New transverse shear deformation theory for bending analysis of FGM plate under patch load

Kumar, Rahul; Lal, Achchhe; Singh, Bhupender; Singh, Jeeoot

doi:10.1016/j.compstruct.2018.10.014

Cited by 64 publications

(17 citation statements)

References 66 publications

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“…The graphs of the dimensionless shear stresses (24) in the depth direction of the selected beams (B-1-1, B-2-2, B-3-3) are shown in Fig. 6.…”

Section: Analytical Study Of Bending Of the Beams With Symmetrically Varying Mechanical Propertiesmentioning

confidence: 99%

“…In addition, the relation with the traditional higher-order theory is explained, which simplifies a comparative study on various higher-order beam theories. Kumar et al [24] analyzed functionally graded material plates using two own new higher order transverse shear deformation theories. The energy principle was used to derive the governing differential equation of the plate.…”

Section: Introductionmentioning

confidence: 99%

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An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction

2020

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The paper is devoted to simply supported beams under three-point bending. Their mechanical properties symmetrically vary in the depth direction. The individual shear deformation theory for beams of such features is proposed. Based on the principle of stationary total potential energy the differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear coefficients and deflections of example beams are calculated. The solution is compared with other analytical results obtained with the use of another deformation function. Moreover, the bending problem of these beams is also numerically studied using the finite element method. Results of analytical and numerical studies are presented in Figures and Tables.

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“…The graphs of the dimensionless shear stresses (24) in the depth direction of the selected beams (B-1-1, B-2-2, B-3-3) are shown in Fig. 6.…”

Section: Analytical Study Of Bending Of the Beams With Symmetrically Varying Mechanical Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction

2020

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“…This contribution must be taken into account for thick or moderately thick plates. To overcome these limitations, lower- or higher-order shear deformation theories (SDT) were proposed (Radwan, 32 Kumar et al., 33 Thai and Vo 34 ). It was concluded that lower-order shear deformation theory such as first-order shear deformation does not lead to accurate results for plate with higher values of thickness to side length ratio.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

Arefi

Arani

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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Comprehensive nonlocal piezoelasticity relations are developed in this paper for a sandwich functionally graded nanoplate subjected to applied electric potential based on higher-order shear and normal deformation theory. To account thickness stretching effect, the higher-order shear and normal deformation theory is developed. Based on this theory, the transverse deflection is decomposed into bending, shear and stretching portions in which the third term is reflected variation of transverse deflection along the thickness direction. Size dependency is accounted in governing equations based on nonlocal elasticity theory. The sandwich nanoplate is made of a functionally graded core integrated with two piezoelectric layers. Distribution of material properties are assumed according to the power-law function in the thickness direction. The Hamilton’s principle is used to derive governing equations of motion. Navier’s technique is implemented to solve partial differential equation of motion. Accuracy and efficiency of the presented technique are verified by a comparison between obtained results and existing results in literature for two cases including and excluding thickness stretching effect. The comparison between the results with and without thickness stretching effect can justify necessity of present work. Large parametric analysis is organized to investigate effect of significant parameters such as external applied voltage, nonlocal parameter, non-homogeneous index, stretching effect, length-to-thickness, length-to-width and core-to-face sheet thickness ratios on the vibrational behavior of the system. As an important result of this study, one can conclude that accounting thickness stretching effect leads to decrease of natural frequencies in comparison with cases disregards thickness stretching.

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“…Reference [9] shows the study of a thick, simply supported FGM plate under bending on the grounds of displacement potential function (DPF). The authors of [10] applied two new higher-order transverse shear deformation theories (NHSDTs) to analyse the buckling and post-buckling states of an FGM plate. Xu et al [11] examined the buckling behaviour of a rectangular plate on the basis of classic plate theory and the post-buckling state was verified by a means of ABAQUS software.…”

Section: Introductionmentioning

confidence: 99%

The Study of Buckling and Post-Buckling of a Step-Variable FGM Box

Czechowski

Kołakowski

2019

Materials

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This work concerns the analysis of a thin-walled box made of ceramic and step-variable functionally graded material (FGM) subjected to compression. The components of the box taken into account were pure alumina and aluminium-alumina graded material. The problem was solved on the basis of a finite element method and Koiter’s asymptotic theory using a semi-analytical method (SAM). It analysed both the buckling state and the post-buckling state of the box. In addition, three conditions were considered: The presence of alumina outside or inside of the box and a mixed case. The obtained results were presented and discussed.

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New transverse shear deformation theory for bending analysis of FGM plate under patch load

Cited by 64 publications

References 66 publications

An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction

An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction

Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

The Study of Buckling and Post-Buckling of a Step-Variable FGM Box

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