• Steel and Composite Structures
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• v.33 no.1
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• pp.123-131
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• 2019

The present investigation is concerned with two dimensional deformation in a homogeneous nonlocal thermoelastic solid with two temperature. The nonlocal thermoelastic solid is subjected to inclined load. Laplace and Fourier transforms are used to solve the problem. The bounding surface is subjected to concentrated and distributed sources. The analytical expressions of displacement, stress components, temperature change are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of angle of inclination and nonlocal parameter on the components of displacements, stresses and conductive temperature. Some special cases are also deduced from the present investigation.

• Advances in materials Research
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• v.12 no.2
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• pp.101-118
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• 2023

The purpose of this paper is to study the effects of magnetic field and gravitational field on fiber-reinforced thermoelastic medium with memory-dependent derivative. Three-phase-lag model of thermoelasticity (3PHL) is used to study the plane waves in a fiber-reinforced magneto-thermoelastic material with memory-dependent derivative. A gravitating magneto-thermoelastic two-dimensional substrate is influenced by both thermal shock and mechanical loads at the free surface. Analytical expressions of the considered variables are obtained by using Laplace-Fourier transforms technique with the eigenvalue approach technique. A numerical example is considered to illustrate graphically the effects of the magnetic field, gravitational field and two types of mechanical loads(continuous load and impact load).

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.429-434
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• 2024

In the current work, the effect of rotation and mechanical force on a nonlocal micropolar thermoelastic solid with temperature-dependent properties was discussed using Erigen's nonlocal thermoelasticity theory. The problem is resolved using Laplace transforms and Fourier series. For the nonlocal and local parameters, the physical fields have been illustrated. The numerical inversion approach is used to acquire the resulting fields in the physical domain. Based on numerical analysis, the effects of rotation, the modulus of elasticity's dependency on temperature, and nonlocal, mechanical force are examined on the physical fields.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.417-424
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• 1983

This paper presents two methods of obtaining approximate analytic solutions for the temperature distributions and heat flow to two-dimensional transient heat conduction problems in a finite strip with constant thermal properties using the Heat Balance Integral. The methods introduced in this study are as follows; one using the Heat Balance Integral only, and the other successively using the Heat Balance Integral and an exact analytic method. Both methods are applicable to a large number of the two-dimensional unsteady conduction problems in finite regions such as extended surfaces with uniform thickness, but in this paper only solutions for the unsteady problems in a finite strip with boundary condition at the base expressed in terms of step function are provided as an illustration. Results obtained by both methods are compared with those by the exact two-dimensional transient analysis. It is found that both approximate methods generate small time solutions, which can not be obtained easily by any exact analytic method for small values of Fourier numbers. In the case of applying the successive use of the Heat Balance Integral and Laplace transforms, the analysis shows good agreement with the exact solutions for any Fourier number in the range of Biot numbers less than 0.5.

• Coupled systems mechanics
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• v.9 no.1
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• pp.77-89
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• 2020

This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.206-213
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• 2013

Transient response of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar homogeneous piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layer vary continuously along the thickness. Laplace and Fourier transforms are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, and thickness of the layers. Computed results yield following conclusions: (a) the DERR increases with the increase of the gradient of the material properties of the FGPM layer; (b) certain direction and magnitude of the electric impact loading impedes crack extension; (c) increase of the thickness of the FGPM layer and the homogeneous piezoelectric layer which has larger material properties than those of the crack plane are beneficial to increase of the resistance of transient fracture of the FGPM layer.