Nonlocal thermoelastic analysis of a functionally graded material microbeam

Peng, Wei; Chen, Like; He, Tianhu

doi:10.1007/s10483-021-2742-9

Cited by 35 publications

(15 citation statements)

References 64 publications

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“…According to nonlocal model previously proposed by Eringen [8,11,[40][41][42], we have the nonlocal constitutive equations for elasticity and heat conduction as follows:…”

Section: The Establishment and Setting Of Model Problemsmentioning

confidence: 99%

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The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

Dong

Nie

et al. 2022

Mathematics and Mechanics of Solids

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This paper proposes an innovative enriched second-order multi-scale (SOMS) computational method to simulate and analyze the nonlocal thermoelastic problems of blend composites with stress and heat flux gradient behaviors. The multiple periodical heterogeneities and periodic configurations of investigated blend composites in different substructures result in a huge computational cost for direct numerical simulations. The significant characteristics of this study are as follows. (1) The nonlocal properties of blend composites in constitutive equations are converted into the source terms of thermoelastic balance equations. The novel macro-micro coupled SOMS computational model for these transformed nonlocal multi-scale problems is derived on the basis of multi-scale asymptotic analysis. The nonlocal thermoelastic behaviors of blend composites can be merely uncovered in the enriched SOMS solutions. (2) The error analysis in the pointwise sense is presented to elucidate the importance and necessity of establishing the enriched SOMS solutions. Furthermore, an explicit error estimate for the SOMS approximate solutions is obtained in the integral sense for these nonlocal multi-scale problems. (3) A multi-scale numerical algorithm is presented to effectively simulate nonlocal thermoelastic problems of blend composites based on finite element method (FEM). Finally, the capability of the proposed enriched SOMS computational method is demonstrated by typical two-dimensional (2D) and three-dimensional (3D) blend composites, presenting not only the excellent numerical accuracy but also the less computational cost. This work proposes a unified multi-scale computational framework for enabling nonlocal thermoelastic behavior analysis of blend composites.

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“…According to nonlocal model previously proposed by Eringen [8,11,[40][41][42], we have the nonlocal constitutive equations for elasticity and heat conduction as follows:…”

Section: The Establishment and Setting Of Model Problemsmentioning

confidence: 99%

“…Subsequently, employing Green's formula and integrating by parts on equation (42), we obtain the consequential equality: Combining equation (41) and Lemma 1 together, we can lead to:…”

Section: The Error Analysis In the Integral Sensementioning

confidence: 99%

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

Dong

Nie

et al. 2022

Mathematics and Mechanics of Solids

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“…The researchers in the study [21] used the Hermitian transfinite modeling technique to investigate the effects of temperature fluctuations on thermally induced stress and heat transmission in a cylinder with a thermosensitive functional grade. Peng et al [22] investigated the non-local extended thermal flexibility of a FGM microbial package and its thermally induced transient behavior. The material is heated by a ramp-style heating load at the left end of the microbeam.…”

Section: Introductionmentioning

confidence: 99%

The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod

askar,

Marin,

Abouelregal

et al. 2023

Preprint

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By laminating piezoelectric and flexible materials during the manufacturing process, we can improve the performance of electronic devices. In smart structure design, it is also important to understand how the functionally graded piezoelectric (FGP) structure changes over time when thermoelasticity is assumed. This is because these structures are often exposed to both moving and still heat sources during many manufacturing processes. Therefore, the electrical and mechanical properties of layered piezoelectric materials that are subjected to electromechanical loads and heat sources must be both analyzed theoretically and practically.Classical thermoelasticity cannot solve the problem of the infinite speed of heat wave propagation, so extended thermoelasticity models are proposed. In this paper, the Lord-Shulman theory with the idea of a memory-dependent derivative (MDD) was used to investigate how a moving axial heat source affects the thermomechanical sensitivity of a FGP rod.The physical characteristics of the FG rod are supposed to change exponentially when travelling in the direction of the rod axis. It is further assumed that the rod is held at both ends and that there is no voltage across them.Laplace transform procedures were used to obtain the physical fields being analyzed. A combination of measures of heterogeneity, kernel functions, time delays, and heat source velocities was used to make comparisons between the results discussed and those in previous literature.It was found that a higher value of the inhomogeneity index reduces the dynamic behavior to axial displacement, temperature change, and electric potential.

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“…Lata and Singh [30] studied the non-local magneto-thermoelastic solid with two temperatures subjected to rotation and inclined loads. Using a nonlocal generalized thermoelasticity model, Peng and Chen [31] studied a micro-scale FGM beam with ramping-type heating on the left end for its dynamic thermoelastic response. Abbas et al [32] used Lord and Shulman's generalized thermoelastic model to study wave propagation in unbounded thermoelastic materials based on nonlocal thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

Kaur

Singh

2022

SN Appl. Sci.

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The purpose of this study is to investigate vibrations in 2D functionally graded nanobeams (FGN) with memory-dependent derivatives. A sinusoidal variation of temperature is assumed. The dimensionless expressions for axial displacement, thermal moment, lateral deflection, strain and temperature distribution are found in the transformed domain using Laplace Transforms, and the expressions in the physical domain are derived by numerical inversion techniques. The nanobeam is simply supported at the both ends and have constant temperatures. The FGN is a non-homogenous composite structure with constant structural variations along with the layer thickness, changing from ceramic at the bottom to metal at the top. Adding non-local MDD to thermoelastic models opens up new possibilities for the study of thermal deformations in solid mechanics. The effect of different kernel functions and periodic frequency of thermal vibration is illustrated graphically for lateral deflection, axial displacement, strain, temperature, and thermal moment. Article highlights A novel model of vibrations in a functionally graded nanobeams is presented. The medium is subjected to sinusoidal variation of temperature. Dynamic response of memory dependent derivative theory of thermoelasticity and non-local parameter is investigated. The effects of kernel functions and periodic frequency of thermal vibration on all physical fields are investigated and shown graphically.

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Nonlocal thermoelastic analysis of a functionally graded material microbeam

Cited by 35 publications

References 64 publications

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

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