A different approach to Eringen's nonlocal integral stress model with applications for beams

Koutsoumaris, C. Chr.; Eptaimeros, K.G.; Tsamasphyros, G.

doi:10.1016/j.ijsolstr.2016.09.007

Cited by 93 publications

(32 citation statements)

References 63 publications

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“…Wang and Dhaliwal 17 introduced the energy and the work equation in nonlocal generalized thermoelasticity and demonstrated that the initial and boundary value problems have a unique solution. Solutions for various problems support this theory 17–27 …”

Section: Introductionmentioning

confidence: 80%

A novel model of nonlocal thermoelasticity with time derivatives of higher order

Abouelregal

2020

Math Methods in App Sciences

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The objective of this work is to introduce a new system of differential equations describing the nonlocal thermoelasticity theory with higher time derivatives and two-phase lags. In order to obtain this model, we used the nonlocal continuum theory proposed by Eringen and the methodology of the Taylor series expansion of higher-order time derivatives. Some generalized thermoelasticity theories follow as limited cases. This model is used to study the thermoelastic interaction in a nonlocal medium. The medium is exposed to an applied magnetic field and a periodic time heat source with a constant strength. Some comparisons have been displayed in figures to estimate the influences of the nonlocal parameter and magnetic field as well as the parameters of higher-order on all the field quantities.

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Section: Introductionmentioning

confidence: 80%

A novel model of nonlocal thermoelasticity with time derivatives of higher order

Abouelregal

2020

Math Methods in App Sciences

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“…Numerical results are now presented to explain the variation of displacement u, temperature θ , the strain e and the non-local thermal stress τ x x as well as discussed on the obtained results. In order to find the solutions for physical field in space-time areas, we must apply a technique of inversion approximation (40) proposed by Zakian [16,48] to equations ( 34), ( 35), ( 38) and ( 39), respectively. For all numerical calculations, Mathematica programming Language is employed.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The non-local continuum theory expressed by Koutsoumaris et al [48], either in integral or differential forms, is commonly utilized for describing the size dependency in micro-and nanoscale structures. Liew et al [49] literary studied the recent works related to the application of non-local elasticity theory for modeling and simulation of graphene sheets.…”

Section: Introductionmentioning

confidence: 99%

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Abouelregal

Sedighi

Shirazi

et al. 2021

Continuum Mech. Thermodyn.

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In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.

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“…Tuna and Kirca [138] derived the exact solution of the integral form of Eringen nonlocal model for the bending analysis of Euler-Bernoulli and Timoshenko beams. Koutsoumaris et al [139] investigated the static response of nanobeams using nonlocal integral elasticity with the modified kernel. Romano and Barretta [140] compared stress-driven and strain driven nonlocal integral models for nano-beams.…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

Advances in modelling and analysis of nano structures: a review

Chandel

Wang

Talha

2020

Nanotechnology Reviews

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AbstractNanostructures are widely used in nano and micro-sized systems and devices such as biosensors, nano actuators, nano-probes, and nano-electro-mechanical systems. The complete understanding of the mechanical behavior of nanostructures is crucial for the design of nanodevices and systems. Therefore, the flexural, stability and vibration analysis of various nanostructures such as nanowires, nanotubes, nanobeams, nanoplates, graphene sheets and nanoshells has received a great attention in recent years. The focus has been made, to present the structural analysis of nanostructures under thermo-magneto-electro-mechanical loadings under various boundary and environmental conditions. This paper also provides an overview of analytical modeling methods, fabrication procedures, key challenges and future scopes of development in the direction of analysis of such structures, which will be helpful for appropriate design and analysis of nanodevices for the application in the various fields of nanotechnology.

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A different approach to Eringen's nonlocal integral stress model with applications for beams

Cited by 93 publications

References 63 publications

A novel model of nonlocal thermoelasticity with time derivatives of higher order

A novel model of nonlocal thermoelasticity with time derivatives of higher order

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Advances in modelling and analysis of nano structures: a review

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