Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review

Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions

In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young\'s modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

On thermal stability of plates with functionally graded coefficient of thermal expansion

Shear deformation and grain refinement in pure Al by asymmetric rolling

Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory

In this paper, the buckling problem of thin rectangular functionally graded plates subjected to proportional biaxial compressive loadings with arbitrary edge supports is investigated Classical plate theory (CPT) based on the physical neutral plane is applied to derive the stability equations Mechanical properties of the FGM plate are assumed to vary continuously along its thickness according to a power law function The displacement function is considered to be in the form of a double Fourier series whose derivatives are determined using Stokes' transformation The advantage of this method is capability of considering any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series To give generality to the problem, the plate is assumed to be elastically restrained by means of rotational and translational springs at the four edges Numerical examples are presented, and the effects of the plate aspect ratio, the FGM power index, and the loading proportionality factor on the buckling load of an FGM plate with different usual boundary conditions are studied The present results are compared with those have been previously reported by other analytical and numerical methods, and very good agreement is seen between the findings indicating validity and accuracy of the proposed approach in the buckling analysis of FGM plates

Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion

Elasto-plastic finite element simulation of asymmetrical plate rolling using an ALE approach

In this article, the forward and backward wave frequencies of rotating truncated conical thick shells are investigated. The shell is composed of epoxy as the matrix and functionally graded (FG) gra...

Free vibration analysis of rotating functionally graded GPL-reinforced truncated thick conical shells under different boundary conditions

In this paper, multi-objective optimization of tandem cold rolling settings for reductions and inter-stand tensions using NSGA-II and Pareto-optimal front are investigated. In this multi-objective optimization, the total power consumption and uniform power distribution are suggested as objective functions, and reduction thicknesses in each stand and inter stand tensions were selected as problem decision variables. Analytical formulations are introduced to determine the rolling forces and power based on the Stone approach. Then, the main variables of the optimization problem, objective functions, linear and nonlinear constraints, are defined. Moreover, some empirical constraints are introduced regarding the practical limitations of cold rolling equipment and the mechanical properties of the material. At first, considering the conditions of a practical tandem rolling line, single-objective optimization is performed separately, and finally, NSGA-II was used for multi-objective optimization. Compared to the initial setting of the rolling line, the obtained single objective schedules have better performance. Moreover, the multi-objective results based on the Pareto-optimal front are investigated, and an optimized setting for rolling schedule has been suggested. Using this proposed schedule the total power consumption is reduced by more than 11% comparing to the initial setting and more uniform power distribution has been obtained in rolling stands. The normalized reductions calculated from this investigation are compared with numerical and experimental results found in the literature and the similarity was observed in the pattern of thickness reduction distribution. 

Pareto multi-objective optimization of tandem cold rolling settings for reductions and inter stand tensions using NSGA-II.

A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation

Fatemeh Farhatnia

Papers

Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion

Elasto-plastic finite element simulation of asymmetrical plate rolling using an ALE approach

Free vibration analysis of rotating functionally graded GPL-reinforced truncated thick conical shells under different boundary conditions

Pareto multi-objective optimization of tandem cold rolling settings for reductions and inter stand tensions using NSGA-II.

A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation