Non-linear rapid heating of FGM beams

Ghiasian, S.E.; Kiani, Y.; Eslami, Mohammad H.

doi:10.1016/j.ijnonlinmec.2014.08.006

Cited by 78 publications

(18 citation statements)

References 30 publications

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“…Beforehand, using the general concept of the separation of variables method, time and space dependency of the primary variables may be separated. Accordingly, each of the functions u 0 , w 0 and ϕ may be written in the next form [45]:…”

Section: Solution Methodsmentioning

confidence: 99%

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Nonlinear free vibration of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

Mirzaei

Kiani

2016

Acta Mech

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In this research, large amplitude free vibrations of a sandwich beam with stiff core and carbon nanotube (CNT)-reinforced face sheets are analysed. The distribution of CNTs across the thickness of the face sheets may be uniform or functionally graded. The equivalent single-layer theory of Timoshenko is used to construct the Hamiltonian of the beam under the von Kármán type of geometrical nonlinearity assumptions. A uniform temperature field through the beam is also included in the formulation. The Ritz method with polynomial basis functions is used to discrete the equations of motion and establish the matrix representation of the governing equations. A nonlinear eigenvalue problem is obtained and solved using a standard continuation procedure. After validating the developed solution method and formulation, parametric studies are conducted to examine the influences of thermal environment, core thickness-to-face sheet thickness ratio, boundary conditions, amplitude of vibrations, CNTs volume fraction and their distribution pattern. It is concluded that an increase in the volume fraction of CNTs results in higher fundamental frequency and decreases the nonlinear-to-linear frequency ratio.

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Section: Solution Methodsmentioning

confidence: 99%

“…The polynomial shape functions associated with the C-C, C-S and S-S type of boundary conditions are given by Ghiasian et al [45]. Here C-S indicates a beam which is clamped at x = 0 and simply supported at x = L. The same shape functions are used in the present study and are given in Table 2.…”

Section: Solution Methodsmentioning

confidence: 99%

Nonlinear free vibration of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

Mirzaei

Kiani

2016

Acta Mech

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“…In this study, Ritz method is used to obtain the governing equations of the post-buckling analysis. As a result, u 0 , w 0 and ϕ which are the essential parameters of the problem may be expressed as 17 …”

Section: Solution Proceduresmentioning

confidence: 99%

“…Ghiasian et al. 17 The same shape functions are considered in this study to approximate the displacement components. The shape functions are given in Table 2.…”

Section: Solution Proceduresmentioning

confidence: 99%

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Nonlinear stability of sandwich beams with carbon nanotube reinforced faces on elastic foundation under thermal loading

Kiani

Mirzaei

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this research, post-buckling response of sandwich beams with carbon nanotube reinforced face sheets subjected to uniform temperature rise loading and resting on a two-parameter elastic foundation is investigated. A single-layer theory formulation based on the first-order shear deformation beam theory is used. Material properties of the media are obtained according to a refined rule of mixtures approach which contains efficiency parameters. Suitable for the large deformations, von-Kármán strains are taken into consideration. The elastic foundation is modelled as the Pasternak model which takes into account the shear interaction of the springs. Material properties of the face sheets are considered to be position and temperature dependent. The governing equations of the system are obtained using the Ritz method for various combinations of clamped, simply supported and sliding supported edges. Post-buckling equilibrium path of the beam is obtained according to an iterative displacement control strategy. Numerical results of the present study are compared with the available data in the open literature. Then, the numerical results are provided to explore the effect of side-to-thickness ratio, volume fraction of carbon nanotube, distribution pattern of carbon nanotube, the ratio of face thickness-to-host thickness, boundary conditions and elastic foundation.

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Thermal shock analysis of functionally graded sandwich curved beams using a new layerwise theory

Pandey

Pradyumna

2021

Z Angew Math Mech

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This work for the first time presents a simple, accurate and straightforward finite element formulation that requires a C0 continuity of transverse displacement for the transient stress analysis of curved beams under thermal shock using a new layerwise theory. The FGM sandwich curved beam is considered to be made of three layers in which the top, middle and the bottom layer is considered to be made of pure ceramic, functionally graded material (FGM) core and pure metal constituents, respectively. The proposed new layerwise theory assumes a higher‐order displacement field for FGM core and first‐order displacement field for both top and bottom layers. The material properties are assumed to be temperature‐dependent. The governing differential equation for the present investigation is formulated using Hamilton's principle. A wide range of comparison studies are presented to establish the accuracy of the present layerwise finite element formulation. A parametric study is conducted to show the simplicity and wider applicability of the proposed formulation. It is shown here that by selecting an appropriate value of volume fraction index, core to facesheet thickness ratio, magnitude of thermal shock, curvature and thickness ratio, the transient thermal stresses induced in FGM sandwich curved beams can be reduced substantially.

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Non-linear rapid heating of FGM beams

Cited by 78 publications

References 30 publications

Nonlinear free vibration of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

Nonlinear free vibration of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

Nonlinear stability of sandwich beams with carbon nanotube reinforced faces on elastic foundation under thermal loading

Thermal shock analysis of functionally graded sandwich curved beams using a new layerwise theory

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