Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect

Al-shujairi, Mohammed; Mollamahmutoglu, C.

doi:10.1016/j.compositesb.2018.08.103

Cited by 68 publications

(11 citation statements)

References 69 publications

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“…To obtain the nondimensional natural frequency of the Euler–Bernoulli curved beams, the GDQ method (Al-shujairi and Mollamahmutoglu, 2018; Khaniki, 2018; Wang, 2018) is used to solve the coupled differential equations with arbitrary boundary conditions.…”

Section: Solution Methodsmentioning

confidence: 99%

Free vibration analysis of Euler–Bernoulli curved beams using two-phase nonlocal integral models

Zhang

Qing

2021

Journal of Vibration and Control

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Eringen’s nonlocal elastic model has been widely applied to address the size-dependent response of micro-/nanostructures, which is observed in experimental tests and molecular dynamics simulation. However, several recent studies have pointed out that some inconsistent results appear while applying it in the analysis of bounded structures, which indicates that it is necessary to adopt other suitable models. In this work, both the well-posed strain-driven and stress-driven two-phase local/nonlocal integral models are used to study the size effect in the free vibration of Euler–Bernoulli curved beams. The governing equations of motion and the associated boundary conditions are derived on the basis of Hamilton’s principle. The two-phase nonlocal integral relation is transformed into an equivalent differential law with two constitutive boundary conditions. Using the generalized differential quadrature method, the governing equation in terms of displacements is solved numerically. The vibration frequencies of the beam under different boundary conditions are obtained and validated by comparing with those existing results. For all boundary conditions, the nonlocal related parameters of the two types of two-phase nonlocal strategies show consistent softening and stiffening effects on vibration response, respectively. Moreover, the effect of the curvature radius of the beam is also investigated.

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Section: Solution Methodsmentioning

confidence: 99%

Free vibration analysis of Euler–Bernoulli curved beams using two-phase nonlocal integral models

Zhang

Qing

2021

Journal of Vibration and Control

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“…Radić and Jeremić [29] studied the buckling and vibrations of orthotropic doublelayered graphene sheets under hygrothermal loadings based on the differential form of nonlocal theory of elasticity. Al-Shujairi and Mollamahmutoǧlu [30] developed a nonlocal strain gradient beam model for the free vibration and buckling responses of FGM sandwich microbeams under thermal conditions. Jamalpoor et al [31] investigated the biaxial buckling and free oscillations of double magneto-electro-elastic nanoplates in viscoelastic media.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes

Song

Sahmani

Safaei

2021

Appl. Math. Mech.-Engl. Ed.

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This study presents the size-dependent nonlinear thermal postbuckling characteristics of a porous functionally graded material (PFGM) microplate with a central cutout with various shapes using isogeometric numerical technique incorporating nonuniform rational B-splines. To construct the proposed non-classical plate model, the nonlocal strain gradient continuum elasticity is adopted on the basis of a hybrid quasithree-dimensional (3D) plate theory under through-thickness deformation conditions by only four variables. By taking a refined power-law function into account in conjunction with the Touloukian scheme, the temperature-porosity-dependent material properties are extracted. With the aid of the assembled isogeometric-based finite element formulations, nonlocal strain gradient thermal postbuckling curves are acquired for various boundary conditions as well as geometrical and material parameters. It is portrayed that for both size dependency types, by going deeper in the thermal postbuckling domain, gaps among equilibrium curves associated with various small scale parameter values get lower, which indicates that the pronounce of size effects reduces by going deeper in the thermal postbuckling regime. Moreover, we observe that the central cutout effect on the temperature rise associated with the thermal postbuckling behavior in the presence of the effect of strain gradient size and absence of nonlocality is stronger compared with the case including nonlocality in absence of the strain gradient small scale effect.

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“…For instance, piezoelectric effects can be involved, so these are also included in the formulation [36][37][38]. A combination of sandwich and functionally graded (FG) materials including thermal effects are also considered and stability issues in the presence of dynamic effects are analyzed in [39,40]. For the influence of thermal phenomena in wave propagation analysis in FG sandwich beams, see [41].…”

Section: Introduction Motivation and Outlinementioning

confidence: 99%

On thermomechanics of multilayered beams

Barretta

Čanađija

Sciarra

2020

International Journal of Engineering Science

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In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven integral formulation of elasticity. The present research extends the treatment in [1] confined to elastically homogeneous nano-scopic structures. It is shown that the non-locality leads to a complex coupling between axial and transverse elastic displacements. Such a size-dependent phenomenon makes the solution of the relevant nonlocal thermoelastostatic problem, governed by a system of two ordinary differential equations with ten standard boundary conditions and non-classical constitutive boundary conditions, significantly more involved with respect to treatments in literature. Thus, a novel solution methodology, based on Laplace transforms, is proposed and illustrated by examining simple structural schemes of current

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Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect

Cited by 68 publications

References 69 publications

Free vibration analysis of Euler–Bernoulli curved beams using two-phase nonlocal integral models

Free vibration analysis of Euler–Bernoulli curved beams using two-phase nonlocal integral models

Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes

On thermomechanics of multilayered beams

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