Discrete shear projection method for mechanical buckling analysis of FGM sandwich plates

Katili, Irwan; Batoz, Jean‐Louis; Bouabdallah, Salim; Maknun, Imam Jauhari; Katili, Andi Makarim

doi:10.1016/j.compstruct.2023.116825

Cited by 10 publications

(6 citation statements)

References 31 publications

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“…As a perspective of future contributions, we propose to evaluate the behaviour of BKWA for composite and FGM plates and compare the results with those obtained using other elements (see Reference 22,36,37). BKWA can also be extended to develop quadrilateral shell elements with a comparison with DKMQ 38 or MITC4+ 39,40 .…”

Section: Discussionmentioning

confidence: 99%

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

Batoz,

Katili,

Widyatmoko

et al. 2024

Numerical Meth Engineering

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This paper presents a general variational principle as theoretical support for creating a simple and efficient quadrilateral plate finite element called BKWA, having only a single displacement and two rotations at corner nodes according to the Reissner‐Mindlin plate theory. The functional is a modified Hellinger‐Reissner in terms of the kinematic variables and independent transverse shear strains. Hence, we consider quadratic rotations, as in DKQ, and linear independent shear strains with constant tangential components on sides, as in MITC4. The quadratic rotation contributions and the mixed shear strain components are wiped out by static condensation. To adequately satisfy the constant curvature patch tests, we also consider the orthogonality conditions between the linear and quadratic bending modes, as in the Bergan free formulation, to avoid ‘spurious bending energy’ for thick plates (also called bending locking). The paper contains comprehensive patch tests and convergence tests with regular and irregular meshes (displacements, internal forces, and strain energy) of circular and square plates. The element is compared with other existing elements (MITC4, DKMQ). It is concluded that BKWA is an efficient element regarding several criteria.

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Section: Discussionmentioning

confidence: 99%

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

Batoz,

Katili,

Widyatmoko

et al. 2024

Numerical Meth Engineering

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“…They were developed utilising a novel shear deformation theory that was inspired by the Zhuravsky shear stress formula. Katili et al (2023) described the problem of buckling of FGM sandwich plates in the numerical FEM analysis. Magnucki et al (2023) using the generalised theory of deformation studied the buckling problem of an axially compressed generalised cylindrical sandwich panel and a rectangular sandwich plate.…”

Section: Introductionmentioning

confidence: 99%

Elastic buckling of a rectangular sandwich plate with an individual functionally graded core

Magnucki,

Magnucka-Blandzi,

Sowiński

2024

Journal of Theoretical and Applied Mechanics

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This paper is devoted to a thin-walled sandwich plate with an individual functionally graded core. The nonlinear shear deformation theory of a straight normal line is applied. A system of three differential equations of equilibrium of this plate is obtained, based on the principle of stationary potential energy, which is reduced to two differential equations and solved analytically. The critical load of the rectangular sandwich plate is determined. A detailed analytical study is carried out for selected exemplary plates. Moreover, a numerical FEM model of this plate is developed. The results of these calculations are compared with each other.

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“…The shear strains at node i are calculated by projecting the constant shear strains on the two sides sharing node i. From Figure 3, the shear strains at node i are determined as follows [10][11]:…”

Section: Discrete Shear Projection Methodsmentioning

confidence: 99%

“…Ko et al (2016Ko et al ( , 2017aKo et al ( , 2017b [7][8][9] improved MITC4 to MITC4+ plate and shell element, which shows excellent performance on selected shell benchmark tests. Katili et al (2021) and (2023) [10][11] recently presented a simple quadrilateral element referred to as Q4s based on the DSPM (discrete shear projection method) for functionally graded materials (FGM) plates. This paper aims to improve the Q4s [10][11] element using incomplete quadratic functions for rotations and the free formulation method of Bergan and Wang [3].…”

Section: Introductionmentioning

confidence: 99%

“…Katili et al (2021) and (2023) [10][11] recently presented a simple quadrilateral element referred to as Q4s based on the DSPM (discrete shear projection method) for functionally graded materials (FGM) plates. This paper aims to improve the Q4s [10][11] element using incomplete quadratic functions for rotations and the free formulation method of Bergan and Wang [3]. The new quadrilateral plate element called Q4γs+ is the paper's primary contribution.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Quadrilateral Element based on the Discrete Shear Projection Method and Free Formulation

Katili,

Katili

Proceedings of the Seventeenth International Conference On Civil, Structural and Environmental Engineering Computing

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This paper presents the enhancement of a previously developed linear quadrilateral plate element by using incomplete quadratic functions. As in the free formulation concept, the couple bending energy between lower (linear) and higher (quadratic) modes is forced to be zero in order to satisfy the constant bending patch test. The discrete shear projection method (DSPM) is used to define the independent transverse shear strains and avoid the shear locking phenomenon. The improved quadrilateral element has four nodes and 3 degrees of freedom (DOFs) per node. It is free of shear locking, has a proper rank, and passes the bending moment patch tests. The application in static analysis exhibits excellent convergence behaviour, reliability, and precision.

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Discrete shear projection method for mechanical buckling analysis of FGM sandwich plates

Cited by 10 publications

References 31 publications

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

Elastic buckling of a rectangular sandwich plate with an individual functionally graded core

An Efficient Quadrilateral Element based on the Discrete Shear Projection Method and Free Formulation

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