Static, free vibration, and buckling analysis of plates using strain-based Reissner–Mindlin elements

Belounar, Abderahim; Benmebarek, Sadok; Houhou, Mohamed Nabil; Belounar, Lamine

doi:10.1007/s40091-019-0226-4

Cited by 17 publications

(9 citation statements)

References 41 publications

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“…It was first used by Ashwell et al (1971) for the case of curved problems. Afterward, this approach was introduced to plane elasticity (Sabir 1985a;Belarbi and Maalam 2005;Belounar 2013, 2014), and then extended for threedimensional elasticity problems (Belarbi and Charif 1999;Belounar and Guerraiche 2014;Guerraiche et al 2018;Messai et al 2019),for plate bending (Belounar and Guenfoud 2005;Himeur and Guenfoud, 2011;Belounar et al 2018Belounar et al , 2019, and as well as for shell structures (Sabir and Lock 1972;Assan 1999;Bahai 2003, 2004a, b;Moussa 1996, 1997).…”

Section: Introductionmentioning

confidence: 99%

Formulation of a new finite element based on assumed strains for membrane structures

Fortas

Belounar

Merzouki³

2019

Int J Adv Struct Eng

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In this paper, a new triangular membrane finite element with in-plane drilling rotation has been developed using the strain-based approach for static and free vibration analyses. The proposed element, having three degrees of freedom at each of the three corner nodes, is based on assumed strain functions satisfying both compatibility and equilibrium equations. Numerical investigations have been conducted using several tests, including static and free vibration problems, and the obtained results are compared with analytical and numerical available solutions. It is found that efficient convergence characteristics and accurate results can be achieved using the developed element.

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Section: Introductionmentioning

confidence: 99%

Formulation of a new finite element based on assumed strains for membrane structures

Fortas

Belounar

Merzouki³

2019

Int J Adv Struct Eng

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“…We can note that the standard out-of-plane inertia ρe of a Reissner-Mindlin plate [25,31] is recovered when zeroing the additional degrees of freedom V j,j+1 = 0.…”

Section: Special Case Of Single-layermentioning

confidence: 99%

Consistent derivation of stress-based generalized models in elastodynamics: Application to layerwise plate models

Bouteiller

Bleyer

Sab

2022

International Journal of Solids and Structures

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The derivation of some class of generalized mechanical models relies on a specific stress expansion without any a priori assumption on the corresponding kinematics. In such situations, their extension to a dynamic setting is not easy, especially when deriving the corresponding generalized inertias since the kinematics is unknown. This paper shows how consistent generalized inertias can be obtained through the use of a complementary energy principle in elastodynamics. The methodology is then applied to extend a stress-based layerwise plate model in the dynamic setting. This approach is finally validated through modal analysis of various anisotropic composite laminates.

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“…The elastic stiffness matrix [ K e ], geometric stiffness matrix[ K e g ] and mass matrix[ M e ] of the plate element may be expressed as follows (Belounar et al , 2019): …”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…The first plate bending element based on the strain approach and the Reissner-Mindlin theory was developed by Belounar and Guenfoud (Belounar and Guenfoud, 2005). The success of the strain approach has been confirmed by several 3-D plates elements (Belarbi and Charif, 1998;Belounar and Guerraiche, 2014;Guerraiche et al, 2018;Khiouani et al, 2020;Messai et al, 2018) and plate bending elements (Belounar et al, 2018(Belounar et al, , 2019(Belounar et al, , 2020Boussem and Belounar, 2020). This approach has been applied to the development of elements for general plane elasticity problems (Bouzidi et al, 2019;Fortas et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Assumed strain finite element for natural frequencies of bending plates

Boussem

Belounar²,

Belounar

2021

WJE

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Purpose This paper aims to describe the formulation of a new finite element by assuming the strain field rather than the displacement field and by using the Reissner–Mindlin plate theory for the free vibration analysis of bending plates. This quadrilateral element consists of four-nodes and twelve degrees of freedom. The suggested element is based on assumed functions of the strain field that satisfy the compatibility equation. Design/methodology/approach After the proposition of the new element, several numerical tests for plates with regular and distorted meshes are presented to assess the performance of the new element. In addition, a parametric study is carried out to analyze the effects of biaxial loads on the natural frequencies of square plates with various boundary conditions. Detailed discussions are proposed after each benchmark problem. Findings The formulated element has verified the shear locking test and passes the patch test. The obtained results from the developed element show an excellent accuracy and fast convergence, and the natural frequencies are in excellent agreement when compared with analytical and other available numerical solutions. Originality/value The present element is simple in its formulation and has been proven to be applicable to thin or thick plate situations with sufficient accuracy. This element with full integration is free from shear locking, however, the numerical results provided by the standard four-node plate element R4 element show locking phenomena in thin plates. In addition to these features, the imposition of the compatibility conditions and the rigid body modes allow obtaining a finite element with higher-order terms for displacements field, which can increase the performance of the finite elements.

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Static, free vibration, and buckling analysis of plates using strain-based Reissner–Mindlin elements

Cited by 17 publications

References 41 publications

Formulation of a new finite element based on assumed strains for membrane structures

Formulation of a new finite element based on assumed strains for membrane structures

Consistent derivation of stress-based generalized models in elastodynamics: Application to layerwise plate models

Assumed strain finite element for natural frequencies of bending plates

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