Section: Introductionmentioning

confidence: 99%

A 6-parameter triangular flat shell element for nonlinear analysis

Rezaiee‐Pajand

Masoodi

Arabi

2019

TECM

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In this paper, an improved flat triangular shell element is proposed. This element has three nodes, and in each node, six degrees of freedom are considered. Since there are three rotational degrees of freedom at each node, the drilling effect can be incorporated in authors' formulation. A new procedure is also suggested for updating the director vectors about which the rotational degrees of freedom are defined. In order to study large displacements and rotations, Total Lagrangian principles are employed. In addition, updating the rotational degrees of freedom is implemented using enriched updated director vectors, which are formulated based on the finite rotation method. On the other hand, small strains are considered in this formulation. By utilizing MITC method, shear and membrane locking is mitigated from new element. To examine the performance, the element passes three basic tests, including isotropy, and patch test. Moreover, a convergence study is also implemented to show the elemental behavior. Several popular benchmarks are considered to illustrate the accuracy and capability of the suggested element in geometrically nonlinear analyses.

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A new flat shell finite element for the linear analysis of thin shell structures

Cited by 11 publications

References 25 publications

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

A four-node rectangular plate finite element using Airy functions with transverse shear

A 6-parameter triangular flat shell element for nonlinear analysis

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