Thermomechanical Deformation in an Orthotropic Micropolar Thermoelastic Solid

Kumar, Rajneesh; Gupta, Rajani Rani

doi:10.1007/s10765-008-0527-5

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…We see that results given by Fig. 5 are in good agreement with the predictions while the phenomenon does not appear in [33][34][35][36]. There exists a very slight difference in the distribution of stresses obtained between L-S theory and the coupled theory but an evident difference in the distribution of stresses obtained between G-L and classical coupled theory.…”

Section: Numerical Example and Discussionsupporting

confidence: 71%

“…It can be seen that there exits a distinct temperature step on thermal wave front in the distribution of temperature at t = 0.15 in Fig. 2 for the generalized theory (G-L or L-S), while this phenomenon does not appear and the finite speed of propagation of thermal wave is not depicted in [33][34][35][36]. There is no difference in the distribution of temperature obtained by magneto-microstretch G-L and magneto-microstretch L-S, but there is an evident difference in the distribution of temperature predicted by magneto-microstretch C-T and magneto-microstretch L-S in Fig.…”

Section: Numerical Example and Discussionmentioning

confidence: 94%

“…The elastodynamics problem of axisymmetric deformation in magneto-micropolar generalized thermoelastic medium was studied by Kumar et al [34]. Kumar et al studied the problem of thermomechanical deformation in magneto-micropolar elastic medium in the study by [35] and investigated the effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources in [36].…”

Section: Introductionmentioning

confidence: 99%

“…The analytical solution of two-dimensional thermoelastic problems can hardly be obtained because of the complicated inverse integrated transformation. Though the inverse integrated transformation can be achieved by numerical method, the results are not as accurate as in analytical solution and the finite speed of heat propagation not depicted [33][34][35][36]. Tian et al [37,38] solved the generalized thermoelastic problems directly in the time domain by finite element method.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional thermoelastic problem of an infinite magneto-microstretch homogeneous isotropic plate

Xiong

Tian

2011

Arch Appl Mech

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In this work, the magneto-thermoelastic problem of an infinite microstretch homogeneous isotropic plate placed in a transverse magnetic field is studied in the context of different theories of generalized thermoelasticity. The upper surface of the infinite plate is subjected to a zonal time-dependent heat shock. The problem is investigated by applying finite element method. The solution is obtained by solving finite element governing equations of the problem in time domain directly. The results, including temperature, stresses, displacements, microrotation, microstretch, induced magnetic field, and induced electric field, are presented graphically. Comparison is made in the results predicted by different theories of generalized thermoelasticity, to show that the micropolar effect has a slight influence on the results while the microstretch effect has a great influence on the results. Finally, a parameter study provides an idea about the influence of the respective terms of the theories.Keywords Magneto-microstretch thermoelasticity · Thermal shock · Finite element method · Microstretch effect · Micropolar effect

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Section: Numerical Example and Discussionsupporting

confidence: 71%

Section: Numerical Example and Discussionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Two-dimensional thermoelastic problem of an infinite magneto-microstretch homogeneous isotropic plate

Xiong

Tian

2011

Arch Appl Mech

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“…The coefficients of this material within micropolar theory are addressed in Ref. [62, 63]. The material properties are shown in Table 1.…”

Section: Resultsmentioning

confidence: 99%

Analytical solution of micropolar functionally graded materials (FGM) hollow cylinder under thermal asymmetric load (r, θ)

et al. 2021

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This paper focuses on the analysis of two‐dimensional steady‐state thermal stresses based on micropolar theory in hollow and solid cylinders which are made of functionally graded materials (FGM) under asymmetric loading condition (r, θ) with the general thermal and mechanical boundary conditions along the inside and outside surfaces. The heat conduction and Navier equations were solved using the separation of variables and complex Fourier series for micropolar theory. Finally, the exact numerical results for both micropolar and classical solutions are illustrated and discussed using two examples: In Example 1, based on the micropolar theory, when thermal tensions are exerted on the inside surface of the cylinder, some of the strain energy is used for the object rotation; therefore, considering this condition, the calculated values resulted from the micropolar theory are smaller than those of the classic theory. In Example 2, by exerting normal tension on the inside surface of the cylinder, the rotation created is very small; therefore, the results of the micropolar and classic theories are similar. In addition to FGM materials, this solution is applicable to minerals and organic matter multiphase fiber and particulate composites, soil, rock, concrete, and various granular materials [59].

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Evaluation of inverse Fourier transforms through romberg integration

Sharma

2010

International Journal of Solids and Structures

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a b s t r a c tThis study deals with evaluation of inverse integral transforms through numerical integration. Arguments are presented to explain that such a numerical evaluation is mathematically incorrect. In recent years, a sudden increase has been noticed in the number of research publications in which Romberg integration is said to have used in evaluating the inverse Fourier transforms. In this regard, even the references cited in these papers do not support such an evaluation but suggest contrary. An immediate concern is to caution the researchers studying the source problems in the field of solid mechanics over the use and approval of an erroneous numerical technique.

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Thermomechanical Deformation in an Orthotropic Micropolar Thermoelastic Solid

Cited by 7 publications

References 31 publications

Two-dimensional thermoelastic problem of an infinite magneto-microstretch homogeneous isotropic plate

Two-dimensional thermoelastic problem of an infinite magneto-microstretch homogeneous isotropic plate

Analytical solution of micropolar functionally graded materials (FGM) hollow cylinder under thermal asymmetric load (r, θ)

Evaluation of inverse Fourier transforms through romberg integration

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