Strain-based finite element formulation for the analysis of functionally graded plates

Belounar, Abderahim; Boussem, Faiçal; Houhou, Mohamed Nabil; Tati, Abdelouahab; Fortas, Lahcene

doi:10.1007/s00419-022-02160-y

Cited by 6 publications

(3 citation statements)

References 37 publications

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“…This approach was used in [17] for curved structures, and it was extended for plan elasticity [11,[18][19][20][21]. A summary of this early work was presented in [22,23], with three-dimensional elasticity problems [24][25][26], plate bending [9,[27][28][29][30], and shell structures [31][32][33][34]. Other studies presented the treatment of non-linear problems [31,[35][36], composite materials [37], functionally graded plates [29,38], and fracture mechanics [39].…”

Section: Introductionmentioning

confidence: 99%

“…A summary of this early work was presented in [22,23], with three-dimensional elasticity problems [24][25][26], plate bending [9,[27][28][29][30], and shell structures [31][32][33][34]. Other studies presented the treatment of non-linear problems [31,[35][36], composite materials [37], functionally graded plates [29,38], and fracture mechanics [39]. These elements are stable and have good efficiency, and the strain approach is very practical for the development of robust finite elements which are insensitive to common problems such as mesh sensitivity and different locking problems.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of an Assumed Strain-based Quadrilateral Membrane Element

Kherfi

Guerraiche

Zouggar

2022

Eng. Technol. Appl. Sci. Res.

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This paper describes the development of a simple quadrilateral strain-based element for plane stress and strain problems. This element has five nodes, four located at its corners and one at the center. Each of the four corner nodes had two essential external degrees of freedom (u, v), while the center node had three degrees of freedom (u, v, ɵ); the static condensation method was used for the internal node. This element was used for both linear and dynamic analysis. Its performance was assessed using a variety of membrane and axisymmetric analysis problems. The obtained results demonstrated the good performance and accuracy of the proposed element.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of an Assumed Strain-based Quadrilateral Membrane Element

Kherfi

Guerraiche

Zouggar

2022

Eng. Technol. Appl. Sci. Res.

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“…A brief review of the strain approach found in the literature for different elements is presented as follows. This approach was applied for isotropic plate bending analysis [17][18][19][20][21][22], functionally graded plates [23,24], composite plate materials [25], general plane elasticity problems [26][27][28][29], and three-dimensional analysis [30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

A Triangular Shell Element Based on Higher-order Strains for the Analysis of Static and Free Vibration

Sekkour

Belounar²,

Belounar³

et al. 2022

Civ Eng J

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This research paper proposes a new triangular cylindrical finite element for static and free vibration analysis of cylindrical structures. The formulation of the proposed element is based on deep shell theory and uses assumed strain functions instead of displacement functions. The assumed strain functions satisfy the compatibility equations. This finite element possesses only the five necessary degrees of freedom for each of the three corner nodes. The element's displacement field, which contains higher-order terms, satisfies the requirement of rigid-body displacement. The element's performance is evaluated using various numerical static and free vibration tests for cylindrical shell problems, including an analysis of the effect of shell openings on natural frequencies. The results of the developed element are evaluated in comparison with published analytical and numerical solutions. The new cylindrical element's formulation is straightforward. Compared to the degenerate nine-node shell element and other elements, the results of the present element have shown excellent accuracy and efficiency in predicting static and free vibration of curved structures. This element only requires the use of very coarse meshes to converge. In addition, the triangular shape of this element is more advantageous than the quadrilateral shape when the geometric domain of the structure is deformed or complicated. Doi: 10.28991/CEJ-2022-08-10-06 Full Text: PDF

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A size-dependent axisymmetric plate element: application to MEMS

Rahaeifard,

Karimzadeh

2024

Arch Appl Mech

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Strain-based finite element formulation for the analysis of functionally graded plates

Cited by 6 publications

References 37 publications

Assessment of an Assumed Strain-based Quadrilateral Membrane Element

Assessment of an Assumed Strain-based Quadrilateral Membrane Element

A Triangular Shell Element Based on Higher-order Strains for the Analysis of Static and Free Vibration

A size-dependent axisymmetric plate element: application to MEMS

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