State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

Trinh, Luan C.; Vo, Thuc P.; Thai, Huu‐Tai; Nguyen, Trung-Kien; Poologanathan, Keerthan

doi:10.1016/j.compositesb.2018.05.017

Cited by 38 publications

(10 citation statements)

References 65 publications

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“…Analytical solution of the presented system of PDEs is possible under Lévy type boundary conditions [68]. Tables 1 and 2), the external load parameter, q in Eq.…”

Section: Lévy Methods and State Space Solutionmentioning

confidence: 99%

Higher-order semi-layerwise models for doubly curved delaminated composite shells

Szekrényes

2020

Arch Appl Mech

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This work deals w ith the development and extension of higher-order models for delaminated doubly curved composite shells with constant radii of curvatures. The mechanical model is based on the method of four equivalent single layers and the system of exact kinematic conditions. A remarkable addition of this work compared to some previous ones, is a modified and improved continuity condition between the delaminated and undelaminated parts of the shell. Using the principle of virtual work, the equilibrium equations of the shell systems are brought to the stage and solved by using the classical Lévy plate formulation under simply supported conditions. Four different scenarios of elliptic and hyperbolic delaminated shells are investigated providing the solutions for the mechanical fields as well as for the J-integral. The analytical results are compared to 3D finite element calculations, and excellent agreement was obtained for the displacement components and normal stresses. On the contrary, it was found that the transverse shear stresses are captured quite differently by the proposed method and the finite element models. Although the role of shear stresses should not be underrated, they seem to be marginal because the distributions of the J-integral components are in very good agreement with the numerically determined energy release rates.

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“…Analytical solution of the presented system of PDEs is possible under Lévy type boundary conditions [68]. Tables 1 and 2), the external load parameter, q in Eq.…”

Section: Lévy Methods and State Space Solutionmentioning

confidence: 99%

Higher-order semi-layerwise models for doubly curved delaminated composite shells

Szekrényes

2020

Arch Appl Mech

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“…Trinh et al. 73 applied the state-space Levy procedure to analyze size dependent static, free vibration and buckling behaviours of FG sandwich plates; the deflections, stresses, natural frequencies and critical buckling loads were analytically obtained by closed form formulations. More recently, Şimşek and Al-shujairi 74 examined for the first time the static, free and forced vibration of FG sandwich beams excited by two successive moving harmonic loads.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

Bensaid

Daikh

Draï

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

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“…Trinh et al. [44] developed the four-variable refined shear deformation theory for static, free vibration and buckling behaviors of FG sandwich microplates. Abdelaziz et al.…”

Section: Introductionmentioning

confidence: 99%

Bending and free vibration analysis of sandwich plates with functionally graded soft core, using the new refined higher-order analysis model

Zhao

Yang

et al. 2020

Jnl of Sandwich Structures & Materials

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This study presents a new higher-order refined analysis model for static and free vibration analysis of a sandwich plate with soft functionally graded material core. The governing equations are derived from equilibrium differential equations of motions. The accuracy and convergence of the present model and numerical solution are validated versus available results. Variable length width ratios, thickness ratios between skins and core and span-to-thickness of sandwich plates have been studied. Obtained results show that suggested model can achieve greater accuracy for sandwich plates with soft functionally graded material core, as compared to existing functionally graded sandwich plate analysis models and models based on finite element method. Finally, parametric study has been carried out to investigate influence of volume fraction distribution, thickness to side ratio and material properties on the plate bending and free vibration.

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State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

Cited by 38 publications

References 65 publications

Higher-order semi-layerwise models for doubly curved delaminated composite shells

Higher-order semi-layerwise models for doubly curved delaminated composite shells

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

Bending and free vibration analysis of sandwich plates with functionally graded soft core, using the new refined higher-order analysis model

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