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Bensaid, Ismail,Cheikh, Abdelmadjid,Mangouchi, Ahmed,Kerboua, Bachir Techno-Press 2017 Advances in materials research Vol.6 No.1
In this work we introduce a higher-order hyperbolic shear deformation model for bending and frees vibration analysis of functionally graded beams. In this theory and by making a further supposition, the axial displacement accounts for a refined hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the beam boundary surfaces, so no need of any shear correction factors (SCFs). The material properties are continuously varied through the beam thickness by the power-law distribution of the volume fraction of the constituents. Based on the present refined hyperbolic shear deformation beam model, the governing equations of motion are obtained from the Hamilton's principle. Analytical solutions for simply-supported beams are developed to solve the problem. To verify the precision and validity of the present theory some numerical results are compared with the existing ones in the literature and a good agreement is showed.
Bekhadda, Ahmed,Cheikh, Abdelmadjid,Bensaid, Ismail,Hadjoui, Abdelhamid,Daikh, Ahmed A. Techno-Press 2019 Advances in aircraft and spacecraft science Vol.6 No.3
In this work, a novel first-order shear deformation beam theory is applied to explore the vibration and buckling characteristics of thick functionally graded beams. The material properties are assumed to vary across the thickness direction in a graded form and are estimated by a power-law model. A Fourier series-based solution procedure is implemented to solve the governing equation derived from Hamilton's principle. The obtained results of natural frequencies and buckling loads of functionally graded beam are checked with those supplied in the literature and demonstrate good achievement. Influences of several parameters such as power law index, beam geometrical parameters, modulus ratio and axial load on dynamic and buckling behaviors of FGP beams are all discussed.
Ismail Bensaid,Ahmed Bekhadda,Bachir Kerboua,Cheikh Abdelmadjid 한국풍공학회 2018 Wind and Structures, An International Journal (WAS Vol.27 No.6
In this research work, nonlinear thermal buckling behavior of functionally graded (FG) plates is explored based a new higher-order shear deformation theory (HSDT). The present model has just four unknowns, by using a new supposition of the displacement field which enforces undetermined integral variables. A shear correction factor is, thus, not necessary. A power law distribution is employed to express the disparity of volume fraction of material distributions. Three kinds of thermal loading, namely, uniform, linear, and nonlinear and temperature rises over z-axis direction are examined. The non-linear governing equations are resolved for plates subjected to simply supported boundary conditions at the edges. The results are approved with those existing in the literature. Impacts of various parameters such as aspect and thickness ratios, gradient index, type of thermal load rising, on the non-dimensional thermal buckling load are all examined.