• Coupled systems mechanics
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• v.8 no.1
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• pp.39-53
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• 2019

Here in this investigation, a two-dimensional thermoelastic problem of thick circular plate of finite thickness under fractional order theory of thermoelastic diffusion has been considered in frequency domain. The effect of frequency in the axisymmetric thick circular plate has been depicted. The upper and lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using Hankel transform techniques. The analytical expressions of displacements, stresses and chemical potential, temperature change and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect frequency has been shown on the various components.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.461-477
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• 2008

An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near crack tips. The domain integral technique, for which all relevant quantities are integrated over any arbitrary element areas around the crack tips, is utilized as the J-integral solution scheme with 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure onto a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Several benchmark problems are analyzed to evaluate the efficiency of the combined domain integral technique and the adaptive finite element method.

• Coupled systems mechanics
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• v.8 no.6
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• pp.501-522
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• 2019

The present study is concerned with the thermoelastic interactions in a two dimensional axisymmetric problem in transversely isotropic thermoelastic solid using new modified couple stress theory without energy dissipation and with two temperatures. The Laplace and Hankel transforms have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region, concentrated thermal source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. The effect of two temperature varying by taking different values for the two temperature on the components of normal stress, tangential stress, conductive temperature and couple stress are depicted graphically.

• Coupled systems mechanics
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• v.11 no.3
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• pp.199-215
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• 2022

The present paper deals with the axisymmetric deformation in homogeneousisotropic thermoelastic solid with two temperatures, with and without energy dissipation using modified couple stresstheory. The effect of energy dissipation and two temperature isstudied due to the concentrated normalforce, normalforce overthe circularregion, thermal pointsource and thermalsource over the circular region. The Laplace and Hankel transform techniques have been used to find the solution to the problem. The displacement components, conductive temperature distribution, stress components and couple stress are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. Effects of two temperature and energy dissipation on the conductive temperature,stress components and couple stress are depicted graphically.

• Coupled systems mechanics
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• v.8 no.5
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• pp.415-437
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• 2019

The present research deals with two-dimensional axisymmetric deformation in transversely isotropic magneto thermoelastic solid with and without energy dissipation, with two temperature and time-harmonic source. The proposed model is helpful for finding the type of relations between mechanical and thermal fields as most of the structural elements of heavy industries are frequently related to mechanical and thermal stresses at a higher temperature. The Hankel transform has been used to find a solution to the problem. The displacement components, stress components, and temperature distribution with the horizontal distance in the physical domain are calculated numerically. The effect of time-harmonic source and two temperature is depicted graphically on the resulting quantities.

• Coupled systems mechanics
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• v.9 no.6
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• pp.521-538
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• 2020

The present study is concerned with the thermoelastic interactions in a two dimensional homogeneous, transversely isotropic thermoelastic solid with new modified couple stress theory without energy dissipation and with two temperatures in frequency domain. The time harmonic sources and Hankel transform technique have been employed to find the general solution to the field equations.Concentrated normal force, normal force over the circular region, thermal point source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are depicted graphically to show the effect of angular frequency on the resulted quantities.

• Structural Engineering and Mechanics
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• v.14 no.1
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• pp.99-118
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• 2002

The scaled-boundary finite element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one coordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) coordinate direction. These coordinate directions are defined by the geometry of the domain and a scaling centre. This paper presents a general development of the scaled boundary finite-element method for two-dimensional problems where two boundaries of the solution domain are similar. Unlike three-dimensional and axisymmetric problems of the same type, the use of logarithmic solutions of the weakened differential equations is found to be necessary. The accuracy and efficiency of the procedure is demonstrated through two examples. The first of these examples uses the standard finite element method to provide a comparable solution, while the second combines both solution techniques in a single analysis. One significant application of the new technique is the generation of transition super-elements requiring few degrees of freedom that can connect two regions of vastly different levels of discretisation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.8
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• pp.1253-1260
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• 2001

Transient thermal analysis of a three-dimensional axisymmetric automotive disk brake is presented in this paper. Temperature fields are obtained using a hybrid FFT-FEM scheme that combines Fourier transform techniques and finite element method. The use of a fast Fourier transform algorithm can avoid singularity problems and lead to inexpensive computing time. The transformed problem is solved with finite element scheme for each frequency domain. Inverse transforms are then performed for time domain solution. Numerical examples are presented for validation tests. Comparisons with analytical results show very good agreement. Also, a 3-D simulation, based upon an automotive brake disk model is performed.

• Structural Engineering and Mechanics
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• v.69 no.6
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• pp.607-614
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• 2019

The present investigation has focus on the study of deformation due to thermomechanical sources in a thick circular plate. The thick circular plate is homogeneous, transversely isotropic with two temperatures and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of stresses, conductive temperature and displacement components are computed in the transformed domain. However, the resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are illustrated graphically. The effects of two temperatures by considering different values of temperature parameters are shown on the various components. Some particular cases are also figured out from the present investigation.

• Coupled systems mechanics
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• v.12 no.3
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• pp.261-276
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• 2023

This article is an application of new modified couple stress thermoelasticity without energy dissipation in association with two-temperature theory. The upper and lower surfaces of the plate are subjected to an axisymmetric heat supply. The solution is found by using Laplace and Hankel transform techniques. The analytical expressions of displacement components, conductive temperature, stress components and couple stress are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of two temperature is shown on the various components.