Refined theories based on non-polynomial kinematics for the thermoelastic analysis of functionally graded plates

Mehar²,

Engineering with Computers

et al. 2021

In the present research, finite element solutions of thermal post-buckling load-bearing strength of functionally graded (FG) sandwich shell structures are reported by adopting a higher-order shear deformation type kinematics. For the numerical calculation, nine nodes are considered for each element. A specialized MATLAB code is developed incorporating the present mathematical model to evaluate the numerical buckling temperature. The Green-Lagrange nonlinear strain is adopted for the formulation of the sandwich structure. The eigenvalue equation of the FG sandwich structure is solved to predict the postbuckling temperature values of the structure. Moreover, three kinds of temperature distributions across the panel thickness are assumed, viz., uniform, linear and nonlinear. In addition, the properties are described using the power law distributions. The numerical solutions are first validated and, subsequently, the impact of alterations of structural parameters, viz., the curvature ratios, core-face thickness ratios, support conditions and power law index (n Z ) including the amplitude ratio on the thermal post-buckling response of FG sandwich curved panels have been studied in details. The investigation reveals different interesting outcomes, which may help for future references for the analysis and design of the graded sandwich structure.

Section: Introductionmentioning

confidence: 99%

Thermal post-buckling analysis of graded sandwich curved structures under variable thermal loadings

Mehar²,

Engineering with Computers

et al. 2021

“…Parida and Mohanty (2018) analyzed the free vibration and buckling of skew FGM plate using the HSDT. Based on Carrera unified formulation, Ramos et al (2016) presented an analytical solution for thermoelastic analysis of FG sandwich plates. investigated the free vibration behavior of rotating FG circular microplate of variable thickness using modified couple stress theory and FSDT.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of FG rotating plate using nonlinear-FEM

Parida

Mohanty

2019

MMMS

Purpose The purpose of this paper is to investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine. Design/methodology/approach A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method. Findings The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail. Originality/value A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

“…A unified framework on higher order shear deformation theories of laminated composite plates was proposed by Nguyen et al [32]. Ramos et al [33] developed refined theories based on non-polynomial kinematics via the Carrera Unified Formulation to deal with thermal problems, which was extended by Mantari et al [34] to investigate the static behavior of…”

Section: Introductionmentioning

confidence: 99%

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

Yarasca

Mantari

Petrolo³

et al. 2017

Composite Structures

Self Cite

This paper presents Best Theory Diagrams (BTDs) employing combinations of Maclaurin, trigonometric and exponential terms to build two-dimensional theories for laminated cross-ply plates. The BTD is a curve in which the least number of unknown variables to meet a given accuracy requirement is read. The used refined models are Equivalent Single Layer and are obtained using the Unified Formulation developed by Carrera. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions have been obtained in the case of simply supported plates loaded by a bisinuisoidal transverse pressure. BTDs have been constructed using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The influence of trigonometric and exponential terms in the BTDs has been studied for different layer configurations, length-to-thickness ratios and stresses. It is shown that the addition of trigonometric and exponential expansion terms to Maclaurin ones may improve the accuracy and computational cost of refined plate theories. The combined use of CUF, AAM and GA is a powerful tool to evaluate the accuracy of any structural theory.