This study presents critical buckling of Functionally graded soft ferromagnetic porous (FGFP) rectangular plates, under magnetic field with simply supported boundary condition. Equilibrium and stability equations of a porous rectangular plate in transverse magnetic field are derived. The geometrical nonlinearities are considered in the Love- Kirchhoff hypothesis sense. The formulations are compared to those of homogeneous isotropic plates were given in the literature. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are studied.

In this paper, an aerothermoelastic analysis of Functionally graded plate containing porosities in yawed hypersonic flows is investigated. Due to some incorrect manufacturing processes, two different types of porosity, namely, even and uneven distributions are taken into account. The third-order piston theory is utilized to estimate the unsteady aerodynamic pressure induced by the hypersonic airflow. The material properties of a plate are assumed to vary across the thickness direction according to a simple power law. Based on classical plate theory, the motion equations are developed with geometric nonlinearity taking into consideration of von Karman strains. The formulations are established based on Hamilton’s principle while the generalized differential quadrature method is employed to solve the nonlinear aerothermoelastic equations. Due to lower computational efforts‎, the method of generalized differential quadrature is used to obtain accurate results. Moreover, the assumed mode method along with the Runge-Kutta integration algorithm is used as a solution method. The reliability and precision of the obtained results are validated by published literature. Then, the influence of porosity distribution, porosity coefficient, and yawed flow angle are discussed in detail. In general, this paper shows that even porosity distribution would have a more destabilizing effect compared with the ‎uneven porous model. And also, for both porosity distributions, the chaotic behavior appears in higher top surface temperature but even porosity distribution has a profound effect on chaotic motion.

In this paper, an analytical solution for bending analysis of Functionally-graded piezoelectric plate with two simply-supported parallel edges and two other arbitrary boundary conditions under uniformly-distributed transverse loading is presented. The five-variable refined plate theory is employed for describing the displacement field. This theory, despite the few numbers of unknown variables, predicts a parabolic distribution for transverse shear stresses across the thickness and also considers the thickness-stretching effect. The governing equations are obtained using Hamilton’s principle and Maxwell's equation. The Levy-type solution in conjunction with the state-space approach is used to solve them. Comparing the results with those obtained by the higher-order shear theories and Abaqus finite element simulation confirms the accuracy and efficiency of the proposed method. It can be seen that for the length-to-thickness ratio of 10 and the power-law index of 0.5, the value of non-dimensional deflection of the plate with the clamped boundary condition is 0.3327, which has the largest amount of stiffness, while the value of the non-dimensional deflection of the plate with two parallel free boundary condition edges having the lowest amount of stiffness is 2.2036. In addition, for the plate with a clamped boundary condition and length-to-thickness ratio of 10, with the increase of the power index from 0.5 to 10, the value of displacement changes from 0.3327 to 0.3545, which means an increase of about 6%.

A model is provided for crack problem in a Functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation, the governing equation for the crack problem is converted to the solution of a singular integral equation system. Then, finite element technique is employed to analyze this problem by considering quadrilateral eight nodded singular element near the crack tips. The effects of material non-homogeneity and crack length on the stress intensity factor are studied and the results of two methods are judged against each other.

Vibration of the structures in contact with fluid is a phenomenon that a structure has the interaction between the fluid. Hydroelastic characteristics of plates in contact with fluid are important in various engineering applications such as in nuclear engineering, liquid storage tanks, reactor internal components, and solar plates and offshore, naval or marine structures. Fluid-coupled vibrations may be caused the structural fatigue and failure. So, the control and debilitation of the hydoelastic characteristics are important in the safety positions. This study is focused on the hydroelastic vibration of FG circular plate in contact with the bounded fluid with clamped boundary conditions. The natural frequencies of the plate coupled with fluid are calculated by finite element software ANSYS. The software method is verified by comparing the results with the results obtained by experimental tests in case homogeneous plate (Aluminum). Finally, the effects of some parameters such as fluid density, fluid height and volume fraction index on natural frequencies are discussed in details.

The small deflection equation for isotropic and Functionally graded thin annular sector subject to transverse loading is derived in polar coordinate. The Poisson’s ratio of the plate is assumed to be constant, but the young’s modulus varies continuously through the radial direction according to the power-law function. A closed-form solution using the extended Kantorovich method and the classical theory of thin plates (Kirchhoff theory) is presented for the plate analysis. The validity of results are confirmed using solution of available references as well as resolving the problems by the Levy’s method and commercial finite element code ABAQUS. A good agreement between mentioned methods either for deflections or stress resultants is obtained.

In this paper, nonlinear static analysis of moderately thick plate made of Functionally graded materials subjected to mechanical transverse loading is carried out using dynamic relaxation method. Mindlin first order shear deformation theory is employed to consider thick plate. Discretized equations are extracted for geometrically nonlinear behavior analysis. Loading Conditions and boundary conditions of the plate are uniformly distributed transverse load and simply supported at the four edges of the thick plate, respectively. In order to generalize the obtained results, the equations are solved by applying dynamic relaxation method based on central finite deference discretization in the non-dimensional form. The effects of problem parameters such as gradient constant of the Functionally graded material and the side to thickness ratio of plate on the results are investigated. According to the obtained results, the need of including elastic large deflection and applying the theory which considers the effects of plate thickness on the plate bending response and also finally the need of employing dynamic relaxation solution method despite the non-linear terms resulted from large deflection of the Functionally graded thick plate are discussed.