STATIC AND DYNAMIC ANALYSIS OF SANDWICH FUNCTIONALLY GRADED MATERIAL PLATE

Abstract

A new emerging class of advanced smart materials as Functionally graded materials (FGMs) are very attractive for an extensive range of engineering applications because these enable the design of various functional performances within a component. Functionally graded material (FGM) represents a new class of composites that consists of a graded pattern of material composition and/or microstructures. The idea of Functionally Graded Material (FGM) was substantially advanced in the early 1980s in Japan, where this new material concept was proposed to increase adhesion and minimize the thermal stresses in metallic-ceramic composites developed for reusable rocket engines[1]. With the advancement of graded material and the requirement of properties like low weight and high strength, have led to the development of functionally graded sandwich plates. The above-expressed properties provide high stiffness to the material, which is primarily required for the structures working under huge excitation and harsh conditions. The conventional sandwich plates under severe conditions and with the passage of time results in reducing the sandwich effect due to delamination of the face sheets. These disadvantages of overlaid composite must be limited by gradually varying the volume fraction of the constituent materials by considering the functionally graded face sheets, as material properties vary continuously in functionally graded materials. This will eliminate interface problems of composite materials between face sheets and the core, and thus resulting in smooth stress distributions relative to the conventional sandwich plate. Based on the function for variation of volume fraction constituent in the thickness direction, broadly three different types of material gradation are available in literature viz. power-law (P-FGM), exponential-law (E-FGM) and sigmoidal-law (S-FGM). The study of S-FGM model over other common FGM models is important from the fact that the former provides more strength and stiffness under the same working conditions. Moreover, the stress concentrations occur at the interfaces in case of P- and E- FGM plate where the material is continuous but rapidly changing. Thus, the objective of this study is to develop a new modified sigmoid law to compute the effective material properties of sandwich FGM plate (S-FGM). Three different types of porosity are considered viz. even, uneven but symmetric and uneven but non-symmetric. A new un-even non-symmetric porosity model has been used in which micro-voids are varied with material property variation in the thickness direction to capture the accurate iv distribution of voids on the plate. In addition, a new temperature profile for sandwich S-FGM plate is derived using 1D steady state heat conduction equation, which provides a nonlinear distribution of temperature along the thickness. The Hamiltonian formulation has been used to derive governing equations based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function [2] (which was earlier formulated for laminated plates). A closed form solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions using Galerkin Vlasov’s method for linear analysis. The governing equations for nonlinear analysis are solved using the Galerkin approach in conjunction with Airy’s stress function method. The time and frequency domain analysis has been performed using a numerical integration scheme and harmonic balance method, respectively. Galerkin Vlasov’s method is employed to study the static, free vibration, mechanical and thermal buckling of perfect and porous sandwich S-FGM plate in a thermal environment. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, porosity volume fraction and elastic medium parameter on the non-dimensional deflection, stresses, frequency, and critical thermal and mechanical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. It is observed that in several cases with uneven symmetric porosity (P-2) distribution, the reduction in effective inertia appears to be more prominent in comparison to the reduction in effective stiffness of the plate and uneven asymmetric porosity (P-3) distribution ascertains the realistic idealization for a plate with micro-voids. The Galerkin approach in conjunction with Airy’s stress function method has been used to analyze the nonlinear vibration analysis of perfect and porous sandwich S-FGM plate under thermal environment. Poincaré maps, phase-plane plots and time responses are demonstrated to study the nonlinear dynamics behavior of sandwich S-FGM plate due to harmonic excitation. Wide-Ranging parametric studies for, linear and nonlinear, frequency and time domain analysis have been performed by taking into consideration the effect of thickness ratio, inhomogeneity parameter, thermal load and foundation parameters for various configurations of the sandwich plates. It is observed that the dynamic behavior of the plate is primarily affected by altering the configurations of sandwich S-FGM plate. The dynamic response clearly shows the route to chaos nature of the system with the varying thermal load from ΔT = 0 to 600 K.