Higher Order Computational Method for Static Flexural Analysis of Thick Beam

Gandhe, G. R.; Pankade, P.M.; Tupe, D. H.; Taur, P.G.

doi:10.1016/j.promfg.2018.02.073

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…The displacement components are defined from the equations ( 7) to (11) along the x and z-directions of the beam, when the rotation of the section θ(x) is measured on the mean line:…”

Section: Displacements Fieldsmentioning

confidence: 99%

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An investigation on the shear deformation under bending conditions of cantilever FGM beams using a new polynomial shear function

Boussouar,

Bachiri,

Taallah

et al. 2024

SEES

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In this paper, a static analysis to establish a mathematical model using high order bending theories considering shear strains in displacement fields which have not been taken into account by other theories for functionally graded material (FGM) cantilever beams under bending. A new polynomial shear function is used in this investigation, when satisfied the stress-free boundary conditions. These theories do not require a shear correction factor and consider a hyperbolic shape function. Material properties are assumed to vary in the thickness direction, a simple power-law distribution in terms of volume fractions of constituents is considered. Illustrative cases, a cantilever FGM beam subjected to a concentrated shear force at the free end, and also as a cantilever FGM beam with uniformly distributed load are presented the originality of this research work, in this investigation. The mathematical model is established by differential equations which are derived by the principle of virtual work. Equilibrium equations and boundary conditions are introduced. The solution model is based on a variation approach (integrals) to predict the field component of displacements and the basic constitutive laws. The solution of the analytical model is presented. The results in terms of displacement fields including rotation of the section, and shear stresses, predicted from the proposed model, are presented.

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“…The displacement components are defined from the equations ( 7) to (11) along the x and z-directions of the beam, when the rotation of the section θ(x) is measured on the mean line:…”

Section: Displacements Fieldsmentioning

confidence: 99%

“…Gandhe et al [11] studied static flexural analysis of thick beams using hyperbolic shear deformation theory. The virtual work principle was used to derive governing equations of beams.…”

Section: Introductionmentioning

confidence: 99%

An investigation on the shear deformation under bending conditions of cantilever FGM beams using a new polynomial shear function

Boussouar,

Bachiri,

Taallah

et al. 2024

SEES

View full text Add to dashboard Cite

show abstract

“…A higher-order beam theory which takes into account shear curvature, transverse stresses and rotatory inertia is presented. The displacement field of the present theory was based on a two variable, in which the transverse displacement is partitioned into the bending and shear parts [12].…”

Section: Introductionmentioning

confidence: 99%

Static Examination of Simply Supported Laminated Composite Beam with Varying Load Using Trigonometric Shear Deformation Theory

Tupe¹

2020

IJST

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Objectives: To study the trigonometric shear deformation theory for the evolution of displacements and stresses of crossply simply supported laminated beam subjected to varying load. Methodology: A trigonometric shear deformation is used. The inplain displacement field uses a sinusoidal function in terms of the thickness coordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of a shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Finding: Stresses and displacements for orthotropic, single-layer, three-layer symmetric square cross-ply laminated beam subjected to varying load. Novelty: The numerical results of the present theory for displacement and stresses are compared with those of classical (ETB), first-order (FSDT), and higher-order shear deformation beam theories.

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Higher Order Computational Method for Static Flexural Analysis of Thick Beam

Cited by 2 publications

References 11 publications

An investigation on the shear deformation under bending conditions of cantilever FGM beams using a new polynomial shear function

An investigation on the shear deformation under bending conditions of cantilever FGM beams using a new polynomial shear function

Static Examination of Simply Supported Laminated Composite Beam with Varying Load Using Trigonometric Shear Deformation Theory

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