Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory

Thom, Do Van; Nguyen, Dinh Kien; Duc, Nguyen Dinh; Doan, Duc Hong; Bui, Tinh Quoc

doi:10.1016/j.tws.2017.07.022

Cited by 132 publications

(20 citation statements)

References 42 publications

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“…Bui et al [95] applied the TSDT and the FEM for the mechanical behaviors of heated FGM plates in a high-temperature environment. Do et al [96] analyzed bi-directional FGM plates using the FEM and the TSDT. Mantari et al [97,98] developed various quasi-3D theories which consisted of four unknowns to study FGM plates.…”

Section: Introductionmentioning

confidence: 99%

A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

et al. 2019

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A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

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Section: Introductionmentioning

confidence: 99%

A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

et al. 2019

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“…Moreover, a new TSDT was employed by Do et al. 50 to analyze the bending and buckling behaviors of bidirectional FG beams via the finite element method. No spectral treatment of shear-locking effect and no shear correction factors were required in their approach.…”

Section: Introductionmentioning

confidence: 99%

“…With the aid of the aforementioned theory, they considered the mechanical behaviors of two types of FG microbeams including unidirectional and bidirectional ones. Moreover, a new TSDT was employed by Do et al 50 to analyze the bending and buckling behaviors of bidirectional FG beams via the finite element method. No spectral treatment of shear-locking effect and no shear correction factors were required in their approach.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibration analysis of fluid-infiltrated porous curved microbeams integrated with reinforced functionally graded graphene platelets face sheets considering thickness stretching effect

Arshid

Amir

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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Size-dependent vibration analysis of three-layered fluid-infiltrated porous curved microbeams, which are integrated with nanocomposite face sheets, is provided in this work. The effect of the fluids within the pores of the core is taken into consideration and the core’s thermomechanical properties vary across the thickness based on three different patterns. Also, the face sheets are made from epoxy, which are reinforced by graphene platelets as lightweight and high-stiffness reinforcements. Graphene platelets dispersion patterns are also considered, which obey three different functions, namely parabolic, linear, and uniform. Moreover, effective thermomechanical properties of the face sheets are determined with the aid of ERM and Halpin–Tsai micromechanical models. The microstructure is under thermal load and it is rested on Pasternak elastic foundation. In the polar coordinate system, the strains are determined for deep curved beams that lead to more accurate results. Based on a refined higher-order shear deformation theory, which includes four variables and considers the thickness stretching effect, and employing the modified couple stress theory for accounting the size effect, the differential motion equations are derived and via an analytical method, they are solved. A verification study is conducted by neglecting some parameters and after that, the results are presented and discussed in detail. It is seen that the porous core and nanocomposite face sheets material properties have significant effects on the vibrational response of the under consideration model. Up to now, no similar work in the available literature has been found, therefore, the results of this study can be considered as a benchmark for future ones. The outcomes of this study may help to design more efficient structures with the desired properties.

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“…The above-mentioned theories are based on polynomial expansion of transverse coordinate following Taylor's series expansion and applied for the modelling of plate and shell structures. [17][18][19] In addition to these polynomial shear deformation theories (PSDTs), the theories with non-polynomial function of transverse coordinate are also developed and these theories are termed as non-polynomial shear deformation theories (NPSDTs). [20][21][22][23][24][25][26][27][28][29][30][31] NPSDTs do not require shear correction factor and satisfy transverse shear free conditions at the top and bottom surface of the plate.…”

Section: Introductionmentioning

confidence: 99%

A non-polynomial axiomatic framework for modelling and bending analysis of doubly curved spherical and cylindrical shells: An analytical solution

Sharma

Grover

Purohit

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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In the present work, the doubly curved spherical and cylindrical laminated composite shells are modelled and analysed in the framework of non-polynomial axiomatic approach. The inverse hyperbolic shear deformation theory originally developed for the laminated composite plates is extended to model the deformation characteristics of laminated composite shells. The mathematical formulation is developed under the assumption of linear structural kinematics and linear-elastic-orthotropic material behaviour. The governing equations of the model are obtained using the principle of virtual work and solved in exact manner for simply supported boundary conditions following the Navier solution methodology. The bending response of thick and thin spherical and cylindrical shells subjected to different types of transverse loads such as point load, uniform load and sinusoidal load is analysed in the framework of developed methodology. The obtained results due to inverse hyperbolic shear deformation theory are compared with other shell theories and on the basis of this comparison, the validity and applicability of the inverse hyperbolic shear deformation theory for doubly curved spherical and cylindrical shells is ensured.

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Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory

Cited by 132 publications

References 42 publications

A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

Size-dependent vibration analysis of fluid-infiltrated porous curved microbeams integrated with reinforced functionally graded graphene platelets face sheets considering thickness stretching effect

A non-polynomial axiomatic framework for modelling and bending analysis of doubly curved spherical and cylindrical shells: An analytical solution

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