A new finite element based on the strain approach with transverse shear effect

Himeur, Mohammed; Benmarce, Abdelaziz; Guenfoud, Mohamed

doi:10.12989/sem.2014.49.6.793

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…In addition, the GTMTPFE element which treat the bending behavior problems can be combined with the membrane element developed by Himeur et al 32 to treat problems of complex structures shell.…”

Section: Discussionmentioning

confidence: 99%

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A higher order triangular plate finite element using Airy functions

Himeur

Guenfoud

2020

Advances in Mechanical Engineering

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The present paper describes the formulation of a new moderately thick plate bending triangular finite element based on Mindlin–Reissner plate theory. It is called a Great Triangular Moderately Thick Plate Finite Element, or GTMTPFE. The formulation is based on the strain approach, on solution of Airy’s function and on the analytical integration in the construction of the stiffness matrix. The strengths associated with this approach consist of: • automatic verification of equilibrium conditions and kinematic compatibility conditions, • the enrichment of the degrees of the interpolation polynomials of displacements, strains and constraints (refinement p), • the consideration distortions sections related to Poisson effects, • the treatment of blocking phenomena related to transverse shear. In general, this approach results in a competitive, robust and efficient new moderately thick plate finite element. This is visible, on the one hand, through its stability against patch tests (constant twists, state of constants moments, transverse shear locking phenomenon, isotropy test). This is visible, through its good response to the patch tests to which it is subjected (constant torsions, state of constant moments, phenomenon of blocking in transverse shears, isotropy test). As has excellent convergence to the reference solution. Thus, it exhibits better performance behavior than other existing plate elements in the literature, particularly for moderately thick plates and for thin plates (L/h ratio greater than 4).

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Section: Discussionmentioning

confidence: 99%

“…Our first work 32 resulted in the construction of membrane triangular finite elements that can be easily combined with flexural finite elements (plates, beams). The present work constitutes a further development of this research, focused on the development of a bending triangular finite element based on Mindlin-Reissner plate theory.…”

Section: Introductionmentioning

confidence: 99%

A higher order triangular plate finite element using Airy functions

Himeur

Guenfoud

2020

Advances in Mechanical Engineering

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Strain based triangular finite element for plate bending analysis

Belounar

Benmebarek

Belounar

2018

Mechanics of Advanced Materials and Structures

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Using Higher-Order Strain Interpolation Function to Improve the Accuracy of Structural Responses

Rezaiee‐Pajand

Ramezani

Gharaei-Moghaddam

2020

Int. J. Appl. Mechanics

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It is widely known that the accuracy of the finite element method has a direct relation with the type of elements and meshes. Another issue which has remained less treated is the impact of loading type on the accuracy of responses. Changing the applied forces from concentrated to distributed loading has a great effect on the accuracy of certain types of elements and this action can greatly reduce their accuracy. Particularly in the coarse meshes, it creates a critical situation. Some elements do not have the ability to provide the exact answers in stated conditions. For example, the well-known plane element, LST, demonstrates promising performance under concentrated shear and bending loading as well as surface traction. In the case of distributed loads and coarse meshes, its accuracy diminishes considerably. To remedy this defect, in this paper, a new higher-order triangular element is proposed by using natural assumed strain approximation. Various numerical examples demonstrate high accuracy and efficiency of the element in comparison with common well-known finite elements in analysis of structures under distributed loading.

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A new finite element based on the strain approach with transverse shear effect

Cited by 4 publications

References 11 publications

A higher order triangular plate finite element using Airy functions

A higher order triangular plate finite element using Airy functions

Strain based triangular finite element for plate bending analysis

Using Higher-Order Strain Interpolation Function to Improve the Accuracy of Structural Responses

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