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This paper presents an analytical solution to the free vibration analysis of functionally graded ... more This paper presents an analytical solution to the free vibration analysis of functionally graded beams by using a refined hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of beams is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. Equations of motion are derived from Hamilton's principle and Navier-type analytical solutions for simply supported beams are compared with the existing solutions to verify the validity of the developed theory. Numerical results are obtained to investigate the effects of the power-law index and sideto-thickness ratio on the natural frequencies. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of FG beams.
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
Mathematical Modelling of Engineering Problems, 2017
Computational Materials Science, 2009
In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded materia... more In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded material (S-FGM) beam of thick thickness subjected to uniformly distributed transverse loading has been investigated. The S-FGM system consists of ceramic (Al 2 O 3) and metal (Al) phases varying through the thickness of beam. Major classes of representative theories such as classical laminate beam theory (CLBT), first-order shear deformation theory (FSDT) and high-order theories (HOTs) have been considered and a unified kinematic formulation is then proposed. The Poisson's ratio of the thick S-FGM beam is assumed to be constant, but their Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by sigmoid function. The numerical illustrations concern bending response of S-FGM rectangular beams. Qualitative and quantitative assessments of displacement and stress fields have been presented and discussed.
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
This paper presents an analytical solution to the free vibration analysis of functionally graded ... more This paper presents an analytical solution to the free vibration analysis of functionally graded beams by using a refined hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of beams is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. Equations of motion are derived from Hamilton's principle and Navier-type analytical solutions for simply supported beams are compared with the existing solutions to verify the validity of the developed theory. Numerical results are obtained to investigate the effects of the power-law index and sideto-thickness ratio on the natural frequencies. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of FG beams.
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
Mathematical Modelling of Engineering Problems, 2017
Computational Materials Science, 2009
In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded materia... more In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded material (S-FGM) beam of thick thickness subjected to uniformly distributed transverse loading has been investigated. The S-FGM system consists of ceramic (Al 2 O 3) and metal (Al) phases varying through the thickness of beam. Major classes of representative theories such as classical laminate beam theory (CLBT), first-order shear deformation theory (FSDT) and high-order theories (HOTs) have been considered and a unified kinematic formulation is then proposed. The Poisson's ratio of the thick S-FGM beam is assumed to be constant, but their Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by sigmoid function. The numerical illustrations concern bending response of S-FGM rectangular beams. Qualitative and quantitative assessments of displacement and stress fields have been presented and discussed.
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...
Journal of Adhesion …, 2010
... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , .... more ... Exponentially-Varying Properties Meradjah Mustapha, Benyoucef Samir, Tounsi Abdelouahed ∗ , ... Roberts [15] and Roberts and Haji-Kazemi [16] obtained the interfacial shear and normal stresses through a partial interaction theory (a staged analysis approach). ...