Free vibration analysis of doubly convex/concave functionally graded sandwich beams

This paper presents the highly accurate analytical investigation of the natural frequencies for doubly convex/concave sandwich beams with simply-supported or clamped-supported boundary conditions. The present sandwich beam is made of a functionally graded material composed of metal and ceramic. The properties are graded in the thickness direction of the two faces according to a volume fraction power-law distribution. The bottom surface of the bottom face and the top surface of the top face are both metal-rich material. The core is made of a fully ceramic material. The thickness of the sandwich beam varies along its length according to a quadratic-law distribution. Two types of configuration with doubly convex and doubly concave thickness variations are presented. The governing equation and boundary conditions are derived using the dynamic version of the principle of minimum of the total energy. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effect of configurations of the constituent materials on the frequencies. Natural vibration frequencies of sandwich beams versus many parameters are graphically presented and remarking conclusions are made

Effects of Porosity, Rotation, Thermomagnetic, and Thickness Variation on Functionally Graded Tapered Annular Disks

This paper presents a study on porous functionally graded piezoelectric (FGP) annular disks. The paper discussed the magneto-electric-hygrothermal effects on rotating variable thickness porous FG annular disks. Material properties coefficients and magnetic permeability are changed in a power function of radius. The disk is subjected to various loading of a uniform magnetic field, hygrothermal effect, and variation of electric potentials and mechanical pressure on the disk. A semi-analytical technique is used to get the mathematical solution of the rotating annular disk. Numerical outcomes are provided to examine the porosity factor and grading index on the rotating of the disk by different four sets of boundary conditions. The results offered a comparison between the porous and non-porous annular disks with various boundary conditions. Finally, the mathematical solution is beneficial to the planning and manufacture of a rotating porous disk influenced by complex loading and conditions

Bending of inhomogeneous sandwich plates with viscoelastic cores

This article presents the bending analysis of an inhomogeneous composite sandwich rectangular plate with viscoelastic core. The sinusoidal plate theory as well as other familiar shear deformation plate theories is used. Different types of intermediate plates are considered according to the thickness of all layers and the symmetry of the plate. Illyushin's approximation and the effective moduli methods are used to treat the governing equations of sandwich plates that reinforced with inhomogeneous fibers. Various results for deflections of and some stresses in such plates are presented. A comparison study is made to investigate the effect of time, inhomogeneity, and constitutive parameters as well as the effect of span-to-thickness and aspect ratios on the bending response of the sandwich plates

Axiomatic/asymptotic evaluation of multilayered plate theories by using single and multi-points error criteria

AbstractThis paper deals with refined theories for multilayered composites plates. Layer-Wise (LW) and Equivalent Single Layer (ESL) theories are evaluated by means of axiomatic–asymptotic approach. Theories with forth order displacement fields in the thickness layer/plate direction z are implemented by referring to the Unified Formulation by Carrera. The effectiveness of each term of the made expansion is evaluated by comparing the related theories with a reference solution. As a result a reduced model is obtained which preserve the accuracy of the full-model (model that include the whole terms of the z-expansion) but it removes the not-significant terms in the same expansion (those terms that do no improve the results according to a given error criteria). Various single-point and multi-point error criteria have been analyzed and compared in order to establish such an effectiveness: error localized in an assigned point along z, error localized at each interface, error located at the z-value corresponding to the maximum value of the considered variables, etc. Applications are given in case of closed form solutions of orthotropic cross-ply, rectangular, simply supported plates loaded by bisinusoidal distribution of transverse pressure. Symmetrically and unsymmetrical laminated cases are considered along with sandwich plates. It is found the reduced model is strongly influenced by the used localized error and that in same case the reduced model which is obtained by of single point criteria can be very much improved by the use of multi-point criteria

Natural Frequencies of Shear Deformable Plates by Polyharmonic Splines

We use the third-order shear deformation theory and a collocation technique with polyharmonic splines to predict natural frequencies of moderately thick isotropic plates. The natural frequencies of vibration are computed for various plates and compared with some available published results. Through numerical experiments, the capability and efficiency of the present method for eigenvalue problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined

Bending of symmetric cross-ply multilayered plates in hygrothermal environments

The bending analysis of symmetric cross-ply laminated plates in a hygrothermal environment is presented. The sinusoidal shear deformation plate theory is used for this purpose. It enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. The governing differential equations for the bending of laminated plates are obtained using various plate theories. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Numerical results for deflection and stresses are presented. The effect of different types of sinusoidal hygrothermal/thermal loadings is investigated. The influence various parameters such as material anisotropy, aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the hygrothermally induced response is also investigated. A concluding remark is made

Bending Analysis of Functionally Graded Plates in the Context of Different Theories of Thermoelasticity

The quasistatic bending response is presented for a simply supported functionally graded rectangular plate subjected to a through-the-thickness temperature field under the effect of various theories of generalized thermoelasticity, namely, classical dynamical coupled theory, Lord and Shulman's theory with one relaxation time, and Green and Lindsay's theory with two relaxation times. The generalized shear deformation theory obtained by the first author is used. Material properties of the plate are assumed to be graded in the thickness direction according to a simple exponential law distribution in terms of the volume fractions of the constituents. The numerical illustrations concern quasistatic bending response of functionally graded square plates with two constituent materials are studied using the different theories of generalized thermoelasticit

Two-temperature dual-phase-lags theory in a thermoelastic solid half-space due to an inclined load

This article addresses the thermoelastic interaction due to inclined load on a homogeneous isotropic half-space in context of two-temperature generalized theory of thermoelasticity with dual-phase-lags. It is assumed that the inclined load is a linear combination of both normal and tangential loads. The governing equations are solved by using the normal mode analysis. The variations of the displacement, stress, conductive temperature, and thermodynamic temperature distributions with the horizontal distance have been shown graphically. Results of some earlier workers have also been deduced from the present investigation as special cases. Some comparisons are graphically presented to estimate the effects of the two-temperature parameter, the dual-phase-lags parameters and the inclination angle. It is noticed that there is a significant difference in the values of the studied fields for different value of the angle of inclination. The method presented here maybe applicable to a wide range of problems in thermodynamics and thermoelasticity

Analysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method

A cell-based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, and mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first-order shear deformation theory and the shear locking is suppressed by the discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence of the gradient index, the plate aspect ratio, skewness of the plate, and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied