Hygrothermal modeling of the buckling behavior of sandwich plates with nanocomposite face sheets resting on a Pasternak foundation

Kiarasi, Faraz; Babaei, Masoud; Dimitri, Rossana; Tornabene, Francesco

doi:10.1007/s00161-020-00929-6

Cited by 32 publications

(7 citation statements)

References 39 publications

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“…The second strain gradient of Mindlin will be implemented to attach the microstructural property into a problem model [39][40][41][42][43]. It is crucial to note that the couple stress models [44][45][46][47][48][49][50] cannot be embedded into the energy formulation while the problem is flexoelectric or flexomagnetic ones.…”

Section: Theoretical Modelingmentioning

confidence: 99%

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Malikan

Wiczenbach

Eremeyev

2021

Continuum Mech. Thermodyn.

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By relying on the Euler–Bernoulli beam model and energy variational formula, we indicate critical temperature causes in the buckling of piezo-flexomagnetic microscale beams. The corresponding size-dependent approach is underlying as a second strain gradient theory. Small deformations of elastic solids are assessed, and the mathematical discussion is linear. Regardless of the pyromagnetic effects, the thermal loading of the thermal environment varies in three states along with the thickness, which is linear, uniform, and parabolic forms. We then establish the results by developing consistent shape functions that independently evaluate boundary conditions. Next, we analytically develop and explore the effective properties of the studied beam concerning vital factors. It was achieved that piezomagnetic-flexomagnetic microbeams are more affected by the thermal environment while the thermal loading is parabolically distributed across the thickness, particularly when the boundaries involve simple supports.

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Section: Theoretical Modelingmentioning

confidence: 99%

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Malikan

Wiczenbach

Eremeyev

2021

Continuum Mech. Thermodyn.

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“…FSDT theory is applied according to the thickness of plate. Hence, the displacement fields are assumed as [34]:…”

Section: Geometry and Materials Propertymentioning

confidence: 99%

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Nazari

Babaei²,

Kiarasi³

et al. 2021

SN Appl. Sci.

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In this study, we present a numerical solution for geometrically nonlinear dynamic analysis of functionally graded material rectangular plates excited to a moving load based on first-order shear deformation theory (FSDT) for the first time. To derive the governing equations of motion, Hamilton’s principle, nonlinear Von Karman assumptions and FSDT are used. Finally, the governing equations of motion are solved by employing the generalized differential quadratic method as a numerical solution. Natural frequencies, dynamic bending behavior and stresses of the plate for linear and nonlinear type of geometrically strain–displacement relations and different factors, including the magnitude and velocity of moving load, length ratio, power law exponent and various edge conditions are obtained and compared. Article highlights Developing generalized differential quadrature method (GDQM) solution based on FSDT for dynamic analysis of FGM plate excited by a moving load for the first time. Comparison of linear and nonlinear dynamic response of plate by considering Von-Karman assumption. Observing considerable difference between linear and nonlinear results

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“…Besides the dynamical modeling and dynamical properties of beam structures with complex boundary conditions [19], the dynamical modeling and dynamical properties of plate structures [20][21][22][23][24], shell structures [25][26][27][28][29][30][31], and other types of structures [32][33][34] with complex boundary conditions have also been investigated [35][36][37][38][39]. For example, Xue et al [20] developed and solved a dynamics model for medium-thick composite laminates with arbitrary boundary conditions based on Mindlin's theory, Hamilton's principle, a modified Fourier series method, and the spring technique, with parametric studies on the effects of several key parameters, such as thickness-to-width ratio, number of plies, and lay-up angle between two plies.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

2023

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The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures.

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Hygrothermal modeling of the buckling behavior of sandwich plates with nanocomposite face sheets resting on a Pasternak foundation

Cited by 32 publications

References 39 publications

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

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