• Advances in concrete construction
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• 제11권4호
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• pp.315-321
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• 2021

In this article, an analytical solution of the dynamical behavior in an orthotropic non-homogeneity elastic material using for elastodynamics equations is investigated. The effects of the magnetic field, the initial stress, and the non-homogeneity on the radial displacement and the corresponding stresses in an orthotropic material are investigated. The analytical solution for the elastodynamic equations has solved regarding displacements. The variation of the stresses, the displacement, and the perturbation magnetic field have shown graphically. Comparisons are made with the previous results in the absence of the magnetic field, the initial stress, and the non-homogeneity. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity.

• Geomechanics and Engineering
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• 제25권4호
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• pp.331-339
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• 2021

In this work, an analytical solution is provided for the dynamical response of an orthotropic non-homogeneous elastic material. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity. The analytical performances for the elastodynamic equations has been solved regarding displacements. The influences of the rotation, the magnetic field, the non-homogeneity based radial displacement and the corresponding stresses in an orthotropic material are investigated. The variations of the stresses, the displacement, and the perturbation magnetic field have been illustrated. The comparisons is performed using the previous solutions in the magnetic field absence, the non-homogeneity and the rotation.

• Structural Engineering and Mechanics
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• 제55권4호
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• pp.871-884
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• 2015

In the present study, separate and combined effects of rotary inertia, shear deformation and material non-homogeneity (MNH) on the values of natural frequencies of the simply supported beam are examined. MNH is characterized considering the parabolic variations of the Young's modulus and density along the thickness direction of the beam, while the value of Poisson's ratio is assumed to remain constant. At first, the equation of the motion including the effects of the rotary inertia, shear deformation and MNH is provided. Then the solutions including frequencies of the first three modes for various combinations of the parameters of the MNH, depth to length ratios, and shear corrections factors are reported. To show the accuracy of the present results, two comparisons are carried out and good agreements are found.

• Structural Engineering and Mechanics
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• 제43권1호
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• pp.89-103
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• 2012

In this study, the stability of laminated homogeneous and non-homogeneous orthotropic truncated conical shells with freely supported edges under a uniform hydrostatic pressure is investigated. It is assumed that the composite material is orthotropic and the material properties depend only on the thickness coordinate. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated non-homogeneous orthotropic truncated conical shells. Applying Galerkin method to the foregoing equations, the expression for the critical hydrostatic pressure is obtained. The appropriate formulas for the single-layer and laminated, cylindrical and complete conical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, effects of non-homogeneity, number and ordering of layers and variations of shell characteristics on the critical hydrostatic pressure are investigated.

• Structural Engineering and Mechanics
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• 제54권1호
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• pp.135-148
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• 2015

The present investigation is concerned with a study effect of magnetic field and non-homogenous on the elastic stresses in rotating orthotropic infinite circular cylinder. A certain boundary conditions closed form stress fields solutions are obtained for rotating orthotropic cylinder under initial magnetic field with constant thickness for three cases: (1) Solid cylinder, (2) Cylinder with a circular hole at the center, (3) Cylinder mounted on a circular rigid shaft. Analytical expressions for the components of the displacement and stress fields in different cases are obtained. The effect of rotation and magnetic field and non-homogeneity on the displacement and stress fields are studied. Numerical results are illustrated graphically for each case. The effects of rotating and magnetic field and non-homogeneity are discussed.

• 한국항공운항학회지
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• 제16권4호
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• pp.26-34
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• 2008

This article provides a comprehensive treatment of cracks in non-homogeneous structural materials such as functionally graded materials (FGMs). It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using laminated composite plate model to simulate the material non-homogeneity, we present an algorithm for solving the system based on Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with arbitrarily varying material properties. As a numerical illustration, transient thermal flow intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of non-homogeneous material with properties varying in the thickness direction.

• 한국항공운항학회지
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• 제19권1호
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• pp.15-23
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• 2011

The purpose of this paper is to investigate the time behavior of a multiple crack problems. It is assumed that the medium contains cracks perpendicular to the crack surfaces, that the thermo-mechanical properties are continuous functions of the thickness coordinate. we use the laminated composite plate model to simulate the material non-homogeneity. By utilizing the Laplace transform and Fourier transform techniques, the multiple crack problems in the non-homogeneous medium is formulated. Singular integral equations are derived and solved to investigate the multiple crack problems. As a numerical illustration, transient thermal stress intensity factors(TSIFs) for a functionally graded material plate subjected to sudden heating on its boundary are provided. The variation in the TSIFs due to the change in material gradient and the crack position is studied.

• Steel and Composite Structures
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• 제19권1호
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• pp.1-19
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• 2015

The buckling analysis is presented for non-homogeneous (NH) orthotropic truncated conical shells subjected to combined loading of axial compression and external pressure. The governing equations have been obtained for the non-homogeneous orthotropic truncated conical shell, the material properties of which vary continuously in the thickness direction. By applying Superposition and Galerkin methods to the governing equations, the expressions for critical loads (axial, lateral, hydrostatic and combined) of non-homogeneous orthotropic truncated conical shells with simply supported boundary conditions are obtained. The results are verified by comparing the obtained values with those in the existing literature. Finally, the effects of non-homogeneity, material orthotropy, cone semi-vertex angle and other geometrical parameters on the values of the critical combined load have been studied.

• Structural Engineering and Mechanics
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• 제56권1호
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• pp.137-156
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• 2015

In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

• Structural Engineering and Mechanics
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• 제19권2호
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• pp.231-236
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• 2005

This study considers the buckling of orthotropic cylindrical thin shells with material nonhomogeneity in the thickness direction, under torsion, which is a power function of time. The dynamic stability and compatibility equations are obtained first. Applying Galerkin's method then applying Ritz type variational method to these equations and taking the large values of loading parameters into consideration, analytic solutions are obtained for critical parameter values. Using those results, the effects of the periodic and power variations of Young's moduli and density, ratio of Young's moduli variations, loading parameters variations and the power of time in the torsional load expression variations are studied via pertinent computations. It is concluded that all these factors contribute to appreciable effects on the critical parameters of the problem in question.