In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton\'s principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.
Abderahman Younsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelouahed Tounsi and Abdelmoumen Anis Bousahla — 1.)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2.)Laboratory of Structures and Advanced Materials in Civil Engineering and Public Works, Department of Civil Engineering, Faculty of Technology, University of Sidi Bel Abbes, Algeria 3.)Multi-scale Modeling and Simulation Laboratory, Department of Physics, Faculty of Exact Sciences, University of Sidi Bel Abbés, Algeria
Fatima Zohra Zaoui — Laboratory for Numerical and Experimental Modeling of Mechanical Phenomena, Faculty of Sciences and Technology, Department of Mechanical Engineering, University Abdelhamid Ibn Badis of Mostaganem, 27000, Algeria
S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia
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