A Finite Element Based on the Strain Approach Using Airy’s Function

Himeur, Mohammed; Zergua, Abdesselam; Guenfoud, Mohamed

doi:10.1007/s13369-014-1543-3

Cited by 5 publications

(7 citation statements)

References 15 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: Resultsmentioning

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: Resultsmentioning

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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“…Three different meshing are considered, which consists of 20 (mesh 1), 80 (mesh 2) and 320 (mesh 3) elements with Convergence and accuracy of the elements in calculating the deflection of point A (midpoint of the free end) are obtained by running simulations in Mathematica. Analytical solution for the deflection at point A is 1.105 mm [12]. Simulation results for the elements in Table I are shown and discussed in section III.…”

Section: B Simulation Setupmentioning

confidence: 99%

“…Various formulations of the strain-based elements can be seen in the literature [11]. Functions that are used to define variation of the strain components within the strain-based element are derived based on Pascal's triangle, polynomial Taylor expansion [10], Airy stress functions [12], theories from solid mechanics and by other means. The strain functions should satisfy compatibility equation:…”

Section: Introductionmentioning

confidence: 99%

“…Method for defining the strain fields by using suitable functions are explained in [10] and [12], which are done by using polynomial Taylor expansion and Airy stress functions, respectively. However, most of the other literatures (using polynomial terms from the Pascal's triangle) do not clearly describe selection of the suitable strain fields for the elements [11].…”

Section: Introductionmentioning

confidence: 99%

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A Study on Formulation of Strain-Based Triangular Elements

Perumal

Chockalingam

2022

JETAP

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This paper presents formulation of triangular elements based on strain approach. Various formulations of the strain-based elements can be seen in the literature. However, most of them do not clearly describe selection of the suitable strain fields for the elements. Therefore, in this work, some guidance for the formulation of strain-based elements are provided based on simulation results that are obtained by using several polynomial functions from Pascal’s triangle. It is seen that higher order terms in the strain functions do not always guarantee better performance for the case considered in this work.

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